W3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "98935853-5815-4752-92d0-a1b6ae94c0c5",
   "metadata": {},
   "source": [
    "# Introduction to Machine Learning (ML)\n",
    "\n",
    "## Definition:\n",
    "Machine learning (ML) uses algorithms trained on data to create models that can perform tasks typically requiring human intelligence. These tasks include recognizing patterns, making decisions, and predictions\n",
    "## How it Works:\n",
    "ML algorithms use a dataset to train a model. The training involves an iterative process where the model makes predictions, compares them to the actual outcomes, and adjusts its parameters to improve accuracy.\n",
    "## Types of Machine Learning:\n",
    "* ### Supervised Learning:\n",
    "The algorithm learns from a labeled dataset, meaning the correct answer is included in the training data.\n",
    "* ### Unsupervised Learning:\n",
    "The algorithm must find patterns and relationships in datasets without any labels.\n",
    "* ### Reinforcement Learning:\n",
    "The algorithm learns by making a sequence of decisions and receiving feedback in the form of rewards or penalties.\r",
    "## Applications: \n",
    "Machine learning powers many applications we use daily, such as recommendation systems, search engines, spam filters, and speech recognition systems.Machine learning is a rapidly evolving field that continues to push the boundaries of what’s possible with technology, making our interactions with digital systems more intuitive and efficient.\n",
    "___\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dacac81-125f-4890-b823-021e09aff53a",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "## Definition:\n",
    "Linear Regression is a statistical method that models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. The goal is to find the best-fit line or the linear equation that can be used to predict outcomes.\n",
    "### Equation\n",
    "The linear equation for a simple linear regression, which involves a single independent variable, is:\n",
    "\n",
    "**$$ y = \\beta_0 + \\beta_1x + \\epsilon $$**\n",
    "\n",
    "where:<br>\n",
    "* y is the dependent variable<br>\n",
    "* x is the independent variable<br>\n",
    "* β0 is the y-intercept<br>\n",
    "* β1 is the slope of the line<br>\n",
    "* ϵ is the error term.<br>\n",
    "\n",
    "## Purpose:\n",
    "The primary use of Linear Regression is to predict values within a continuous range, rather than trying to classify them into categories. For example, predicting prices of houses, sales of a product, or temperature forecasts.\n",
    "## Assumptions:\n",
    "Linear Regression assumes that there is a linear relationship between the independent and dependent variables. Other assumptions include homoscedasticity, independence of errors, and normal distribution of errors\n",
    "## Applications:\n",
    "It’s widely used in economics, business, engineering, and the natural and social sciences as it provides a clear understanding of the relationships between variables. Linear Regression is valued for its ease of interpretation and understanding, making it a staple for many predictive modeling tasks\n",
    "## Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff0d31bf-17bb-4cef-a0f1-3355ea621d50",
   "metadata": {},
   "source": [
    "### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b0972c5-93e8-44e5-a3e5-34fd76aadd53",
   "metadata": {},
   "outputs": [],
   "source": [
    " BNVimport numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8350a9d-dec8-4f38-ba04-1ddd239528ab",
   "metadata": {},
   "source": [
    "### Generate a random regression problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "993001da-f5a2-4b97-a73b-907ab6937eba",
   "metadata": {},
   "outputs": [],
   "source": [
    "lrX, lry = make_regression(n_samples=100, n_features=1, noise=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72b22b11-3f49-4c40-a596-37b38c705ef2",
   "metadata": {},
   "source": [
    "### Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a42fbfeb-5d47-4916-927a-8f4ef1365ab9",
   "metadata": {},
   "outputs": [],
   "source": [
    "lrX_train, lrX_test, lry_train, lry_test = train_test_split(lrX, lry, test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53753052-e9d0-41fb-9381-30a919f25344",
   "metadata": {},
   "source": [
    "### Create linear regression object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6a47a6ea-777b-46a3-b039-dde252b18ba8",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02a19902-c473-4156-847f-9cc1448ab7b2",
   "metadata": {},
   "source": [
    "### Train the model using the training sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d2dffb5-1a35-4c74-b7c0-9804ba4d6cfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(lrX_train, lry_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9724b215-f59d-4f95-9aac-2808d710220b",
   "metadata": {},
   "source": [
    "### Make predictions using the testing set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8b951ff4-6d46-4d1e-88c3-1c5ec732a9e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "lry_pred = lr.predict(lrX_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2d80ed6-51b2-461c-b088-121c2a5141c2",
   "metadata": {},
   "source": [
    "### Plot outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fd6cba0c-e030-40c4-81e9-4d5aec7eeab3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lrX_test, lry_test, color='black', label='Actual data')\n",
    "plt.plot(lrX_test, lry_pred, color='blue', linewidth=3, label='Fitted line')\n",
    "\n",
    "plt.title('Linear Regression Result')\n",
    "plt.xlabel('Independent variable')\n",
    "plt.ylabel('Dependent variable')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9d1c8da-1933-4bbb-87cc-4e20ff2bb05e",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To validate your Linear Regression model, you can use several statistical metrics to assess its performance. Here are some common methods:\n",
    "\n",
    "* #### R-squared (Coefficient of Determination):\n",
    "This metric indicates the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, Generally, a higher R-squared value means that the model fits the data better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e32e5a7d-e459-4bad-90cd-ed73c3a9511b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared:  0.9721095523164569\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "lrr_squared = metrics.r2_score(lry_test, lry_pred)\n",
    "print('R-squared: ', lrr_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c39f532-b706-4b8d-b0db-35321c34f040",
   "metadata": {},
   "source": [
    "* #### Mean Absolute Error (MAE):\n",
    "This is the average of the absolute differences between the predicted values and the actual values. It gives an idea of how big the errors are on average. The Mean Absolute Error (MAE) is considered better when it is closer to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9cc66168-04ad-4364-9158-ddc0735d024e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error:  7.148104288854194\n"
     ]
    }
   ],
   "source": [
    "lrmae = metrics.mean_absolute_error(lry_test, lry_pred)\n",
    "print('Mean Absolute Error: ', lrmae)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e508a1c5-74dd-4671-9fae-b37fa8359d61",
   "metadata": {},
   "source": [
    "* #### Mean Squared Error (MSE):\n",
    "This is the average of the squares of the errors. It penalizes larger errors more than MAE does.The Mean Squared Error (MSE) is considered better when it is closer to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "15e87667-1290-429f-8a96-bd751fed028a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error:  71.12663664494545\n"
     ]
    }
   ],
   "source": [
    "lrmse = metrics.mean_squared_error(lry_test, lry_pred)\n",
    "print('Mean Squared Error: ', lrmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f877c7ec-9496-4831-85ec-eb43c49d395b",
   "metadata": {},
   "source": [
    "* #### Root Mean Squared Error (RMSE):\n",
    "This is the square root of MSE. It’s in the same units as the dependent variable and is often used to compare different regression models. The Root Mean Squared Error (RMSE) is better when it is as close to 0 as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e7a89ed0-f5f9-4c4b-9d4b-c57379cc385b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Squared Error:  8.433660927790816\n"
     ]
    }
   ],
   "source": [
    "lrrmse = np.sqrt(lrmse)\n",
    "print('Root Mean Squared Error: ', lrrmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83469986-8c61-45c5-af20-59c44168e501",
   "metadata": {},
   "source": [
    "#### At the End make it better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "91eab4ec-a623-4827-bc24-73e4c10335f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "90caaacf-1fe4-4f06-a520-d7d97f79dedb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Method</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>MSE</th>\n",
       "      <th>MAE</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Simple Linear Regression</td>\n",
       "      <td>8.433661</td>\n",
       "      <td>71.126637</td>\n",
       "      <td>7.148104</td>\n",
       "      <td>0.97211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Method      RMSE        MSE       MAE       R2\n",
       "0  Simple Linear Regression  8.433661  71.126637  7.148104  0.97211"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_results = pd.DataFrame(['Simple Linear Regression', lrrmse, lrmse, lrmae, lrr_squared]).transpose()\n",
    "lr_results.columns = ['Method', 'RMSE', 'MSE', 'MAE', 'R2']\n",
    "lr_results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3cccc7-8b36-4ad7-9e8e-666644220379",
   "metadata": {},
   "source": [
    "#### Residuals plots\n",
    "Additionally, you can use residual plots to visually check for the validity of your model. Residuals are the differences between the actual values and the predicted values. A well-fitted model will have residuals that are randomly scattered around zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ef9c77eb-67ed-42ca-ab3f-f0421b6aaae6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals = lry_test - lry_pred\n",
    "\n",
    "plt.scatter(lry_pred, residuals, color='red', label='Residuals')\n",
    "plt.axhline(y=0, color='blue', linestyle='--')\n",
    "plt.xlabel('Predicted Values')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "700f30e9-5486-42d7-8506-2b915cfad24e",
   "metadata": {},
   "source": [
    "___\n",
    "# Support Vector Machine (SVM) \n",
    "Support Vector Machine (SVM) is a powerful and versatile supervised machine learning algorithm used for both classification and regression tasks, though it is primarily known for classification. Here’s an overview of SVM:\n",
    "Objective: The main goal of SVM is to find the optimal hyperplane that separates different classes in the feature space with the maximum margin possible1.\n",
    "\n",
    "## Core Idea:\n",
    "SVM classifies data by finding the optimal hyperplane which maximizes the margin between different classes in an N-dimensional space.\n",
    "## Hyperplane:\n",
    "This is the decision boundary that separates different classes. The dimension of the hyperplane depends on the number of input features.\n",
    "## Support Vectors: \n",
    "These are the data points nearest to the hyperplane, which influence its position. SVM aims to maximize the distance (margin) from these points to the hyperplane \n",
    "## Margin:\n",
    "It’s the distance between the hyperplane and the nearest data point from either class. A larger margin is associated with a lower generalization error of the classifier\n",
    "## Kernels: \n",
    "SVM can handle linear and non-linear data. For non-linear data, it uses kernel functions to transform the input space into a higher-dimensional space where a linear separator can be used.\n",
    "## Robustness to Outliers: \n",
    "SVM is known for its robustness to outliers. It focuses on the support vectors and the margin, which helps in ignoring the outliers while finding the hyperplane1.\n",
    "## Applications: \n",
    "SVM is used in various domains like text classification, image recognition, spam detection, and more due to its effectiveness in high-dimensional spaces and its ability to handle nonlinear relationships.\n",
    "\n",
    "SVM’s ability to find the maximum separating hyperplane by considering the closest points of different classes makes it a strong model, especially when dealing with complex datasets.\n",
    "## Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00d14395-b51a-479c-bea2-4535e1ee06d1",
   "metadata": {},
   "source": [
    "### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "af67fbda-a83a-4f86-a99a-5493c4ced4e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aef769a-87a6-4599-8bf4-f2cc8fcf6356",
   "metadata": {},
   "source": [
    "### Load The Iris Dataset from `sklearn`\n",
    "This data sets consists of 3 different types of irises’ (Setosa, Versicolour, and Virginica) petal and sepal length, stored in a 150x4 numpy.ndarray\n",
    "\r\n",
    "The rows being the samples and the columns being: Sepal Length, Sepal Width, Petal Length and Petal Width."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6a8a7667-150c-422c-9b05-d2c3fff26196",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()\n",
    "svmX = iris.data[:, :2]  \n",
    "svmy = iris.target"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e268b7fb-3763-480a-9113-78cd4ac05496",
   "metadata": {},
   "source": [
    "### Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a174bb89-983f-4028-9b3c-58ac30084967",
   "metadata": {},
   "outputs": [],
   "source": [
    "svmX_train, svmX_test, svmy_train, svmy_test = train_test_split(svmX, svmy, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef6dbcbe-806a-4fa7-ba34-dc966aa7060c",
   "metadata": {},
   "source": [
    "### Create an SVM classifier with a linear kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7cdf3bde-3c4f-45dd-a7dd-56bba769acd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SVC(kernel=&#x27;linear&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;SVC<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.svm.SVC.html\">?<span>Documentation for SVC</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>SVC(kernel=&#x27;linear&#x27;)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "SVC(kernel='linear')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf = SVC(kernel='linear')\n",
    "clf.fit(svmX_train, svmy_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64ce53c2-6816-4edb-8c1a-5858a3fecd7b",
   "metadata": {},
   "source": [
    "### Predict using the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "86ce9cfe-8eec-40fd-8e42-a250ac17fbec",
   "metadata": {},
   "outputs": [],
   "source": [
    "svmy_pred = clf.predict(svmX_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b496070-d58a-4cad-95c7-a997531529a9",
   "metadata": {},
   "source": [
    "### Create a mesh to plot the decision boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0fe5b553-7842-4745-9402-e2441e2c13d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "h = .02  # step size in the mesh\n",
    "svmx_min, svmx_max = svmX[:, 0].min() - 1, svmX[:, 0].max() + 1\n",
    "svmy_min, svmy_max = svmX[:, 1].min() - 1, svmX[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(svmx_min, svmx_max, h), np.arange(svmy_min, svmy_max, h))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47a90d14-963c-475e-824d-e92a18c6fdee",
   "metadata": {},
   "source": [
    "### Plot outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2257d014-e651-428c-a050-4c233a4e2cd8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the decision boundary by assigning a color to each point in the mesh\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(svmX_train[:, 0], svmX_train[:, 1], c=svmy_train, cmap=plt.cm.coolwarm, edgecolors='k')\n",
    "# and testing points\n",
    "plt.scatter(svmX_test[:, 0], svmX_test[:, 1], c=svmy_test, cmap=plt.cm.coolwarm, edgecolors='k', alpha=0.6)\n",
    "\n",
    "plt.xlabel('Sepal length')\n",
    "plt.ylabel('Sepal width')\n",
    "plt.title('SVM on Iris Dataset')\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "667a4891-a72e-4ee3-807c-af4b9055aaa5",
   "metadata": {},
   "source": [
    "### Validation\n",
    "#### Confusion Matrix\n",
    "A Confusion Matrix is a table used in machine learning to evaluate the performance of a classification model on a set of test data. It’s particularly useful for visualizing the accuracy of a model and understanding its errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bc166a91-f33f-4bfa-ae09-7d5e2c4efd7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HjtSbb75pazy01gEA7lDDCWtVjpeUm5ur+Ph43+6oqKgLftwwDF111VWaNWuWJKlbt2768ssvNX/+fGVkZNQ8jnNQkQMAXOHsGLmVTZLi4+OrbBdL5M2aNVOnTp2q7OvYsaMOHTpk6/cikQMAEAC9e/dWdnZ2lX179+5Vq1atbL0OiRwA4A6mDZsfxowZoy1btmjWrFnav3+/lixZoldeeUWZmZn2fJ8fVGuM/L333qv2CW+77bYaBwMAQKDU9hKtPXr00IoVKzRx4kRNnz5d6enpmj17toYMGVLjGC6kWol80KBB1TqZx+OR1+u1Eg8AAGHjN7/5jX7zm98E9BrVSuSGYQQ0CAAAakWIrpduhaXbz0pKShQdHW1XLAAABEy4Pv3M78luXq9XM2bMUPPmzdWgQQMdPHhQkjRp0iS9/vrrtgcIAIAtanmyW23xO5HPnDlTCxcu1NNPP6169er59l9++eV67bXXbA0OAAD8PL8T+aJFi/TKK69oyJAhioyM9O3v0qWL9uzZY2twAADYx2PDFnr8HiP/7rvv1LZt2/P2G4ah8vJyW4ICAMB2Vtvj4dJa79SpkzZs2HDe/r/85S/q1q2bLUEBAIDq8bsinzx5sjIyMvTdd9/JMAy98847ys7O1qJFi7Rq1apAxAgAgHVU5JUGDhyo999/X3//+99Vv359TZ48Wbt379b777+vm266KRAxAgBg3dmnn1nZQlCN7iO/7rrrtGbNGrtjAQAAfqrxgjBbt27V7t27JVWOm3fv3t22oAAAsNtPH0Va0+NDkd+J/Ntvv9Xdd9+tzz77TA0bNpQknTp1Stdcc42WLl2qFi1a2B0jAADWMUZe6YEHHlB5ebl2796t/Px85efna/fu3TIMQw888EAgYgQAABfhd0W+bt06bdq0Se3bt/fta9++vV544QVdd911tgYHAIBtrE5YC5fJbmlpaRdc+MXr9So1NdWWoAAAsJvHrNysHB+K/G6tP/PMM3rkkUe0detW376tW7dq1KhR+q//+i9bgwMAwDZh+tCUalXkjRo1ksfzY0uhuLhYPXv2VJ06lYdXVFSoTp06uu+++zRo0KCABAoAAM5XrUQ+e/bsAIcBAECAuXmMPCMjI9BxAAAQWGF6+1mNF4SRpJKSEpWVlVXZFx8fbykgAABQfX5PdisuLtaIESOUlJSk+vXrq1GjRlU2AABCUphOdvM7kT/++OP6+OOPNW/ePEVFRem1117TtGnTlJqaqkWLFgUiRgAArAvTRO53a/3999/XokWL1KdPHw0bNkzXXXed2rZtq1atWmnx4sUaMmRIIOIEAAAX4HdFnp+frzZt2kiqHA/Pz8+XJF177bVav369vdEBAGAXHmNaqU2bNsrJyVHLli3VoUMHLV++XFdffbXef/9930NUEDgDhp7QHQ8dU2LTCh38KkYv/aG5snfGBjss2O13R6Sj3vP331ZfGsVclHBy94BdurbHN2rZ7JRKy+roq31JemVZD317JCHYoYUdVnb7wbBhw7Rr1y5J0oQJEzR37lxFR0drzJgxeuyxx2wPED+64baTenDKYS1+NkWZ/dvp4FfRmrnkoBIan79kLhzupSTpv5v9uD3dpHL/DTHBjQu2u6Jjnt5b01Ejpg7Q43/sr8g6hp4ev1rRUfy5RvX4ncjHjBmjkSNHSpL69eunPXv2aMmSJdqxY4dGjRrl17nWr1+vAQMGKDU1VR6PRytXrvQ3HFcZ/OAJrV6SqL8tS9ShfdGaM76FSr/3qP/d+cEODXZrGCkl/mTbUiKlRkpdooIdGWw28en++mjDpfrmu0Y6eKixnn75OiU3Kdalrf8v2KGFnzCd7OZ3Ij9Xq1atNHjwYF1xxRV+H1tcXKwuXbpo7ty5VsMIe3XqGrr0ijPaviHOt880PdqxIU6dup8JYmQIuHJT+vsZ6Zb6kic0x+hgn/qxlZX46WL+0YbqqdYY+Zw5c6p9wrPVenXceuutuvXWW6v9eTeLT/Qqso506njVn+zkiTpKa1sapKhQKz77XioypP71gx0JAszjMZV5z+f6IjtJX3/LXAi7eWRxjNy2SOxVrUT+3HPPVetkHo/Hr0Tur9LSUpWW/pi0CgsLA3YtIGR8WCxdHS01iQx2JAiwkRmb1brFSY2a8etghwIHqVYiz8nJCXQc1ZKVlaVp06YFO4ygKMyPlLdCati0osr+Rk0qdPK4pZV2EcqOVkjbS6WpjYMdCQLskXs361+65WrMk7/SiXy6LwERpg9NsTxGXpsmTpyogoIC35abmxvskGpNRXmE9v1vrLpde9q3z+Mx1fXaIn21jdvPwtbqYqlhhPQv0cGOBAFj6pF7N+vaq77RuFm3KO943C8fgpoJ08lujirloqKiFBXl3gkg77zSRONm52rvrlhl74jV7cOPKzrW0N+WJgY7NASCYUqrz0g315ciQ7MSgHUjh27Wjb0OatJzN+pMSV01SqicvFp8pp7Kyh31VzSChP9LHGTde42U0Nirex/LU6OmFTr4zxg9MSRdp07UDXZoCITtpdIxr3QLHZdwNrDfHknSc3/4sMr+p1++Th9tuDQYIYUvHmNqv6KiIu3fv9/3OicnRzt37lRiYqJatmwZxMhC13sLmui9BU2CHQZqw1XR0toWwY4CAXbjPfcFOwTXCNeV3YKayLdu3aq+ffv6Xo8dO1aSlJGRoYULFwYpKgAAnKNGk902bNige+65R7169dJ3330nSfrzn/+sjRs3+nWePn36yDTN8zaSOADAdmE62c3vRP7222+rf//+iomJ0Y4dO3z3dRcUFGjWrFm2BwgAgC1I5JWefPJJzZ8/X6+++qrq1v1xklXv3r21fft2W4MDAAA/z+8x8uzsbF1//fXn7U9ISNCpU6fsiAkAANuF62Q3vyvylJSUKjPNz9q4caPatGljS1AAANju7MpuVrYQ5HciHz58uEaNGqXPP/9cHo9Hhw8f1uLFizVu3Dg99NBDgYgRAADrwnSM3O/W+oQJE2QYhm688UadOXNG119/vaKiojRu3Dg98sgjgYgRAABchN+J3OPx6IknntBjjz2m/fv3q6ioSJ06dVKDBg0CER8AALYI1zHyGi8IU69ePXXq1MnOWAAACByWaK3Ut29feTwXH/D/+OOPLQUEAACqz+9E3rVr1yqvy8vLtXPnTn355ZfKyMiwKy4AAOxlsbUeNhX5c889d8H9U6dOVVFRkeWAAAAIiDBtrddorfULueeee/TGG2/YdToAAFANtj39bPPmzYqOjrbrdAAA2CtMK3K/E/ngwYOrvDZNU0eOHNHWrVs1adIk2wIDAMBO3H72g4SEhCqvIyIi1L59e02fPl0333yzbYEBAIBf5lci93q9GjZsmDp37qxGjRoFKiYAAFBNfk12i4yM1M0338xTzgAAzhOma637PWv98ssv18GDBwMRCwAAAXN2jNzKFor8TuRPPvmkxo0bp1WrVunIkSMqLCyssgEAgNpT7THy6dOn69FHH9WvfvUrSdJtt91WZalW0zTl8Xjk9XrtjxIAADuEaFVtRbUT+bRp0/T73/9en3zySSDjAQAgMNx+H7lpVn6DG264IWDBAAAA//h1+9nPPfUMAIBQxoIwktq1a/eLyTw/P99SQAAABITbW+tS5Tj5uSu7AQCA4PErkd91111KSkoKVCwAAARMuLbWq30fOePjAABHC+LKbk899ZQ8Ho9Gjx5d85NcRLUT+dlZ6wAAoPr+53/+Ry+//LKuuOKKgJy/2oncMAza6gAA5wpCRV5UVKQhQ4bo1VdfDdjDxvxeohUAACeya631c5cmLy0tveg1MzMz9etf/1r9+vUL2PcikQMA3MGmijwtLU0JCQm+LSsr64KXW7p0qbZv337R9+3i16x1AADcLjc3V/Hx8b7XUVFRF/zMqFGjtGbNGkVHRwc0HhI5AMAdbFoQJj4+vkoiv5Bt27bp2LFjuvLKK337vF6v1q9frxdffFGlpaWKjIy0EMyPSOQAAFeozfvIb7zxRn3xxRdV9g0bNkwdOnTQ+PHjbUviEokcAADbxcXF6fLLL6+yr379+mrcuPF5+60ikQMA3IG11gEAcK5gL9H66aefWjvBRXD7GQAADkZFDgBwB1rrAAA4WJgmclrrAAA4GBU5AMAVPD9sVo4PRSRyAIA7hGlrnUQOAHCFYN9+FiiMkQMA4GBU5AAAd6C1DgCAw4VoMraC1joAAA5GRQ4AcIVwnexGIgcAuEOYjpHTWgcAwMGoyAEArkBrHQAAJ6O1DgAAQg0VORyjznD+d3WTjza+HuwQUAsKTxtq1K52rkVrHQAAJwvT1jqJHADgDmGayBkjBwDAwajIAQCuwBg5AABORmsdAACEGipyAIAreExTHrPmZbWVYwOJRA4AcAda6wAAINRQkQMAXIFZ6wAAOBmtdQAAEGqoyAEArkBrHQAAJwvT1jqJHADgCuFakTNGDgCAg1GRAwDcgdY6AADOFqrtcStorQMA4GBU5AAAdzDNys3K8SGIRA4AcAVmrQMAgJBDRQ4AcAdmrQMA4Fweo3KzcnwoorUOAICDUZEDANyB1joAAM4VrrPWSeQAAHcI0/vIGSMHAMDBqMgBAK5Aax0AACcL08lutNYBAHAwKnIAgCvQWgcAwMmYtQ4AAEINFTkAwBVorQMA4GTMWgcAAKGGihwA4Aq01gEAcDLDrNysHB+CSOQAAHdgjBwAAIQaKnIAgCt4ZHGM3LZI7EUiBwC4Ayu7AQCAUEMiBwC4wtnbz6xs/sjKylKPHj0UFxenpKQkDRo0SNnZ2bZ/LxI5AMAdTBs2P6xbt06ZmZnasmWL1qxZo/Lyct18880qLi625/v8gDFyAAACYPXq1VVeL1y4UElJSdq2bZuuv/56265DIgcAuILHNOWxMGHt7LGFhYVV9kdFRSkqKuoXjy8oKJAkJSYm1jiGC6G1DgBwB8OGTVJaWpoSEhJ8W1ZW1i9f2jA0evRo9e7dW5dffrmtX4uKHAAAP+Tm5io+Pt73ujrVeGZmpr788ktt3LjR9nhI5AAAV7CrtR4fH18lkf+SESNGaNWqVVq/fr1atGhR4+tfDIkcAOAOtbzWummaeuSRR7RixQp9+umnSk9Pt3DxiyORAwDcoZZXdsvMzNSSJUv07rvvKi4uTnl5eZKkhIQExcTE1DyOczDZDQCAAJg3b54KCgrUp08fNWvWzLctW7bM1utQkQMAXKEmq7Ode7w/zFpam51E7jADhp7QHQ8dU2LTCh38KkYv/aG5snfGBjss2OyyLif0/363X23bn1LjJqWaMfFqbdnQLNhhwQZfbKmv/34pSfu+iFX+0bqa8nqOrrm1wPe+aUqLnknR6iWNVVQYqU5XFWvkU7lq3qYsiFGHCR6aYr/aWoc2XNxw20k9OOWwFj+bosz+7XTwq2jNXHJQCY3Lgx0abBYd41XO/gTNe/aKYIcCm5WciVCby77XiFnfXvD95XOT9O4bTfXIU7l6ftVeRcca+s/fXaKyklB9iCaCLaiJvLbWoQ0Xgx88odVLEvW3ZYk6tC9ac8a3UOn3HvW/Oz/YocFm27Yk68+vdtTm9anBDgU26/GvpzV0fJ56/6QKP8s0pZWvNdXdo/J0zS2FatOpRI/P+Ub/d7SuNq1OCEK04cVjWN9CUVBb67W1Dm04qFPX0KVXnNHSF5N8+0zTox0b4tSp+5kgRgbALnmH6in/WF1deV2Rb1/9eEMdup3R7m311WfQqeAFFw7CtLUeUmPkv7QObWlpqUpLS32vz13vNpzFJ3oVWUc6dbzqT3byRB2ltS29yFEAnCT/WOWf74ZNqw6XNWxa7nsPOFfI3H5WnXVos7Kyqqxvm5aWVstRAgAcq5YfY1pbQiaRn12HdunSpRf9zMSJE1VQUODbcnNzazHC4CrMj5S3QmrYtKLK/kZNKnTyOP9SB8JBYlLln+9Tx+tW2X/qeF3fe6i5s0u0WtlCUUgk8rPr0H7yySc/uw5tVFSUb41bf9e6dbqK8gjt+99Ydbv2tG+fx2Oq67VF+mobt58B4SClZZkSk8q1Y2MD377i0xHasyNWHbszCRgXFtRSrrbWoQ0X77zSRONm52rvrlhl74jV7cOPKzrW0N+W2vtsWwRfdEyFUpv/+Bd3SrMzatO2QKdP19Xxo/zDzcm+L47Q4Zwfn5aVl1tPB76MUVzDCiW1KNegB47rreeT1Ty9VCkty/Tm083UOLlc19xy/ix3+InJbvarrXVow8W69xopobFX9z6Wp0ZNK3TwnzF6Yki6Tp2o+8sHw1Eu7XBKT73wme/18JFfSpL+/kGanpt1ZbDCgg327orV43e09b1+eWpzSdJNd+Zr3OxDujPzmErOROj5x9NUVBipy3oUa+big6oXHZpJxFFM+Z4pXuPjQ5DHrK015C50cc+FFzhYsGCBhg4d+ovHFxYWKiEhQX00UHU8JLNwV6dN62CHgFr0140rgx0CakHhaUON2h1UQUFBwIZLz+aKf+02QXUio2t8ngpviT7e8VRAY62JoLfWAQBAzTHdGQDgDqYsjpHbFomtSOQAAHcI08luIXH7GQAAqBkqcgCAOxiSrDxEjoemAAAQPFZXZ2NlNwAAYDsqcgCAO4TpZDcSOQDAHcI0kdNaBwDAwajIAQDuEKYVOYkcAOAO3H4GAIBzcfsZAAAIOVTkAAB3YIwcAAAHM0zJYyEZG6GZyGmtAwDgYFTkAAB3oLUOAICTWUzkCs1ETmsdAAAHoyIHALgDrXUAABzMMGWpPc6sdQAAYDcqcgCAO5hG5Wbl+BBEIgcAuANj5AAAOBhj5AAAINRQkQMA3IHWOgAADmbKYiK3LRJb0VoHAMDBqMgBAO5Aax0AAAczDEkW7gU3QvM+clrrAAA4GBU5AMAdaK0DAOBgYZrIaa0DAOBgVOQAAHcI0yVaSeQAAFcwTUOmhSeYWTk2kEjkAAB3ME1rVTVj5AAAwG5U5AAAdzAtjpGHaEVOIgcAuINhSB4L49whOkZOax0AAAejIgcAuAOtdQAAnMs0DJkWWuuhevsZrXUAAByMihwA4A601gEAcDDDlDzhl8hprQMA4GBU5AAAdzBNSVbuIw/NipxEDgBwBdMwZVporZskcgAAgsg0ZK0i5/YzAABcZ+7cuWrdurWio6PVs2dP/eMf/7D1/CRyAIArmIZpefPXsmXLNHbsWE2ZMkXbt29Xly5d1L9/fx07dsy270UiBwC4g2lY3/z07LPPavjw4Ro2bJg6deqk+fPnKzY2Vm+88YZtX8vRY+RnJx5UqNzSPf5wCKM02BGgFhWeDs3xSNirsKjyd66NiWRWc0WFyiVJhYWFVfZHRUUpKirqvM+XlZVp27Ztmjhxom9fRESE+vXrp82bN9c8kHM4OpGfPn1akrRRHwQ5EtSKnGAHgNrUqF2wI0BtOn36tBISEgJy7nr16iklJUUb86znigYNGigtLa3KvilTpmjq1KnnffbEiRPyer1KTk6usj85OVl79uyxHMtZjk7kqampys3NVVxcnDweT7DDqTWFhYVKS0tTbm6u4uPjgx0OAojf2j3c+lubpqnTp08rNTU1YNeIjo5WTk6OysrKLJ/LNM3z8s2FqvHa5OhEHhERoRYtWgQ7jKCJj4931R94N+O3dg83/taBqsR/Kjo6WtHR0QG/zk81adJEkZGROnr0aJX9R48eVUpKim3XYbIbAAABUK9ePXXv3l1r16717TMMQ2vXrlWvXr1su46jK3IAAELZ2LFjlZGRoauuukpXX321Zs+ereLiYg0bNsy2a5DIHSgqKkpTpkwJ+rgMAo/f2j34rcPTb3/7Wx0/flyTJ09WXl6eunbtqtWrV583Ac4Kjxmqi8cCAIBfxBg5AAAORiIHAMDBSOQAADgYiRwAAAcjkTtMoB+Hh9Cwfv16DRgwQKmpqfJ4PFq5cmWwQ0KAZGVlqUePHoqLi1NSUpIGDRqk7OzsYIcFByGRO0htPA4PoaG4uFhdunTR3Llzgx0KAmzdunXKzMzUli1btGbNGpWXl+vmm29WcXFxsEODQ3D7mYP07NlTPXr00IsvviipcoWgtLQ0PfLII5owYUKQo0OgeDwerVixQoMGDQp2KKgFx48fV1JSktatW6frr78+2OHAAajIHeLs4/D69evn2xeIx+EBCK6CggJJUmJiYpAjgVOQyB3i5x6Hl5eXF6SoANjJMAyNHj1avXv31uWXXx7scOAQLNEKACEiMzNTX375pTZu3BjsUOAgJHKHqK3H4QEIjhEjRmjVqlVav369qx/PDP/RWneI2nocHoDaZZqmRowYoRUrVujjjz9Wenp6sEOCw1CRO0htPA4PoaGoqEj79+/3vc7JydHOnTuVmJioli1bBjEy2C0zM1NLlizRu+++q7i4ON+cl4SEBMXExAQ5OjgBt585zIsvvqhnnnnG9zi8OXPmqGfPnsEOCzb79NNP1bdv3/P2Z2RkaOHChbUfEALG4/FccP+CBQs0dOjQ2g0GjkQiBwDAwRgjBwDAwUjkAAA4GIkcAAAHI5EDAOBgJHIAAByMRA4AgIORyAEAcDASOWDR0KFDqzwrvE+fPho9enStx/Hpp5/K4/Ho1KlTF/2Mx+PRypUrq33OqVOnqmvXrpbi+vrrr+XxeLRz505L5wFwYSRyhKWhQ4fK4/HI4/GoXr16atu2raZPn66KioqAX/udd97RjBkzqvXZ6iRfAPg5rLWOsHXLLbdowYIFKi0t1QcffKDMzEzVrVtXEydOPO+zZWVlqlevni3XTUxMtOU8AFAdVOQIW1FRUUpJSVGrVq300EMPqV+/fnrvvfck/dgOnzlzplJTU9W+fXtJUm5uru688041bNhQiYmJGjhwoL7++mvfOb1er8aOHauGDRuqcePGevzxx3XuKsfnttZLS0s1fvx4paWlKSoqSm3bttXrr7+ur7/+2reeeqNGjeTxeHxraxuGoaysLKWnpysmJkZdunTRX/7ylyrX+eCDD9SuXTvFxMSob9++VeKsrvHjx6tdu3aKjY1VmzZtNGnSJJWXl5/3uZdffllpaWmKjY3VnXfeqYKCgirvv/baa+rYsaOio6PVoUMHvfTSS37HAqBmSORwjZiYGJWVlfler127VtnZ2VqzZo1WrVql8vJy9e/fX3FxcdqwYYM+++wzNWjQQLfccovvuD/96U9auHCh3njjDW3cuFH5+flasWLFz1733nvv1VtvvaU5c+Zo9+7devnll9WgQQOlpaXp7bffliRlZ2fryJEjev755yVJWVlZWrRokebPn69//vOfGjNmjO655x6tW7dOUuU/OAYPHqwBAwZo586deuCBBzRhwgS//5vExcVp4cKF+uqrr/T888/r1Vdf1XPPPVflM/v379fy5cv1/vvva/Xq1dqxY4cefvhh3/uLFy/W5MmTNXPmTO3evVuzZs3SpEmT9Oabb/odD4AaMIEwlJGRYQ4cONA0TdM0DMNcs2aNGRUVZY4bN873fnJysllaWuo75s9//rPZvn170zAM377S0lIzJibG/Oijj0zTNM1mzZqZTz/9tO/98vJys0WLFr5rmaZp3nDDDeaoUaNM0zTN7OxsU5K5Zs2aC8b5ySefmJLMkydP+vaVlJSYsbGx5qZNm6p89v777zfvvvtu0zRNc+LEiWanTp2qvD9+/PjzznUuSeaKFSsu+v4zzzxjdu/e3fd6ypQpZmRkpPntt9/69n344YdmRESEeeTIEdM0TfOSSy4xlyxZUuU8M2bMMHv16mWapmnm5OSYkswdO3Zc9LoAao4xcoStVatWqUGDBiovL5dhGPrd736nqVOn+t7v3LlzlXHxXbt2af/+/YqLi6tynpKSEh04cEAFBQU6cuRIlcfG1qlTR1ddddV57fWzdu7cqcjISN1www3Vjnv//v06c+aMbrrppir7y8rK1K1bN0nS7t27z3t8ba9evap9jbOWLVumOXPm6MCBAyoqKlJFRYXi4+OrfKZly5Zq3rx5lesYhqHs7GzFxcXpwIEDuv/++zV8+HDfZyoqKpSQkOB3PAD8RyJH2Orbt6/mzZunevXqKTU1VXXqVP3fvX79+lVeFxUVqXv37lq8ePF552ratGmNYoiJifH7mKKiIknSX//61yoJVKoc97fL5s2bNWTIEE2bNk39+/dXQkKCli5dqj/96U9+x/rqq6+e9w+LyMhI22IFcHEkcoSt+vXrq23bttX+/JVXXqlly5YpKSnpvKr0rGbNmunzzz/X9ddfL6my8ty2bZuuvPLKC36+c+fOMgxD69atU79+/c57/2xHwOv1+vZ16tRJUVFROnTo0EUr+Y4dO/om7p21ZcuWX/6SP7Fp0ya1atVKTzzxhG/fN998c97nDh06pMOHDys1NdV3nYiICLVv317JyclKTU3VwYMHNWTIEL+uD8AeTHYDfjBkyBA1adJEAwcO1IYNG5STk6NPP/1UI0eO1LfffitJGjVqlJ566imtXLlSe/bs0cMPP/yz94C3bt1aGRkZuu+++7Ry5UrfOZcvXy5JatWqlTwej1atWqXjx4+rqKhIcXFxGjdunMaMGaM333xTBw4c0Pbt2/XCCy/4JpD9/ve/1759+/TYY48pOztbS5Ys0cKFC/36vpdeeqkOHTqkpUuX6sCBA5ozZ84FJ+5FR0crIyNDu3bt0oYNGzRy5EjdeeedSklJkSRNmzZNWVlZmjNnjvbu3asvvvhCCxYs0LPPPutXPABqhkQO/CA2Nlbr169Xy5YtNXjwYHXs2FH333+/SkpKfBX6o48+qn//939XRkaGevXqpbi4ON1+++0/e9558+bpjjvu0MMPP6wOHTpo+PDhKi4uliQ1b95c06ZN04QJE5ScnKwRI0ZIkmbMmKFJkyYpKytLHTt21C233KK//vWvSk9Pl1Q5bv32229r5cqV6tKli+bPn69Zs2b59X1vu+02jRkzRiNGjFDXrl21adMmTZo06bzPtW3bVoMHD9avfvUr3Xzzzbriiiuq3F72wAMP6LXXXtOCBQvUuXNn3XDDDVq4cKEvVgCB5TEvNksHAACEPCpyAAAcjEQOAICDkcgBAHAwEjkAAA5GIgcAwMFI5AAAOBiJHAAAByORAwDgYCRyAAAcjEQOAICDkcgBAHAwEjkAAA72/wG5rsTvkDnUDwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cm = confusion_matrix(svmy_test, svmy_pred)\n",
    "disp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=clf.classes_)\n",
    "disp.plot()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f03d055-e8be-48b9-af73-c8bbc1a12ff5",
   "metadata": {},
   "source": [
    "___\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af8a73c1-cd47-4c7a-ba99-4e68ad185729",
   "metadata": {},
   "source": [
    "# K Means Clustering\n",
    "K-means is an unsupervised learning algorithm used in machine learning for clustering analysis. In unsupervised learning, algorithms are used to group unlabelled datasets, and k-means is particularly effective for partitioning a dataset into distinct clusters based on similarity.\n",
    "Here’s a high-level overview of how the k-means algorithm works:\r\n",
    "## Initialization: \n",
    "Choose the number of clusters, ( K ), and select ( K ) random points as cluster centers or centroids.\n",
    "## Assignment:\n",
    "Assign each data point to the nearest centroid, forming ( K ) clusters.\n",
    "## Update:\n",
    "Calculate the new centroids (mean) of the clusters by taking the average of all data points in the cluster.\n",
    "## Iteration:\n",
    "Repeat the assignment and update steps until the centroids no longer change significantly, indicating that the clusters are stable.\n",
    "\n",
    "The goal of k-means is to minimize the within-cluster variance, which is the sum of the squared distances between each data point and its corresponding centroid. This process iteratively refines the positions of the centroids, resulting in a set of clusters where each data point is closer to its own cluster’s centroid than to any other.\r\n",
    "\r\n",
    "K-means is widely used because it’s simple, efficient, and can handle large datasets. However, it does have some limitations, such as sensitivity to the initial placement of centroids and difficulty in clustering data with varying shapes and densiti. It’s also important to predefine the value of ( K ), which may not be straightforward and often requires additional methods like the elbow method to estimate the optimal number of clusters.es\r\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aac407fd-e52d-4931-9714-593f93e0cbba",
   "metadata": {},
   "source": [
    "## Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bdcc936-c2dc-42d0-b6a6-3e26ce11aec6",
   "metadata": {},
   "source": [
    "### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "624c4e9d-0ee3-4f1f-8396-eb84f789b559",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cac1499e-fdea-465f-9780-a8e4b5dec78e",
   "metadata": {},
   "source": [
    "### Generate synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5992cd30-7e9a-40e3-acb2-d9d834a21bdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = make_blobs(n_samples=300, centers=4, cluster_std=0.60, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "270cf5a7-7cdf-457e-a5b4-ee89a426c081",
   "metadata": {},
   "source": [
    "The `line X, _ = make_blobs(n_samples=300, centers=4, cluster_std=0.60, random_state=0)` is a function call to `make_blobs`, which is a convenient tool from the `scikit-learn` library used to generate synthetic datasets, particularly for clustering algorithms like K-Means.\n",
    "\n",
    "* `n_samples=300`: This specifies the total number of data points to generate. In this case, it’s set to 300.\n",
    "* `centers=4`: This determines the number of centers to generate, or in other words, the number of clusters. Here, we are generating data that should ideally be grouped into 4 clusters\n",
    "*  `cluster_std=0.60`: This parameter sets the standard deviation of the clusters. The standard deviation controls the spread of the data points around the cluster center. A smaller value will make the clusters tighter and more distinct, while a larger value will make them more spread out and possibly overlapping. Here, it’s set to 0.6\n",
    "\n",
    "* `random_state=0`: This is a seed for the random number generator. Using the same seed ensures that the random numbers are generated in the same order, which means that the function will produce the same results every time it’s run with that seed. This is useful for reproducibility.\n",
    "\n",
    "The function returns two values:\n",
    "\n",
    "* `X:` This is the array of shape [n_samples, n_features] containing the generated data points.\n",
    "* `_:` This is a placeholder for the second return value, which is the true integer labels for cluster membership of each sample. The underscore is used because we don’t need these labels for the K-Means algorithm, as it is an unsupervised learning method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "41e44f24-a649-4cb4-a665-f87e35a3f806",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Arad\\AppData\\Local\\Temp\\ipykernel_22204\\523021443.py:1: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored\n",
      "  plt.scatter(X[:, 0], X[:, 1], s=50, cmap='jet')\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=50, cmap='jet')\n",
    "plt.title('Raw Data')\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627ad536-284c-46f2-90f0-bfce9fe99b3e",
   "metadata": {},
   "source": [
    "### Apply K-Means clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bd05d60f-6831-451e-b11c-869c6dd65d8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=4)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=4)\n",
    "kmeans.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "988046c4-58d0-4ad7-9f70-86f76c4f5ffc",
   "metadata": {},
   "source": [
    "### Predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f65b5035-77b0-4971-8a6e-d2fb9cb8b710",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_kmeans = kmeans.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d3ba4af-e1e0-46cd-b51e-f9456e9e7997",
   "metadata": {},
   "source": [
    "### Plot the Outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "26321859-cbe9-4d0b-8fcf-4b39c11ce20a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y_kmeans, s=50, cmap='jet')\n",
    "centers = kmeans.cluster_centers_\n",
    "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5)\n",
    "plt.title('K-Means Clustering')\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "514356a4-f909-4e1e-8664-4676b1c065d4",
   "metadata": {},
   "source": [
    "### Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef8346e2-3f75-45fb-ac87-9777461a826b",
   "metadata": {},
   "source": [
    "#### Silhouette Score\n",
    "he silhouette score is a metric used to evaluate the quality of clusters in a clustering algorithm. It measures how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The silhouette score ranges from -1 to +1, where:\n",
    "* A high value close to +1 indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters, suggesting the object is in the appropriate cluster.\n",
    "* A value of 0 indicates that the object is on or very close to the decision boundary between two neighboring clusters, which may suggest overlapping clusters.\n",
    "* Negative values indicate that the object might have been assigned to the wrong cluster.\n",
    "#### Equation\n",
    "The silhouette score for the data point ( i ) is then calculated as:\n",
    "\n",
    "$$ s(i) = \\frac{b(i) - a(i)}{\\max\\{a(i), b(i)\\}} $$\r\n",
    "\r\n",
    "Where:\r\n",
    "- \\( a(i) \\) is the mean distance between \\( i \\) and all other data points in the same cluster.\r\n",
    "- \\( b(i) \\) is the smallest mean distance from \\( i \\) to all points in any other cluster, of which \\( i \\) is not a member."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "25181fdf-042e-41f4-a8e3-77fd5ee66330",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhouette Score: 0.6819938690643478\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "\n",
    "silhouette_avg = silhouette_score(X, y_kmeans)\n",
    "print(f'Silhouette Score: {silhouette_avg}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b6c50080-e64b-401a-ac2a-dea9d2724115",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhouette Score: 0.68\n"
     ]
    }
   ],
   "source": [
    "print(f'Silhouette Score: {silhouette_avg:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7eaa7567-40c5-4f40-861d-fd898129a7c0",
   "metadata": {},
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a7d7737-6de7-486f-9454-e9506d059a8e",
   "metadata": {},
   "source": [
    "# Principal Component Analysis (PCA)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7872f295-c5c3-4971-a516-5add8f749759",
   "metadata": {},
   "source": [
    "PCA, or Principal Component Analysis, is a statistical technique used for dimensionality reduction in data analysis. It transforms a large set of variables, which may be correlated, into a smaller set of uncorrelated variables called principal components. These principal components are obtained by orthogonal transformation and capture the most significant variance in the data, making them useful for exploratory data analysis, visualization, and preprocessing data for machine learning algorithms.\n",
    "\n",
    "The process involves the following steps:\n",
    "\n",
    "## Standardization:\n",
    "The data is standardized to have a mean of zero and a standard deviation of one.\n",
    "## Covariance Matrix Computation:\n",
    "A covariance matrix is computed to understand how variables in the data are varying from the mean with respect to each other.\n",
    "## Eigenvalue and Eigenvector Calculation:\n",
    "Eigenvalues and eigenvectors of the covariance matrix are calculated. Eigenvectors determine the directions of the new feature space, and eigenvalues determine their magnitude.\n",
    "## Sorting and Selecting Principal Components:\n",
    "Eigenvectors are sorted by their eigenvalues in descending order to rank the principal components. The top principal components are selected based on the amount of variance they capture from the data.\n",
    "## Transformation:\n",
    " The original data is transformed into the new subspace using the selected principal components.\n",
    "\n",
    "PCA is widely used in fields like finance, genetics, computer vision, and many others where data dimensionality poses a challenge. It helps to simplify the complexity in high-dimensional data while retaining trends and patterns."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac15339c-2baf-473c-919a-7c45a9ae58c0",
   "metadata": {},
   "source": [
    "## Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bcb81ce-8ed0-4d23-9155-ae09085ebd9f",
   "metadata": {},
   "source": [
    "### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8a51a0c8-201a-4463-a509-d1a3d7237536",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f27f6ee5-a090-4447-9c69-c4b2df7e4716",
   "metadata": {},
   "source": [
    "### Hypothetical dataset (features X and target y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "25f99d60-5057-4e5b-8172-07c7e405adfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "pcX = np.random.rand(100, 10)  # 100 samples with 10 features each\n",
    "pcy = np.random.rand(100)      # 100 target values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df956f0b-33b6-40fc-b8f4-a1787e64fc61",
   "metadata": {},
   "source": [
    "### Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dca94224-8510-4a5d-b800-56ac7d52a92a",
   "metadata": {},
   "outputs": [],
   "source": [
    "pcX_train, pcX_test, pcy_train, pcy_test = train_test_split(pcX, pcy, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94a1d375-b66a-402e-bd02-4657e00d2cf7",
   "metadata": {},
   "source": [
    "### Standardizing the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3c1cef96-dc08-4b8d-89b8-87d86f58bdef",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "X_train_scaled = scaler.fit_transform(pcX_train)\n",
    "X_test_scaled = scaler.transform(pcX_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a25ad666-014a-4b42-98c0-e111f91c9c7f",
   "metadata": {},
   "source": [
    "### Applying PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b30b8368-24fd-48a6-b9f9-5f5427a5c431",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=0.95)  # Keep 95% of variance\n",
    "X_train_pca = pca.fit_transform(X_train_scaled)\n",
    "X_test_pca = pca.transform(X_test_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fe0b089-133a-42d6-baf8-575b22d8cdf7",
   "metadata": {},
   "source": [
    "### Plot the Outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ab56b0c-eff9-40c7-a700-1cb750526dd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(X_train_pca[:, 0], X_train_pca[:, 1], c=pcy_train, cmap='viridis', edgecolor='k', s=50)\n",
    "plt.xlabel('Principal Component 1')\n",
    "plt.ylabel('Principal Component 2')\n",
    "plt.title('2D PCA Result')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7276a64-ff0b-49c1-8d66-7100cbed60ab",
   "metadata": {},
   "source": [
    "### Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "312046e9-8d81-4a8c-9c5a-ec294d081c8e",
   "metadata": {},
   "source": [
    "#### Explained Variance Ratio\n",
    "The explained variance ratio in PCA (Principal Component Analysis) represents the proportion of the dataset’s total variance that is explained by each principal component. It is calculated by dividing the variance captured by a principal component by the total variance in the dataset.\n",
    "\n",
    "$$\r\n",
    "\\text{Explained Variance Ratio}_i = \\frac{\\text{Variance of } i^{th} \\text{ component}}{\\text{Total Variance}}\r\n",
    "$$\r\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8f4400e2-95e5-4a96-9c5c-bd1c632c184b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Ratio: [0.15815564 0.1522736  0.12146642 0.11117203 0.10836669 0.08668584\n",
      " 0.08035136 0.06939911 0.06096011 0.0511692 ]\n"
     ]
    }
   ],
   "source": [
    "explained_variance = pca.explained_variance_ratio_\n",
    "print(f'Explained Variance Ratio: {explained_variance}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3d0db6d-8d17-47f5-b67e-df1049bbe972",
   "metadata": {},
   "source": [
    "#### Cumulative Explained Variance\n",
    "The cumulative explained variance in PCA (Principal Component Analysis) refers to the cumulative sum of the explained variances of the principal components. It indicates the total variance explained by the first ( n ) components. This is useful for determining how many components are needed to capture a certain percentage of the total variance in the dataset.\n",
    "\n",
    "$$\r\n",
    "\\text{Cumulative Explained Variance}_n = \\sum_{i=1}^{n} \\text{Explained Variance Ratio}_i\r\n",
    "$$\r\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "587576ab-e1a9-4c58-a0ca-e614391482f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cumulative Explained Variance: [0.15815564 0.31042924 0.43189566 0.54306769 0.65143438 0.73812022\n",
      " 0.81847158 0.88787069 0.9488308  1.        ]\n"
     ]
    }
   ],
   "source": [
    "cumulative_explained_variance = np.cumsum(explained_variance)\n",
    "print(f'Cumulative Explained Variance: {cumulative_explained_variance}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6b5c4bc-03d1-47ba-b05c-56b300892196",
   "metadata": {},
   "source": [
    "#### Numeric Narratives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8bac66d6-0b68-4d8e-8911-07d156eec6ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fx8db3Vd9P5555hlFR0crNDRU3t7eioyMzNCzfKeKFSsqLi5OS5cuVb169bR69WqtWLHCah1/f3+dPHlSe/fu1WOPPSYvL69Mf5aenp5q06aNRo4cqUOHDqljx46WZZUqVVJYWJjCw8M1depU1a5dWxcvXlRMTIwCAwPVsmXLDPsLDg5Ww4YN1aZNG33wwQeqVKmS/vjjD61evVpt27ZVUFCQhg8frqtXr2rGjBkqUKCA1qxZox49eujbb7+17MfNzU1du3bVlClTlJCQoL59+6pdu3aZDi0vXLiwihYtqrlz56pkyZKKi4vT0KFDc3TtsxMZGalWrVqpTJkyeuWVV+Tg4KB9+/bpwIEDeu+99xQcHKxKlSqpa9eumjx5shISEqw+CMlOWFiYWrVqpd9++02dO3e2WlaxYkV9/fXXCg0Nlclk0siRI+86IVxmKlasqM8++0zr1q1TQECAPv/8c+3YsUMBAQE53oe/v7+6du2qHj16aMaMGapZs6ZOnz6t+Ph4tWvXTr1799a8efPUsWNHDR48WEWKFNHx48e1dOlSzZ8/P9v3MQAAgC08XBwf+g495D67zl5uq4YNG1oeyXTb+vXrc3QPan5Xrlw57d69W82aNdPAgQNVvXp1Pffcc4qJidHs2bMt6y1YsEA3b95U3bp11b9/f7333nu5cvxhw4apadOmatWqlVq2bKk2bdqofPnyWa7/4osvasCAAerTp49q1aqlrVu3Zpi9+uWXX1bz5s3VrFkzFS9eXP/+97+z3F9YWJj27dunJk2aqEyZMlbLFi5cqPDwcA0cOFCVK1dWmzZttGPHjgzr3WYymbRmzRo99dRT6t69uypVqqQOHTro9OnT8vHx0caNGzV9+nR9/vnnKliwoBwcHPT555/r559/trrWFSpU0EsvvaQWLVro+eefV2BgoD7++ONMj+ng4KClS5dq165dql69ugYMGKDJkydneb45FRISom+//Vbff/+96tWrpyeeeELTpk1T2bJlLcddsWKFrl+/rvr16+v111+3uv87O88884yKFCmiI0eOqFOnTlbLoqKiVLhwYTVq1EihoaEKCQmx6gnPqf/7v//TSy+9pPbt26tBgwb666+/sp0BPiuzZ8/WK6+8orfeektVqlRRz549lZSUJEkqVaqUtmzZorS0ND3//POqUaOG+vfvL29vb8stGQAAAMC9MpmNmIUrhxITE3X8+HFJt4YBR0VFqVmzZipSpIjKlCmjYcOG6ezZs/rss88k3XpkWPXq1dW7d2/16NFDP/74o/r27avVq1fnePbyhIQEFSpUSFevXs0wadeNGzd08uRJBQQE3Nf9rsDo0aO1cuXKXBu+j4cHvycAAIAtrqXctDwNiQnK8pfssuWd7NqNs3PnTtWuXdtyf3FERIRq166tyMhISbfuPb5ztuOAgACtXr1a69evV82aNTV16lTNnz/fsMeFAQAAAABwP+z6McvTTz+d7eOuoqOjM91mz549BlYFAAAAAEDu4IZFwACjR49maDkAAAAAQjcAAAAAAEYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXTDislk0sqVKyVJp06dkslksmkW7ju3z8y97DMn/P39NX369Fzdp602btwok8mkK1eu5Hibp59+Wv379zesptu6deumNm3aGH6czDyocwQAAAAeRnZ9TjdyT7du3XTlypVsA6+t/Pz8dO7cORUrVizH25w7d06FCxfOtRryu6+//lrOzs72LsNQj8I5AgAAAFkhdOfQtPVHH+jxBjxX6YEeLzOOjo7y9fW1aRtb13/UFSlSxN4lGCYlJUUuLi75+hwBAACAu2F4eT719NNPq2/fvho8eLCKFCkiX19fjR492mqdY8eO6amnnpKbm5uqVaum9evXWy2/cyh4enq6HnvsMc2ePdtqnT179sjBwUGnT5+WlHF4+fbt21W7dm25ubkpKChIe/bssdo+Ojpa3t7eVm0rV66UyWSyvD5x4oRat24tHx8fFShQQPXq1dMPP/xg8zWZP3++qlatKjc3N1WpUkUff/yxZVmPHj0UGBio5ORkSbcCY+3atRUeHm51LZYuXapGjRrJzc1N1atX16ZNm7I83l9//aWOHTuqdOnS8vDwUI0aNfTvf//bap1/Dr329/fXhAkT1KNHD3l5ealMmTKaO3eu1TZnzpxRu3bt5O3trSJFiqh169Y6deqUZXlaWpoiIiLk7e2tokWLavDgwTKbzVnWmZCQIHd3d3333XdW7StWrJCXl5euXbsmSRoyZIgqVaokDw8PlStXTiNHjlRqaqpl/dGjR6tWrVqaP3++AgIC5Obmluk5fv755woKCpKXl5d8fX3VqVMnxcfHW5bfHqYfExOjoKAgeXh4qFGjRjpy5IhVfd98843q1asnNzc3FStWTG3btrUsS05O1qBBg1S6dGl5enqqQYMG2rhxY5bXAAAAADAKoTsfW7RokTw9PbVt2zZ98MEHGjt2rCVYp6en66WXXpKLi4u2bdumOXPmaMiQIVnuy8HBQR07dtSSJUus2hcvXqzGjRurbNmyGbZJTExUq1atVK1aNe3atUujR4/WoEGDbD6PxMREtWjRQjExMdqzZ4+aN2+u0NBQxcXF5XgfixcvVmRkpMaPH69Dhw5pwoQJGjlypBYtWiRJmjFjhpKSkjR06FBJ0vDhw3XlyhXNnDnTaj/vvPOOBg4cqD179qhhw4YKDQ3VX3/9lekxb9y4obp162r16tU6cOCAevXqpS5dumj79u3Z1jp16lTLBxRvvfWW3nzzTUvgTE1NVUhIiLy8vPTzzz9ry5YtKlCggJo3b66UlBTL9tHR0VqwYIE2b96sS5cuacWKFVker2DBgmrVqlWmP9s2bdrIw8NDkuTl5aXo6GgdPHhQH374oebNm6dp06ZZbXP8+HF99dVX+vrrr7O8bz81NVXjxo3Tvn37tHLlSp06dUrdunXLsN7w4cM1depU7dy5U05OTurRo4dl2erVq9W2bVu1aNFCe/bsUUxMjOrXr29Z3qdPH8XGxmrp0qX69ddf9eqrr6p58+Y6duxY1hceAAAAMADDy/OxwMBAjRo1SpJUsWJFzZw5UzExMXruuef0ww8/6PDhw1q3bp1KlSolSZowYYJeeOGFLPcXFhamqVOnKi4uTmXKlFF6erqWLl2qESNGZLr+kiVLlJ6erk8//VRubm56/PHH9d///ldvvvmmTedRs2ZN1axZ0/J63LhxWrFihVatWqU+ffrkaB+jRo3S1KlT9dJLL0mSAgICdPDgQX3yySfq2rWrChQooH/9619q2rSpvLy8NH36dG3YsEEFCxa02k+fPn308ssvS5Jmz56ttWvX6tNPP9XgwYMzHLN06dJWHzK8/fbbWrdunZYvX24VEP+pRYsWeuuttyTd6l2eNm2aNmzYoMqVK2vZsmVKT0/X/PnzLaMBFi5cKG9vb23cuFHPP/+8pk+frmHDhlnOdc6cOVq3bl221ycsLExdunTRtWvX5OHhoYSEBK1evdoqrN/5c/b399egQYO0dOlSq3NPSUnRZ599puLFi2d5rDvDc7ly5TRjxgzVq1dPiYmJKlCggGXZ+PHj1bRpU0nS0KFD1bJlS924cUNubm4aP368OnTooDFjxljWv/0eiYuL08KFCxUXF2d5bw8aNEhr167VwoULNWHChGyvBQAAAJCbCN35WGBgoNXrkiVLWobxHjp0SH5+fpZQIkkNGzbMdn+1atVS1apVtWTJEg0dOlSbNm1SfHy8Xn311UzXP3TokAIDAy3DjHNyjMwkJiZq9OjRWr16tc6dO6ebN2/q+vXrOe7pTkpK0okTJ/Taa6+pZ8+elvabN2+qUKFCVrUNGjRI48aN05AhQ/Tkk09m2Ned9Ts5OSkoKEiHDh3K9LhpaWmaMGGCli9frrNnzyolJUXJycmWnuOs3PlzM5lM8vX1tfzc9u3bp+PHj8vLy8tqmxs3bujEiRO6evWqzp07pwYNGmSoM7sh5i1atJCzs7NWrVqlDh066KuvvlLBggUVHBxsWWfZsmWaMWOGTpw4ocTERN28eTPDhxJly5bNNnBLsox62Ldvny5fvqz09HRJt8JytWrVMr0OJUuWlCTFx8erTJky2rt3r9XP8k779+9XWlqaKlWynhchOTlZRYsWzbY2AAAedWazWddT0+xdRr5yLYXr+agjdOdj/5wx2mQyWQLOvQoLC7OE7iVLlqh58+b3FWQcHBwyhME77xOWbvVSrl+/XlOmTFGFChXk7u6uV155xTKc+m4SExMlSfPmzbMKo9KtyeJuS09P15YtW+To6Kjjx4/fy+lYmTx5sj788ENNnz5dNWrUkKenp/r373/XurP7uSUmJqpu3bpavHhxhu3uFnaz4+LioldeeUVLlixRhw4dtGTJErVv315OTrd+RcTGxiosLExjxoxRSEiIChUqpKVLl2rq1KlW+/H09Mz2OElJSQoJCVFISIgWL16s4sWLKy4uTiEhIRmuy53X4Xav/u3r4O7unuUxEhMT5ejoqF27dln9fCVZ9aQDAABrZrNZr8yJ1a7Tl+1dCpCvcE/3I6pq1ao6c+aMzp07Z2n75Zdf7rpdp06ddODAAe3atUtffvmlwsLCsj3Gr7/+qhs3bmR5jOLFi+vvv/9WUlKSpe2f9wJv2bJF3bp1U9u2bVWjRg35+vpaTRx2Nz4+PipVqpR+//13VahQweorICDAst7kyZN1+PBhbdq0yTIU+Z/urP/mzZvatWuXqlatmulxt2zZotatW6tz586qWbOmypUrp6NH728W/Dp16ujYsWMqUaJEhnMpVKiQChUqpJIlS2rbtm0Z6rybsLAwrV27Vr/99pt+/PFHq5/t1q1bVbZsWQ0fPlxBQUGqWLGiZfI8Wxw+fFh//fWXJk2apCZNmqhKlSpWk6jlVGBgoGJiYjJdVrt2baWlpSk+Pj7DNWJ2fQAAsnY9NY3AbaCgsoXl7ux49xWR79DT/YgKDg5WpUqV1LVrV02ePFkJCQkaPnz4Xbfz9/dXo0aN9NprryktLU0vvvhilut26tRJw4cPV8+ePTVs2DCdOnVKU6ZMsVqnQYMG8vDw0Lvvvqu+fftq27Ztio6OtlqnYsWK+vrrrxUaGiqTyaSRI0fa3GM/ZswY9e3bV4UKFVLz5s2VnJysnTt36vLly4qIiNCePXsUGRmpL7/8Uo0bN1ZUVJT69eunpk2bqly5cpb9zJo1SxUrVlTVqlU1bdo0Xb582eoe5X/W/eWXX2rr1q0qXLiwoqKidOHCBash1LYKCwvT5MmT1bp1a40dO1aPPfaYTp8+ra+//lqDBw/WY489pn79+mnSpEmqWLGiqlSpoqioKF25cuWu+37qqafk6+ursLAwBQQEWI0KqFixouLi4rR06VLVq1cvw/3eOVWmTBm5uLjoo48+0htvvKEDBw5o3LhxNu9n1KhRevbZZ1W+fHl16NBBN2/e1Jo1aywzrIeFhSk8PFxTp05V7dq1dfHiRcXExCgwMFAtW7a0+XgAADxqdo4IlocLATE3uTs7Wj2hB48OerofUQ4ODlqxYoWuX7+u+vXr6/XXX9f48eNztG1YWJj27duntm3bZjvMt0CBAvrmm2+0f/9+1a5dW8OHD9f7779vtU6RIkX0r3/9S2vWrLE8UuufjzaLiopS4cKF1ahRI4WGhiokJER16tSx6Xxff/11zZ8/XwsXLlSNGjXUtGlTRUdHKyAgQDdu3FDnzp3VrVs3hYaGSpJ69eqlZs2aqUuXLkpL+999OJMmTdKkSZNUs2ZNbd68WatWrVKxYsUyPeaIESNUp04dhYSE6Omnn5avr6/atGljU93/5OHhoZ9++kllypTRSy+9pKpVq+q1117TjRs3LPdXDxw4UF26dFHXrl3VsGFDeXl5WT1OKysmk0kdO3bUvn37MoxgePHFFzVgwAD16dNHtWrV0tatWzVy5Eib6y9evLiio6P1xRdfqFq1apo0aVKGD2Jy4umnn9YXX3yhVatWqVatWnrmmWesZoVfuHChwsPDNXDgQFWuXFlt2rTRjh07VKZMGZuPBQDAo8jDxVEeLk585eIXgfvRZTJnN7tSPpSQkKBChQrp6tWrGSaBunHjhk6ePGn1jGFAuvWc7oCAAO3Zs0e1atWydzmwI35PAADyq2spN1Ut8tYTTw6ODZGHC4Nigexkly3vRE83AAAAAAAGIXQDAAAAAGAQxowAOeDv75/tc64BAAAAIDP0dAMAAAAAYBBCNwAAAAAABiF0Z4JhxACywu8HAAAA2ILQfQdnZ2dJ0rVr1+xcCYCH1e3fD7d/XwAAAADZYSK1Ozg6Osrb21vx8fGSJA8PDx5iD0DSrR7ua9euKT4+Xt7e3nJ0dLR3SQAAAMgDCN3/4OvrK0mW4A0Ad/L29rb8ngAAAADuhtD9DyaTSSVLllSJEiWUmppq73IAPEScnZ3p4QYAAIBNCN1ZcHR05I9rAAAAAMB9YSI1AAAAAAAMQugGAAAAAMAghG4AAAAAAAxC6AYAAAAAwCCEbgAAAAAADELoBgAAAADAIIRuAAAAAAAMQugGAAAAAMAgTvYuAAAAALgXZrNZ11PT7F1GvnEthWsJGIHQDQAAgDzHbDbrlTmx2nX6sr1LAYBsMbwcAAAAec711DQCt0GCyhaWu7OjvcsA8g16ugEAAJCn7RwRLA8XQmJucXd2lMlksncZQL5B6AYAAECe5uHiKA8X/qwF8HBieDkAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGcbJ3AQAAAI8Cs9ms66lp9i4j37iWwrUEkDcQugEAAAxmNpv1ypxY7Tp92d6lAAAeMIaXAwAAGOx6ahqB2yBBZQvL3dnR3mUAQJbo6QYAAHiAdo4IlocLITG3uDs7ymQy2bsMAMgSoRsAAOAB8nBxlIcLf4IBwKPC7sPLZ82aJX9/f7m5ualBgwbavn17tutPnz5dlStXlru7u/z8/DRgwADduHHjAVULAAAAAEDO2TV0L1u2TBERERo1apR2796tmjVrKiQkRPHx8Zmuv2TJEg0dOlSjRo3SoUOH9Omnn2rZsmV69913H3DlAAAAAADcnV1Dd1RUlHr27Knu3burWrVqmjNnjjw8PLRgwYJM19+6dasaN26sTp06yd/fX88//7w6dux4195xAAAAAADswW6hOyUlRbt27VJwcPD/inFwUHBwsGJjYzPdplGjRtq1a5clZP/+++9as2aNWrRo8UBqBgAAAADAFnabxePPP/9UWlqafHx8rNp9fHx0+PDhTLfp1KmT/vzzTz355JMym826efOm3njjjWyHlycnJys5OdnyOiEhIXdOAAAAAACAu7D7RGq22LhxoyZMmKCPP/5Yu3fv1tdff63Vq1dr3LhxWW4zceJEFSpUyPLl5+f3ACsGAAAAADzK7NbTXaxYMTk6OurChQtW7RcuXJCvr2+m24wcOVJdunTR66+/LkmqUaOGkpKS1KtXLw0fPlwODhk/Qxg2bJgiIiIsrxMSEgjeAAAAAIAHwm493S4uLqpbt65iYmIsbenp6YqJiVHDhg0z3ebatWsZgrWjo6MkyWw2Z7qNq6urChYsaPUFAAAAAMCDYLeebkmKiIhQ165dFRQUpPr162v69OlKSkpS9+7dJUnh4eEqXbq0Jk6cKEkKDQ1VVFSUateurQYNGuj48eMaOXKkQkNDLeEbAAAAAICHhV1Dd/v27XXx4kVFRkbq/PnzqlWrltauXWuZXC0uLs6qZ3vEiBEymUwaMWKEzp49q+LFiys0NFTjx4+31ykAAAAAAJAlkzmrcdn5VEJCggoVKqSrV68y1BwAADwQ11JuqlrkOknSwbEh8nCxa78HACAX5DRb5qnZywEAAAAAyEsI3QAAAAAAGITQDQAAAACAQQjdAAAAAAAYhNANAAAAAIBBCN0AAAAAABiE0A0AAAAAgEEI3QAAAAAAGITQDQAAAACAQQjdAAAAAAAYhNANAAAAAIBBCN0AAAAAABiE0A0AAAAAgEEI3QAAAAAAGITQDQAAAACAQQjdAAAAAAAYhNANAAAAAIBBnOxdAAAAePiYzWZdT02zdxn5xrUUriUAPKoI3QAAwIrZbNYrc2K16/Rle5cCAECex/ByAABg5XpqGoHbIEFlC8vd2dHeZQAAHiB6ugEAQJZ2jgiWhwshMbe4OzvKZDLZuwwAwANE6AYAAFnycHGUhwt/LgAAcK/u6X/RtLQ0rVy5UocOHZIkPf7443rxxRfl6Mgn4QAAAAAA3GZz6D5+/Lhatmyp//73v6pcubIkaeLEifLz89Pq1atVvnz5XC8SAAAAAIC8yOaJ1Pr27aty5crpzJkz2r17t3bv3q24uDgFBASob9++RtQIAAAAAECeZHNP96ZNm/TLL7+oSJEilraiRYtq0qRJaty4ca4WBwAAAABAXmZzT7erq6v+/vvvDO2JiYlycXHJlaIAAAAAAMgPbA7drVq1Uq9evbRt2zaZzWaZzWb98ssveuONN/Tiiy8aUSMAAAAAAHmSzaF7xowZKl++vBo2bCg3Nze5ubmpcePGqlChgj788EMjagQAAAAAIE+y+Z5ub29v/ec//9GxY8d0+PBhSVLVqlVVoUKFXC8OAAAAAIC87J6e0y1JFStWVMWKFXOzFgAAAAAA8pUche6IiAiNGzdOnp6eioiIyHbdqKioXCkMAAAAAIC8Lkehe8+ePUpNTbV8DwAAAAAA7i5HoXvDhg2Zfg8AAAAAALJm8+zlPXr0yPQ53UlJSerRo0euFAUAAAAAQH5gc+hetGiRrl+/nqH9+vXr+uyzz3KlKAAAAAAA8oMcz16ekJAgs9kss9msv//+W25ubpZlaWlpWrNmjUqUKGFIkQAAAAAA5EU5Dt3e3t4ymUwymUyqVKlShuUmk0ljxozJ1eIAAAAAAMjLchy6N2zYILPZrGeeeUZfffWVihQpYlnm4uKismXLqlSpUoYUCQAAAABAXpTj0N20aVNJ0smTJ+Xn5ycHB5tvBwcAAAAA4JGS49B9W9myZSVJ165dU1xcnFJSUqyWBwYG5k5lAAAAAADkcTaH7osXL6p79+767rvvMl2elpZ230UBAAAAAJAf2DxGvH///rpy5Yq2bdsmd3d3rV27VosWLVLFihW1atUqI2oEAAAAACBPsrmn+8cff9R//vMfBQUFycHBQWXLltVzzz2nggULauLEiWrZsqURdQIAAAAAkOfY3NOdlJRkeR534cKFdfHiRUlSjRo1tHv37tytDgAAAACAPMzm0F25cmUdOXJEklSzZk198sknOnv2rObMmaOSJUvmeoEAAAAAAORVNg8v79evn86dOydJGjVqlJo3b67FixfLxcVF0dHRuV0fAAAAAAB5ls2hu3Pnzpbv69atq9OnT+vw4cMqU6aMihUrlqvFAQAAAACQl9k0vDw1NVXly5fXoUOHLG0eHh6qU6cOgRsAAAAAgH+wKXQ7Ozvrxo0bRtUCAAAAAEC+YvNEar1799b777+vmzdvGlEPAAAAAAD5hs33dO/YsUMxMTH6/vvvVaNGDXl6elot//rrr3OtOAAAAAAA8jKbQ7e3t7defvllI2oBAMBmZrNZ11PT7F1GvnIthesJAEBusTl0L1y40Ig6AACwmdls1itzYrXr9GV7lwIAAJApm+/pBgDgYXE9NY3AbaCgsoXl7uxo7zIAAMjTbO7pBgDgYbRzRLA8XAiIucnd2VEmk8neZQAAkKcRugEA+YKHi6M8XPhvDQAAPFwYXg4AAAAAgEHuK3TfuHEjt+oAAAAAACDfsTl0p6ena9y4cSpdurQKFCig33//XZI0cuRIffrpp7leIAAAAAAAeZXNofu9995TdHS0PvjgA7m4uFjaq1evrvnz5+dqcQAAAAAA5GU2h+7PPvtMc+fOVVhYmBwd/zdLbM2aNXX48OFcLQ4AAAAAgLzM5tB99uxZVahQIUN7enq6UlNTc6UoAAAAAADyA5tDd7Vq1fTzzz9naP/yyy9Vu3btXCkKAAAAAID8wOYHmkZGRqpr1646e/as0tPT9fXXX+vIkSP67LPP9O233xpRIwAAAAAAeZLNPd2tW7fWN998ox9++EGenp6KjIzUoUOH9M033+i5554zokYAAAAAAPIkm3u6JalJkyZav359btcCAAAAAEC+YnNP944dO7Rt27YM7du2bdPOnTtzpSgAAAAAAPIDm0N37969debMmQztZ8+eVe/evXOlKAAAAAAA8gObQ/fBgwdVp06dDO21a9fWwYMHc6UoAAAAAADyA5tDt6urqy5cuJCh/dy5c3Jysv0W8VmzZsnf319ubm5q0KCBtm/fnu36V65cUe/evVWyZEm5urqqUqVKWrNmjc3HBQAAAADAaDaH7ueff17Dhg3T1atXLW1XrlzRu+++a/Ps5cuWLVNERIRGjRql3bt3q2bNmgoJCVF8fHym66ekpOi5557TqVOn9OWXX+rIkSOaN2+eSpcubetpAAAAAABgOJu7pqdMmaKnnnpKZcuWVe3atSVJe/fulY+Pjz7//HOb9hUVFaWePXuqe/fukqQ5c+Zo9erVWrBggYYOHZph/QULFujSpUvaunWrnJ2dJUn+/v62ngIAAAAAAA+EzT3dpUuX1q+//qoPPvhA1apVU926dfXhhx9q//798vPzy/F+UlJStGvXLgUHB/+vGAcHBQcHKzY2NtNtVq1apYYNG6p3797y8fFR9erVNWHCBKWlpdl6GgAAAAAAGO6entPt6empXr163deB//zzT6WlpcnHx8eq3cfHR4cPH850m99//10//vijwsLCtGbNGh0/flxvvfWWUlNTNWrUqEy3SU5OVnJysuV1QkLCfdUNAAAAAEBO3VPoPnbsmDZs2KD4+Hilp6dbLYuMjMyVwjKTnp6uEiVKaO7cuXJ0dFTdunV19uxZTZ48OcvQPXHiRI0ZM8awmgAAAAAAyIrNoXvevHl68803VaxYMfn6+spkMlmWmUymHIfuYsWKydHRMcNM6BcuXJCvr2+m25QsWVLOzs5ydHS0tFWtWlXnz59XSkqKXFxcMmwzbNgwRUREWF4nJCTYNAweAAAAAIB7ZXPofu+99zR+/HgNGTLkvg7s4uKiunXrKiYmRm3atJF0qyc7JiZGffr0yXSbxo0ba8mSJUpPT5eDw63b0Y8ePaqSJUtmGrilW484c3V1va9aAQAAAAC4FzZPpHb58mW9+uqruXLwiIgIzZs3T4sWLdKhQ4f05ptvKikpyTKbeXh4uIYNG2ZZ/80339SlS5fUr18/HT16VKtXr9aECRPUu3fvXKkHAAAAAIDcZHNP96uvvqrvv/9eb7zxxn0fvH379rp48aIiIyN1/vx51apVS2vXrrVMrhYXF2fp0ZYkPz8/rVu3TgMGDFBgYKBKly6tfv363XevOwAAAAAARjCZzWazLRtMnDhRUVFRatmypWrUqGF5XvZtffv2zdUCc1tCQoIKFSqkq1evqmDBgvYuBwBwH66l3FS1yHWSpINjQ+Thck/zgwIAANgsp9nS5r9O5s6dqwIFCmjTpk3atGmT1TKTyfTQh24AAAAAAB4Um0P3yZMnjagDAAAAAIB8x+aJ1AAAAAAAQM7c081v//3vf7Vq1SrFxcUpJSXFallUVFSuFAYAAAAAQF5nc+iOiYnRiy++qHLlyunw4cOqXr26Tp06JbPZrDp16hhRIwAAAAAAeZLNw8uHDRumQYMGaf/+/XJzc9NXX32lM2fOqGnTprn2/G4AAAAAAPIDm0P3oUOHFB4eLklycnLS9evXVaBAAY0dO1bvv/9+rhcIAAAAAEBeZXPo9vT0tNzHXbJkSZ04ccKy7M8//8y9ygAAAAAAyONsvqf7iSee0ObNm1W1alW1aNFCAwcO1P79+/X111/riSeeMKJGAAAAAADyJJtDd1RUlBITEyVJY8aMUWJiopYtW6aKFSsyczkAAAAAAHewOXSXK1fO8r2np6fmzJmTqwUBAAAAAJBf2HxPNwAAAAAAyJkc9XQXKVJER48eVbFixVS4cGGZTKYs17106VKuFQcAAAAAQF6Wo9A9bdo0eXl5SZKmT59uZD0AAAAAAOQbOQrdXbt2lSTdvHlTJpNJISEh8vHxMbQwAAAAAADyOpsmUnNyctIbb7yhQ4cOGVUPAORrZrNZ11PT7F1GvnEthWsJAAAebjbPXl6/fn3t2bNHZcuWNaIeAMi3zGazXpkTq12nL9u7FAAAADwgNofut956SwMHDtR///tf1a1bV56enlbLAwMDc604AMhPrqemEbgNElS2sNydHe1dBgAAQAY2h+4OHTpIkvr27WtpM5lMMpvNMplMSktjqB8A3M3OEcHycCEk5hZ3Z8dsn6wBAABgLzaH7pMnTxpRBwA8UjxcHOXhYvOvYAAAAOQxNv/Fx73cAAAAAADkzD13sxw8eFBxcXFKSUmxan/xxRfvuygAAAAAAPIDm0P377//rrZt22r//v2We7klWe6l455uAAAAAABucbB1g379+ikgIEDx8fHy8PDQb7/9pp9++klBQUHauHGjASUCAAAAAJA32dzTHRsbqx9//FHFihWTg4ODHBwc9OSTT2rixInq27ev9uzZY0SdAAAAAADkOTb3dKelpcnLy0uSVKxYMf3xxx+Sbk2wduTIkdytDgAAAACAPMzmnu7q1atr3759CggIUIMGDfTBBx/IxcVFc+fOVbly5YyoEQAAAACAPMnm0D1ixAglJSVJksaOHatWrVqpSZMmKlq0qJYtW5brBQIAAAAAkFfZHLpDQkIs31eoUEGHDx/WpUuXVLhwYcsM5gAAAAAA4B7u6f7Xv/5l6em+rUiRIgRuAAAAAAD+webQPWDAAPn4+KhTp05as2YNz+UGAAAAACALNofuc+fOaenSpTKZTGrXrp1Kliyp3r17a+vWrUbUBwAAAABAnmVz6HZyclKrVq20ePFixcfHa9q0aTp16pSaNWum8uXLG1EjAAAAAAB5ks0Tqd3Jw8NDISEhunz5sk6fPq1Dhw7lVl0AAAAAAOR5Nvd0S9K1a9e0ePFitWjRQqVLl9b06dPVtm1b/fbbb7ldHwAAAAAAeZbNPd0dOnTQt99+Kw8PD7Vr104jR45Uw4YNjagNAAAAAIA8zebQ7ejoqOXLlyskJESOjo5G1AQAAAAAQL5gc+hevHixEXUAAAAAAJDv3NM93QAAAAAA4O4I3QAAAAAAGITQDQAAAACAQQjdAAAAAAAYJEcTqSUkJOR4hwULFrznYgAAAAAAyE9yFLq9vb1lMplytMO0tLT7KggAAAAAgPwiR6F7w4YNlu9PnTqloUOHqlu3bmrYsKEkKTY2VosWLdLEiRONqRIAAAAAgDwoR6G7adOmlu/Hjh2rqKgodezY0dL24osvqkaNGpo7d666du2a+1UCAAAAAJAH2TyRWmxsrIKCgjK0BwUFafv27blSFAAAAAAA+YHNodvPz0/z5s3L0D5//nz5+fnlSlEAAAAAAOQHORpefqdp06bp5Zdf1nfffacGDRpIkrZv365jx47pq6++yvUCAQAAAADIq2zu6W7RooWOHj2q0NBQXbp0SZcuXVJoaKiOHj2qFi1aGFEjAAAAAAB5ks093dKtIeYTJkzI7VoAAAAAAMhXbO7plqSff/5ZnTt3VqNGjXT27FlJ0ueff67NmzfnanEAAAAAAORlNofur776SiEhIXJ3d9fu3buVnJwsSbp69Sq93wAAAAAA3MHm0P3ee+9pzpw5mjdvnpydnS3tjRs31u7du3O1OAAAAAAA8jKbQ/eRI0f01FNPZWgvVKiQrly5khs1AQAAAACQL9gcun19fXX8+PEM7Zs3b1a5cuVypSgAAAAAAPIDm0N3z5491a9fP23btk0mk0l//PGHFi9erEGDBunNN980okYAAAAAAPIkmx8ZNnToUKWnp+vZZ5/VtWvX9NRTT8nV1VWDBg3S22+/bUSNAAAAAADkSTaHbpPJpOHDh+udd97R8ePHlZiYqGrVqqlAgQJG1AcAAAAAQJ5lc+i+zcXFRdWqVcvNWgAAAAAAyFdsDt1JSUmaNGmSYmJiFB8fr/T0dKvlv//+e64VB8C+zGazrqem2buMfONaCtcSAADgUWNz6H799de1adMmdenSRSVLlpTJZDKiLgB2Zjab9cqcWO06fdnepQAAAAB5ls2h+7vvvtPq1avVuHFjI+oB8JC4nppG4DZIUNnCcnd2tHcZAAAAeABsDt2FCxdWkSJFjKgFwENq54hgebgQEnOLu7Mjo4QAAAAeETaH7nHjxikyMlKLFi2Sh4eHETUBeMh4uDjKw+We510EAAAAHlk2/xU9depUnThxQj4+PvL395ezs7PV8t27d+dacQAAAAAA5GU2h+42bdoYUAYAAAAAAPmPzaF71KhRRtQBAAAAAEC+42DvAgAAAAAAyK9y1NNdpEgRHT16VMWKFVPhwoWznXX30qVLuVYcAAAAAAB5WY5C97Rp0+Tl5SVJmj59upH1AAAAAACQb+QodHft2jXT73PLrFmzNHnyZJ0/f141a9bURx99pPr16991u6VLl6pjx45q3bq1Vq5cmet1AQAAAABwP+7rnu4bN24oISHB6stWy5YtU0REhEaNGqXdu3erZs2aCgkJUXx8fLbbnTp1SoMGDVKTJk3utXwAAAAAAAxlc+hOSkpSnz59VKJECXl6eqpw4cJWX7aKiopSz5491b17d1WrVk1z5syRh4eHFixYkOU2aWlpCgsL05gxY1SuXDmbjwkAAAAAwINgc+gePHiwfvzxR82ePVuurq6aP3++xowZo1KlSumzzz6zaV8pKSnatWuXgoOD/1eQg4OCg4MVGxub5XZjx45ViRIl9Nprr931GMnJyffdGw8AAAAAwL2w+Tnd33zzjT777DM9/fTT6t69u5o0aaIKFSqobNmyWrx4scLCwnK8rz///FNpaWny8fGxavfx8dHhw4cz3Wbz5s369NNPtXfv3hwdY+LEiRozZkyOawIAAAAAILfY3NN96dIly5DuggULWh4R9uSTT+qnn37K3er+4e+//1aXLl00b948FStWLEfbDBs2TFevXrV8nTlzxtAaAQAAAAC4zeae7nLlyunkyZMqU6aMqlSpouXLl6t+/fr65ptv5O3tbdO+ihUrJkdHR124cMGq/cKFC/L19c2w/okTJ3Tq1CmFhoZa2tLT02+diJOTjhw5ovLly1tt4+rqKldXV5vqAgAAAAAgN9jc0929e3ft27dPkjR06FDNmjVLbm5uGjBggN555x2b9uXi4qK6desqJibG0paenq6YmBg1bNgww/pVqlTR/v37tXfvXsvXiy++qGbNmmnv3r3y8/Oz9XQAAAAAADCMzT3dAwYMsHwfHBysw4cPa9euXapQoYICAwNtLiAiIkJdu3ZVUFCQ6tevr+nTpyspKUndu3eXJIWHh6t06dKaOHGi3NzcVL16davtb/eu/7MdAAAAAAB7szl0/1PZsmVVtmzZe96+ffv2unjxoiIjI3X+/HnVqlVLa9eutUyuFhcXJweH+3qcOAAAAAAAdmEym83mu600Y8aMHO+wb9++91WQ0RISElSoUCFdvXpVBQsWtHc5wEPrWspNVYtcJ0k6ODZEHi73/RkdAAAAkG/kNFvm6K/oadOm5eigJpPpoQ/dAAAAAAA8KDkK3SdPnjS6DgAAAAAA8p37ulnabDYrB6PTAQAAAAB4JN1T6P70009VvXp1ubm5WWYUnz9/fm7XBgAAAABAnmbzzEiRkZGKiorS22+/bXmWdmxsrAYMGKC4uDiNHTs214sEAAAAACAvsjl0z549W/PmzVPHjh0tbS+++KICAwP19ttvE7oBAAAAAPj/bB5enpqaqqCgoAztdevW1c2bN3OlKAAAAAAA8gObQ3eXLl00e/bsDO1z585VWFhYrhQFAAAAAEB+YPPwcunWRGrff/+9nnjiCUnStm3bFBcXp/DwcEVERFjWi4qKyp0qAQAAAADIg2wO3QcOHFCdOnUkSSdOnJAkFStWTMWKFdOBAwcs65lMplwqEQAAAACAvMnm0L1hwwYj6gAAAAAAIN+x+Z7uixcvZrls//7991UMAAAAAAD5ic2hu0aNGlq9enWG9ilTpqh+/fq5UhQAAAAAAPmBzaE7IiJCL7/8st58801dv35dZ8+e1bPPPqsPPvhAS5YsMaJGAAAAAADyJJtD9+DBgxUbG6uff/5ZgYGBCgwMlKurq3799Ve1bdvWiBoBAAAAAMiTbA7dklShQgVVr15dp06dUkJCgtq3by9fX9/crg0AAAAAgDzN5tC9ZcsWBQYG6tixY/r11181e/Zsvf3222rfvr0uX75sRI0AAAAAAORJNofuZ555Ru3bt9cvv/yiqlWr6vXXX9eePXsUFxenGjVqGFEjAAAAAAB5ks3P6f7+++/VtGlTq7by5ctry5YtGj9+fK4VBgAAAABAXmdzT/c/A7dlRw4OGjly5H0XBAAAAABAfpHj0N2iRQtdvXrV8nrSpEm6cuWK5fVff/2latWq5WpxAAAAAADkZTkO3evWrVNycrLl9YQJE3Tp0iXL65s3b+rIkSO5Wx0AAAAAAHlYjkO32WzO9jUAAAAAALB2T8/pBgAAAAAAd5fj0G0ymWQymTK0AQAAAACAzOX4kWFms1ndunWTq6urJOnGjRt644035OnpKUlW93sDAAAAAAAbQnfXrl2tXnfu3DnDOuHh4fdfEQAAAAAA+USOQ/fChQuNrAMAAAAAgHwnx6EbeNiZzWZdT02zdxn5xrUUriUAAABwvwjdyBfMZrNemROrXacv27sUAAAAALDgkWHIF66nphG4DRJUtrDcnR3tXQYAAACQJ9HTjXxn54hgebgQEnOLu7MjjwcEAAAA7hGhG/mOh4ujPFx4awMAAACwP4aXAwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgkIcidM+aNUv+/v5yc3NTgwYNtH379izXnTdvnpo0aaLChQurcOHCCg4OznZ9AAAAAADsxe6he9myZYqIiNCoUaO0e/du1axZUyEhIYqPj890/Y0bN6pjx47asGGDYmNj5efnp+eff15nz559wJUDAAAAAJA9k9lsNtuzgAYNGqhevXqaOXOmJCk9PV1+fn56++23NXTo0Ltun5aWpsKFC2vmzJkKDw+/6/oJCQkqVKiQrl69qoIFC953/Xg4XEu5qWqR6yRJB8eGyMPFyc4VAQAAAMjPcpot7drTnZKSol27dik4ONjS5uDgoODgYMXGxuZoH9euXVNqaqqKFCmS6fLk5GQlJCRYfQEAAAAA8CDYNXT/+eefSktLk4+Pj1W7j4+Pzp8/n6N9DBkyRKVKlbIK7neaOHGiChUqZPny8/O777oBAAAAAMgJu9/TfT8mTZqkpUuXasWKFXJzc8t0nWHDhunq1auWrzNnzjzgKgEAAAAAjyq73vharFgxOTo66sKFC1btFy5ckK+vb7bbTpkyRZMmTdIPP/ygwMDALNdzdXWVq6trrtQLAAAAAIAt7NrT7eLiorp16yomJsbSlp6erpiYGDVs2DDL7T744AONGzdOa9euVVBQ0IMoFQAAAAAAm9l9iueIiAh17dpVQUFBql+/vqZPn66kpCR1795dkhQeHq7SpUtr4sSJkqT3339fkZGRWrJkifz9/S33fhcoUEAFChSw23kAAAAAAPBPdg/d7du318WLFxUZGanz58+rVq1aWrt2rWVytbi4ODk4/K9Dfvbs2UpJSdErr7xitZ9Ro0Zp9OjRD7J0AAAAAACyZffndD9oPKc7f+I53QAAAAAepDzxnG4AAAAAAPIzQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAZxsncBeHiZzWZdT02zdxk5ci0lb9QJAAAA4NFC6EaWrqemqVrkOnuXAQAAAAB5FqH7ITZt/VG7Hj81Ld2ux78XQWULy93Z0d5lAAAAAIAkQjey4eRg0ltPl7d3GRZ9nqlw13XcnR1lMpkeQDUAAAAAcHeEbmTJZDLJ2fHhCbAeLrxdAQAAAOQtpBg8Uuw9ZP9hM+C5SvYuAQAAAMjXeGQYAAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABnGydwEA8rZp64/au4SHzoDnKtm7BAAAADwk6OkGAAAAAMAghG4AAAAAAAxC6AYAAAAAwCCEbgAAAAAADMJEagDwEGKCOmtMTgcAAPIqQjcA4JHABxnW+CADAIAHg+HlAAAAAAAYhNANAAAAAIBBCN0AAAAAABiE0A0AAAAAgEEI3QAAAAAAGITQDQAAAACAQQjdAAAAAAAYhOd0AwCAe8Kzz63x7HMAQGbo6QYAAAAAwCCEbgAAAAAADMLwcgAAgIcEQ/YzYtg+gLyOnm4AAAAAAAxC6AYAAAAAwCCEbgAAAAAADELoBgAAAADAIEykBgAAgHyNCeqsMTkd8GDR0w0AAAAAgEEI3QAAAAAAGITh5QAAAABswpB9awzZR3bo6QYAAAAAwCCEbgAAAAAADELoBgAAAADAINzTDQAAAAB2xn3y1vLTffL0dAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgEEI3AAAAAAAGIXQDAAAAAGAQQjcAAAAAAAYhdAMAAAAAYBBCNwAAAAAABiF0AwAAAABgkIcidM+aNUv+/v5yc3NTgwYNtH379mzX/+KLL1SlShW5ubmpRo0aWrNmzQOqFAAAAACAnLN76F62bJkiIiI0atQo7d69WzVr1lRISIji4+MzXX/r1q3q2LGjXnvtNe3Zs0dt2rRRmzZtdODAgQdcOQAAAAAA2bN76I6KilLPnj3VvXt3VatWTXPmzJGHh4cWLFiQ6foffvihmjdvrnfeeUdVq1bVuHHjVKdOHc2cOfMBVw4AAAAAQPbsGrpTUlK0a9cuBQcHW9ocHBwUHBys2NjYTLeJjY21Wl+SQkJCslwfAAAAAAB7cbLnwf/880+lpaXJx8fHqt3Hx0eHDx/OdJvz589nuv758+czXT85OVnJycmW11evXpUkJSQk3E/pD8SNpER7l/BQyY2fGdfUGtfUGFzX3Mc1zX1c09zHNTUG1zX3cU1zH9c09+WFvHa7RrPZnO16dg3dD8LEiRM1ZsyYDO1+fn52qAb34117F5APcU2NwXXNfVzT3Mc1zX1cU2NwXXMf1zT3cU1zX166pn///bcKFSqU5XK7hu5ixYrJ0dFRFy5csGq/cOGCfH19M93G19fXpvWHDRumiIgIy+v09HRdunRJRYsWlclkus8zAGyXkJAgPz8/nTlzRgULFrR3OUCWeK8iL+B9iryC9yryAt6ntjGbzfr7779VqlSpbNeza+h2cXFR3bp1FRMTozZt2ki6FYpjYmLUp0+fTLdp2LChYmJi1L9/f0vb+vXr1bBhw0zXd3V1laurq1Wbt7d3bpQP3JeCBQvyywx5Au9V5AW8T5FX8F5FXsD7NOey6+G+ze7DyyMiItS1a1cFBQWpfv36mj59upKSktS9e3dJUnh4uEqXLq2JEydKkvr166emTZtq6tSpatmypZYuXaqdO3dq7ty59jwNAAAAAAAysHvobt++vS5evKjIyEidP39etWrV0tq1ay2TpcXFxcnB4X+TrDdq1EhLlizRiBEj9O6776pixYpauXKlqlevbq9TAAAAAAAgU3YP3ZLUp0+fLIeTb9y4MUPbq6++qldffdXgqgBjuLq6atSoURluewAeNrxXkRfwPkVewXsVeQHvU2OYzHeb3xwAAAAAANwTh7uvAgAAAAAA7gWhGwAAAAAAgxC6AQAAAAAwCKEbeEAmTpyoevXqycvLSyVKlFCbNm105MgRe5cFZGvSpEkymUzq37+/vUsBMjh79qw6d+6sokWLyt3dXTVq1NDOnTvtXRZgkZaWppEjRyogIEDu7u4qX768xo0bJ6ZUgr399NNPCg0NValSpWQymbRy5Uqr5WazWZGRkSpZsqTc3d0VHBysY8eO2afYfIDQDTwgmzZtUu/evfXLL79o/fr1Sk1N1fPPP6+kpCR7lwZkaseOHfrkk08UGBho71KADC5fvqzGjRvL2dlZ3333nQ4ePKipU6eqcOHC9i4NsHj//fc1e/ZszZw5U4cOHdL777+vDz74QB999JG9S8MjLikpSTVr1tSsWbMyXf7BBx9oxowZmjNnjrZt2yZPT0+FhIToxo0bD7jS/IHZywE7uXjxokqUKKFNmzbpqaeesnc5gJXExETVqVNHH3/8sd577z3VqlVL06dPt3dZgMXQoUO1ZcsW/fzzz/YuBchSq1at5OPjo08//dTS9vLLL8vd3V3/+te/7FgZ8D8mk0krVqxQmzZtJN3q5S5VqpQGDhyoQYMGSZKuXr0qHx8fRUdHq0OHDnasNm+ipxuwk6tXr0qSihQpYudKgIx69+6tli1bKjg42N6lAJlatWqVgoKC9Oqrr6pEiRKqXbu25s2bZ++yACuNGjVSTEyMjh49Kknat2+fNm/erBdeeMHOlQFZO3nypM6fP2/1N0ChQoXUoEEDxcbG2rGyvMvJ3gUAj6L09HT1799fjRs3VvXq1e1dDmBl6dKl2r17t3bs2GHvUoAs/f7775o9e7YiIiL07rvvaseOHerbt69cXFzUtWtXe5cHSLo1IiMhIUFVqlSRo6Oj0tLSNH78eIWFhdm7NCBL58+flyT5+PhYtfv4+FiWwTaEbsAOevfurQMHDmjz5s32LgWwcubMGfXr10/r16+Xm5ubvcsBspSenq6goCBNmDBBklS7dm0dOHBAc+bMIXTjobF8+XItXrxYS5Ys0eOPP669e/eqf//+KlWqFO9T4BHC8HLgAevTp4++/fZbbdiwQY899pi9ywGs7Nq1S/Hx8apTp46cnJzk5OSkTZs2acaMGXJyclJaWpq9SwQkSSVLllS1atWs2qpWraq4uDg7VQRk9M4772jo0KHq0KGDatSooS5dumjAgAGaOHGivUsDsuTr6ytJunDhglX7hQsXLMtgG0I38ICYzWb16dNHK1as0I8//qiAgAB7lwRk8Oyzz2r//v3au3ev5SsoKEhhYWHau3evHB0d7V0iIElq3LhxhscuHj16VGXLlrVTRUBG165dk4OD9Z/bjo6OSk9Pt1NFwN0FBATI19dXMTExlraEhARt27ZNDRs2tGNleRfDy4EHpHfv3lqyZIn+85//yMvLy3JPTKFCheTu7m7n6oBbvLy8Mswz4OnpqaJFizL/AB4qAwYMUKNGjTRhwgS1a9dO27dv19y5czV37lx7lwZYhIaGavz48SpTpowef/xx7dmzR1FRUerRo4e9S8MjLjExUcePH7e8PnnypPbu3asiRYqoTJky6t+/v9577z1VrFhRAQEBGjlypEqVKmWZ4Ry24ZFhwANiMpkybV+4cKG6dev2YIsBbPD000/zyDA8lL799lsNGzZMx44dU0BAgCIiItSzZ097lwVY/P333xo5cqRWrFih+Ph4lSpVSh07dlRkZKRcXFzsXR4eYRs3blSzZs0ytHft2lXR0dEym80aNWqU5s6dqytXrujJJ5/Uxx9/rEqVKtmh2ryP0A0AAAAAgEG4pxsAAAAAAIMQugEAAAAAMAihGwAAAAAAgxC6AQAAAAAwCKEbAAAAAACDELoBAAAAADAIoRsAAAAAAIMQugEAAAAAMAihGwCQ7/n7+2v69Om5tr9u3bqpTZs2ubY/Sdq4caNMJpOuXLmSq/tFRqdOnZLJZNLevXvvaz+jR49WrVq1cqUmAED+RegGAOQZ3bp1k8lkkslkkouLiypUqKCxY8fq5s2b2W63Y8cO9erVK9fq+PDDDxUdHZ1r+0PuMZlMWrlyZbbr+Pn56dy5c6pevfqDKQoA8EhzsncBAADYonnz5lq4cKGSk5O1Zs0a9e7dW87Ozho2bFiGdVNSUuTi4qLixYvnag2FChXK1f3hwXJ0dJSvr6+9ywAAPCLo6QYA5Cmurq7y9fVV2bJl9eabbyo4OFirVq2S9L9h3+PHj1epUqVUuXJlSRmHl5tMJs2fP19t27aVh4eHKlasaNnHbb/99ptatWqlggULysvLS02aNNGJEyesjnPb008/rT59+qhPnz4qVKiQihUrppEjR8psNlvW+fzzzxUUFCQvLy/5+vqqU6dOio+Pt+ncr1y5ov/7v/+Tj4+P3NzcVL16dX377beW5V999ZUef/xxubq6yt/fX1OnTrXa3t/fX++9957Cw8NVoEABlS1bVqtWrdLFixfVunVrFShQQIGBgdq5c6dlm+joaHl7e2vlypWqWLGi3NzcFBISojNnzljte/bs2SpfvrxcXFxUuXJlff7551bLc3LNDxw4oBdeeEEFChSQj4+PunTpoj///NPqOvft21eDBw9WkSJF5Ovrq9GjR1udnyS1bdtWJpPJ8vqf/jm8/PbQ/piYGAUFBcnDw0ONGjXSkSNHrLabNGmSfHx85OXlpddee003btzIsO/58+eratWqcnNzU5UqVfTxxx9blvXo0UOBgYFKTk6WdOtDodq1ays8PDzTOgEA+QOhGwCQp7m7uyslJcXyOiYmRkeOHNH69eutAuk/jRkzRu3atdOvv/6qFi1aKCwsTJcuXZIknT17Vk899ZRcXV31448/ateuXerRo0e2w9gXLVokJycnbd++XR9++KGioqI0f/58y/LU1FSNGzdO+/bt08qVK3Xq1Cl169Ytx+eZnp6uF154QVu2bNG//vUvHTx4UJMmTZKjo6MkadeuXWrXrp06dOig/fv3a/To0Ro5cmSGYfDTpk1T48aNtWfPHrVs2VJdunRReHi4OnfurN27d6t8+fIKDw+3+sDg2rVrGj9+vD777DNt2bJFV65cUYcOHSzLV6xYoX79+mngwIE6cOCA/u///k/du3fXhg0bcnzNr1y5omeeeUa1a9fWzp07tXbtWl24cEHt2rXLcJ09PT21bds2ffDBBxo7dqzWr18v6dZtBJK0cOFCnTt3zvI6p4YPH66pU6dq586dcnJyUo8ePSzLli9frtGjR2vChAnauXOnSpYsaRWoJWnx4sWKjIzU+PHjdejQIU2YMEEjR47UokWLJEkzZsxQUlKShg4dajnelStXNHPmTJvqBADkMWYAAPKIrl27mlu3bm02m83m9PR08/r1682urq7mQYMGWZb7+PiYk5OTrbYrW7asedq0aZbXkswjRoywvE5MTDRLMn/33Xdms9lsHjZsmDkgIMCckpJy1zrMZrO5adOm5qpVq5rT09MtbUOGDDFXrVo1y3PZsWOHWZL577//NpvNZvOGDRvMksyXL1/OdP1169aZHRwczEeOHMl0eadOnczPPfecVds777xjrlatmuV12bJlzZ07d7a8PnfunFmSeeTIkZa22NhYsyTzuXPnzGaz2bxw4UKzJPMvv/xiWefQoUNmSeZt27aZzWazuVGjRuaePXtaHfvVV181t2jRwvL6btd83Lhx5ueff95qH2fOnDFLspxz06ZNzU8++aTVOvXq1TMPGTLE6jgrVqzI9BrddvLkSbMk8549e8xm8/+u/Q8//GBZZ/Xq1WZJ5uvXr5vNZrO5YcOG5rfeestqPw0aNDDXrFnT8rp8+fLmJUuWWK0zbtw4c8OGDS2vt27danZ2djaPHDnS7OTkZP7555+zrRUAkPfR0w0AyFO+/fZbFShQQG5ubnrhhRfUvn17qyHGNWrUkIuLy133ExgYaPne09NTBQsWtAz33rt3r5o0aSJnZ+cc1/XEE0/IZDJZXjds2FDHjh1TWlqapFs90aGhoSpTpoy8vLzUtGlTSVJcXFyO9r9371499thjqlSpUqbLDx06pMaNG1u1NW7c2KoGyfq8fXx8JN26Zv9su3Pou5OTk+rVq2d5XaVKFXl7e+vQoUPZHvv28syO/c9rvm/fPm3YsEEFChSwfFWpUkWSLMP6/7kPSSpZsqTNw/Szcue+S5YsKel/1+HQoUNq0KCB1foNGza0fJ+UlKQTJ07otddeszqH9957z6r+hg0batCgQRo3bpwGDhyoJ598MldqBwA8vJhIDQCQpzRr1kyzZ8+Wi4uLSpUqJScn6//KPD09c7SffwZqk8mk9PR0SbeGrOempKQkhYSEKCQkRIsXL1bx4sUVFxenkJAQq6Hx2cmtmu4879sfEmTWdvta5KbsrnliYqJCQ0P1/vvvZ9judgC+2z5ysz5br0NiYqIkad68eRnC+e1bAG7vb8uWLXJ0dNTx48fvt2QAQB5ATzcAIE/x9PRUhQoVVKZMmQyBO7cEBgbq559/Vmpqao632bZtm9XrX375RRUrVpSjo6MOHz6sv/76S5MmTVKTJk1UpUoVm3tnAwMD9d///ldHjx7NdHnVqlW1ZcsWq7YtW7aoUqVKVqHvXty8edNqcrUjR47oypUrqlq1arbHrlatWo6PUadOHf3222/y9/dXhQoVrL5y+kGKdCs439mzn1uqVq2a6c/4Nh8fH5UqVUq///57hvoDAgIs602ePFmHDx/Wpk2btHbtWi1cuDDXawUAPFwI3QAA/EOfPn2UkJCgDh06aOfOnTp27Jg+//zzDLNZ3ykuLk4RERE6cuSI/v3vf+ujjz5Sv379JEllypSRi4uLPvroI/3+++9atWqVxo0bZ1NNTZs21VNPPaWXX35Z69ev18mTJ/Xdd99p7dq1kqSBAwcqJiZG48aN09GjR7Vo0SLNnDlTgwYNuvcL8f85Ozvr7bff1rZt27Rr1y5169ZNTzzxhOrXry9JeueddxQdHa3Zs2fr2LFjioqK0tdff23TsXv37q1Lly6pY8eO2rFjh06cOKF169ape/fuNoVof39/xcTE6Pz587p8+bLN55qVfv36acGCBVq4cKGOHj2qUaNG6bfffrNaZ8yYMZo4caJmzJiho0ePav/+/Vq4cKGioqIkSXv27FFkZKTmz5+vxo0bKyoqSv369dPvv/+ea3UCAB4+hG4AAP6haNGi+vHHH5WYmKimTZuqbt26mjdvXrb3eIeHh+v69euqX7++evfurX79+qlXr16SpOLFiys6OlpffPGFqlWrpkmTJmnKlCk21/XVV1+pXr166tixo6pVq6bBgwdbAmmdOnW0fPlyLV26VNWrV1dkZKTGjh1r0wzpWfHw8NCQIUPUqVMnNW7cWAUKFNCyZcssy9u0aaMPP/xQU6ZM0eOPP65PPvlECxcu1NNPP53jY5QqVUpbtmxRWlqann/+edWoUUP9+/eXt7e3HBxy/ufK1KlTtX79evn5+al27dq2nGa22rdvr5EjR2rw4MGqW7euTp8+rTfffNNqnddff13z58/XwoULVaNGDTVt2lTR0dEKCAjQjRs31LlzZ3Xr1k2hoaGSpF69eqlZs2bq0qWLIb3zAICHg8lsvuOZIAAAwGZPP/20atWqZfUs8PwiOjpa/fv315UrV+xdCgAAeRI93QAAAAAAGITQDQAAAACAQRheDgAAAACAQejpBgAAAADAIIRuAAAAAAAMQugGAAAAAMAghG4AAAAAAAxC6AYAAAAAwCCEbgAAAAAADELoBgAAAADAIIRuAAAAAAAMQugGAAAAAMAg/w+FipjEQOGkIwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "plt.bar(range(1, len(explained_variance) + 1), explained_variance, alpha=0.5, align='center', label='Individual explained variance')\n",
    "plt.step(range(1, len(cumulative_explained_variance) + 1), cumulative_explained_variance, where='mid', label='Cumulative explained variance')\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Principal component index')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "149ec9c1-ec58-4cd5-bfe5-ae9aeeb09986",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "As we conclude our machine learning class, we reflect on the powerful techniques we’ve explored and the insights we’ve gained. Principal Component Analysis (PCA) has shown us how to simplify complexity in high-dimensional data, while K-means clustering has provided a method for uncovering hidden patterns and structures. Linear Regression has been our go-to for predicting numerical outcomes with a linear approach, and Support Vector Machines (SVM) have offered a versatile framework for both classification and regression tasks, capable of handling linear and non-linear boundaries.\r\n",
    "\r\n",
    "Each method has its unique strengths: PCA for dimensionality reduction, K-means for partitioning, Linear Regression for its simplicity and interpretability, and SVM for its effectiveness in higher-dimensional spaces. Together, these techniques form a robust toolkit for any aspiring data scientist, empowering us to turn data into meaningful stories and make predictions with confidence.\r\n",
    "\r\n",
    "As we move forward, let’s carry the knowledge that machine learning is not just about algorithms and models, but about the thoughtful application of these tools to solve real-world problems. It’s the art of discerning which technique to apply and how to interpret the results that truly makes a difference. So, let’s continue to learn, experiment, and innovate, using PCA, K-means, Linear Regression, and SVM as our guides in the ever-evolving landscape of machine learning."
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