Chapter7Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7 Cluster Analysis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1 Overview \n",
    "\n",
    "Cluster analysis is one of the most-widely used techniques in analysis of complicated data, such as the genomics data. Cluster analysis aims to detecting homogeneous subgroups among the observations or the features. The identities of these subgroups are unknown, but can often lead to meaningful interpretation after linked with additional information. \n",
    "\n",
    "It is important to note that, unlike in classification, there are no labels in cluster analysis. Cluster analysis is one of <span style=\"color:blue\"> unsupervised analyses </span>, where classification is a supervised analyses. In a supervised analysis, features and the <span style=\"color:red\">outcome </span> are both observed. However, in an unsupervised analysis, one only observes <span style=\"color:blue\">features </span>. Sometimes unsupervised analysis can be used as a <span style=\"color:blue\">pre-supervised </span> step.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Briefly, cluster analysis aims to grouping objects into meaningful subsets, or <span style=\"color:red\">clusters</span>, so that objects within each cluster are more __similar__ than objects across cluster.\n",
    "\n",
    "We can cluster <span style=\"color:red\">observations</span> or <span style=\"color:blue\">features</span>.\n",
    "- <span style=\"color:red\">observations</span>: clustering cancer samples to find cancer sub-types\n",
    "- <span style=\"color:blue\">features</span>: clustering genes based on similar functions\n",
    "\n",
    "Before conducting a cluster analysis, there are two questions that need to be answered. \n",
    "- What is a **meaningful** cluster?\n",
    "- How to measure **similarity**?\n",
    "\t\n",
    "    \n",
    "\t\t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2 Defining meaningful clusters\n",
    "\n",
    "The best practice to define meaningful clusters is always to rely on domain knowledge, such as prior knowledge, known patterns. In the absence of such knowledge, the definition of \"meaningful\" can be quite subjective. Consider the following examples. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Example 1.** \n",
    "\n",
    "<img src=\"../Figures/Ch7/clusterdef.png\" style=\"width:80%\"/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 2.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1);\n",
    "n=200;\n",
    "x1=runif(n);y1= sin(pi*x1)+rnorm(n)*0.15;\n",
    "x2=runif(n)+0.5;y2=0.5-sin(pi*(x2-0.5))+rnorm(n)*0.15;\n",
    "data.mat=rbind(cbind(x1,y1),cbind(x2,y2));\n",
    "#par(mfrow=c(1,2))\n",
    "plot(data.mat,pch=16,xlab=\"x\",ylab=\"y\",xlim=c(0,1.5),ylim=c(-1,1.2))\n",
    "#plot(y1~x1,pch=16,xlab=\"x\",ylab=\"y\",col=\"red\",xlim=c(0,1.5),ylim=c(-1,1.2))\n",
    "#points(y2~x2,col=\"blue\",pch=16)\n",
    "#par(mfrow=c(1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example 3.** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairs(iris[,-5],pch=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.3 Similarity and dissimilarity measures\n",
    "\n",
    "For simplicity, we consider the case when all features are numeric. The data matrix $X$ is an $n\\times p$ matrix with $n$ observations and $p$ features. \n",
    "\n",
    "Suppose that we would like to cluster the $n$ observations.  Then, the similarity/dissimilarity measures can be recorded in an $n \\times n$ matrix. \n",
    "\n",
    "- <span style=\"color:blue\">Similarity measure.</span> A numerical measure $s(i, j)$ that indicates how <span style=\"color:red\">similar</span> two objects are (<span style=\"color:red\">high $s \\equiv$ high similarity</span>). Generally normalized to be in $[0,1]$. We know that <span style=\"color:red\">$s(i, j) \\ge 0$</span> and <span style=\"color:red\">$s(i, j) = s(j, i)$ </span>\n",
    "    \n",
    "    \n",
    "- <span style=\"color:blue\">Dissimilarity measure.</span> A numerical measure $d(i, j)$ that indicates how <span style=\"color:red\">different</span> two objects are (<span style=\"color:red\">lower $d \\equiv$ high similarity</span>). Any **distance** naturally defines a dissimilarity measure. We know that <span style=\"color:red\">$d(i, j) \\ge 0$</span> and <span style=\"color:red\">$d(i, j) = d(j, i)$</span>.\n",
    "    \n",
    "Note that we can often find a corresponding dissimilarity measure for each similarity measure, and _vice versa_. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.3.1 Common Dissimilarity Measures\n",
    "\t\n",
    "**Euclidean** distance: <span style=\"color:red\">sum of squared difference between feature values</span>\n",
    "$$\n",
    "d_E(i,j)= \\left[ \\sum_{l=1}^p (X_{i,l}-X_{j,l})^2  \\right]^{1/2}\n",
    "$$\n",
    "**Manhattan** distance:\n",
    "\t\t<span style=\"color:green\">sum of absolute difference between feature values</span>\n",
    "$$\n",
    "d_M(i,j)= \\sum_{l=1}^p |X_{i,l}-X_{j,l}|\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "X<-iris[,-5]\n",
    "d.E<-dist(X,method=\"euclidean\")\n",
    "d.M<-dist(X,method=\"manhattan\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.3.2 Common Similarity Measures\n",
    "\n",
    "The correlation coefficient is a popular choice to measure the similarity between observations.   \n",
    "\t\n",
    "- <span style=\"color:red\">Pearson correlation:</span> This is the \"usual\" correlation coefficient, and measures the **linear** association between $X_i$ and $X_j$. \n",
    "\t\t\t\n",
    "- <span style=\"color:red\">Spearman correlation.</span> This is essentially the Pearson correlation applied to **ranked** observations. The Spearman correlation corresponds to an **increasing monotonic trend** between $X_i$ and $X_j$ (more appropriate for non-Gaussian observations). \n",
    "    \n",
    "- <span style=\"color:red\">Kendall's $\\tau$.</span> This correlation coefficient uses directly rankings among pairs of observations. \n",
    "\t\t\n",
    "Among the three correlation coefficients, the Pearson correlation is the most commonly used one for convenience. However, it does not always reflect the \"similarity\" among observations. For instance, the following example ([link](https://en.wikipedia.org/wiki/Correlation_and_dependence)) contains strikingly different patterns with Pearson correlations all equal to 0.816.\n",
    "\t\n",
    "<img src=\"../Figures/Ch7/corrplots.png\" style=\"width:80%\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4 Common clustering methods\n",
    "\t\n",
    "    \n",
    "    \n",
    "\t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 7.4.1 Hierarchical Clustering \n",
    "\t\n",
    "Hierarchical clustering gives sequence of solutions organized in a <span style=\"color:red\">hierarchical tree structure</span>, called the <span style=\"color:red\">**dendrogram**</span>\n",
    "    \n",
    "**Bottom-Up** or Agglomerative: Start from $n$ individual clusters, and group them together into using a measure of similarity.\n",
    "- Start from $n$ individual clusters\n",
    "- At each step, <span style=\"color:red\">merge the closest pair of clusters</span> until all objects form a single cluster\n",
    "        \n",
    "**Top-Down** or Divisive: Start from one cluster containing all objects, and break them down using a measure of distance\n",
    "- Start from 1 cluster\n",
    "- At each step, <span style=\"color:red\">split the most heterogenous cluster</span> until every cluster has only one member\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "-- \u001b[1mAttaching packages\u001b[22m ------------------------------------------------------------------------------- tidyverse 1.3.0 --\n",
      "\n",
      "\u001b[32mv\u001b[39m \u001b[34mggplot2\u001b[39m 3.3.2     \u001b[32mv\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.4\n",
      "\u001b[32mv\u001b[39m \u001b[34mtibble \u001b[39m 3.0.4     \u001b[32mv\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.2\n",
      "\u001b[32mv\u001b[39m \u001b[34mtidyr  \u001b[39m 1.1.2     \u001b[32mv\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n",
      "\u001b[32mv\u001b[39m \u001b[34mreadr  \u001b[39m 1.4.0     \u001b[32mv\u001b[39m \u001b[34mforcats\u001b[39m 0.5.0\n",
      "\n",
      "-- \u001b[1mConflicts\u001b[22m ---------------------------------------------------------------------------------- tidyverse_conflicts() --\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'merge'</li><li>'height'</li><li>'order'</li><li>'labels'</li><li>'method'</li><li>'call'</li><li>'dist.method'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'merge'\n",
       "\\item 'height'\n",
       "\\item 'order'\n",
       "\\item 'labels'\n",
       "\\item 'method'\n",
       "\\item 'call'\n",
       "\\item 'dist.method'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'merge'\n",
       "2. 'height'\n",
       "3. 'order'\n",
       "4. 'labels'\n",
       "5. 'method'\n",
       "6. 'call'\n",
       "7. 'dist.method'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"merge\"       \"height\"      \"order\"       \"labels\"      \"method\"     \n",
       "[6] \"call\"        \"dist.method\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAABiVBMVEUAAAAKCgoLCwsMDAwP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\nt0bFbjIQCQAPQCQAPACRAPDA3wOB1b4QTIIerAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Cluster Dendrogram\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "iris.hcl <- iris[,-5] %>%  dist() %>% hclust(method = \"average\")\n",
    "\n",
    "names(iris.hcl)\n",
    "plot(iris.hcl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAQlBMVEUAAAAAujgzMzNNTU1h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\n/D9xtHNDrdK8wgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAASFBMVEUAAAAAsPYAv30zMzNN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\nveWRHc0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "iris %>% mutate(cluster = cutree(iris.hcl,3)) %>%\n",
    "  ggplot(aes(x=Sepal.Length, y=Sepal.Width, color = as.factor(cluster))) + \n",
    "  geom_point()\n",
    "\n",
    "\n",
    "iris %>% mutate(cluster = cutree(iris.hcl,5)) %>%\n",
    "  ggplot(aes(x=Sepal.Length, y=Sepal.Width, color = as.factor(cluster))) + \n",
    "  geom_point()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.4.2 K-means Clustering\n",
    "\n",
    "The basic idea of K-means clustering is, given a number of clusters $K$, find the set of cluster centers, and cluster assignments that minimize average distance between each obs and its center. This is the most popular partition-based method. \n",
    "\n",
    "- Motivated by a simple and intuitive mathematical problem\n",
    "- <span style=\"color:red\"> Uses Euclidean distance</span> between points and centers\n",
    "- Computationally efficient, and can be applied to datasets with a large number of samples (variables)\n",
    "- <span style=\"color:red\">No hierarchy among clusters</span>, if $K$ is changed, the cluster memberships will also change\n",
    "\t\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'cluster'</li><li>'centers'</li><li>'totss'</li><li>'withinss'</li><li>'tot.withinss'</li><li>'betweenss'</li><li>'size'</li><li>'iter'</li><li>'ifault'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'cluster'\n",
       "\\item 'centers'\n",
       "\\item 'totss'\n",
       "\\item 'withinss'\n",
       "\\item 'tot.withinss'\n",
       "\\item 'betweenss'\n",
       "\\item 'size'\n",
       "\\item 'iter'\n",
       "\\item 'ifault'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'cluster'\n",
       "2. 'centers'\n",
       "3. 'totss'\n",
       "4. 'withinss'\n",
       "5. 'tot.withinss'\n",
       "6. 'betweenss'\n",
       "7. 'size'\n",
       "8. 'iter'\n",
       "9. 'ifault'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"cluster\"      \"centers\"      \"totss\"        \"withinss\"     \"tot.withinss\"\n",
       "[6] \"betweenss\"    \"size\"         \"iter\"         \"ifault\"      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAQlBMVEUAAAAAujgzMzNNTU1h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\n/D9xtHNDrdK8wgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris.k3 <- iris[,-5] %>% kmeans(3)\n",
    " \n",
    "names(iris.k3)\n",
    "\n",
    "iris %>% mutate(cluster = iris.k3$cluster) %>%\n",
    "  ggplot(aes(x=Sepal.Length, y=Sepal.Width, color = as.factor(cluster))) + \n",
    "  geom_point()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAASFBMVEUAAAAAsPYAv30zMzNN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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "iris.k5 <- iris[,-5] %>%  kmeans(5)\n",
    " \n",
    "iris %>% mutate(cluster = iris.k5$cluster) %>%\n",
    "  ggplot(aes(x=Sepal.Length, y=Sepal.Width, color = as.factor(cluster))) + \n",
    "  geom_point()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.4.3 Spectral clustering \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAABNTU1h0E9oaGh8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\nggAhQYCQIEBIECAkCBASBPwHNuw4IC6trGUAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"kernlab\")\n",
    "iris.spec3=specc(iris[,-5],centers=3)\n",
    "plot(iris[,c(\"Sepal.Length\",\"Sepal.Width\")],col=iris.spec3,pch=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spectral clustering works very well in Example 2, compared to K-means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data in Example 2\n",
    "set.seed(1);\n",
    "n=200;\n",
    "x1=runif(n);y1= sin(pi*x1)+rnorm(n)*0.15;\n",
    "x2=runif(n)+0.5;y2=0.5-sin(pi*(x2-0.5))+rnorm(n)*0.15;\n",
    "data.mat=rbind(cbind(x1,y1),cbind(x2,y2));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nvSdUbu0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Spectral clustering: \n",
    "ex2.spec2=specc(data.mat,centers=2)\n",
    "plot(data.mat,col=ex2.spec2,pch=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnfU2vh4eHp6enw8PD///9O34MyAAAACXBIWXMAABJ0\nAAASdAHeZh94AAAgAElEQVR4nO2d2WLjKBAA5STrZDJO4v//2s04h3Vw00ADVQ+7jg66kboM\nkmzPcgWAbJbWCQCMACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAA\niAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBI\nAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQg\nACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIg\nEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIB\nCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAA\niAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgQAWRFoDO\nSKhyeXEahACQBJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQ\nAJEABEAkAAEQCUAARAIQAJEABEAkYZK+dAzdg0iiJH9/HzoHkURBpFlBJEkyflIG+gaRJEGk\naUEkSRBpWhBJFDyaFUQSBZFmBZGEQaM5QSQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAE\nQCQAARAJQABEAhAAkQAEQKR68HnWgUGkWvANi6FBJGGsriDS0CCSKHZb+Bb62CCSKIg0K4gk\nicMWRBobRJLkbsvRGDwaGkSSZNliWtcoMygMIoniEInnSEODSKK4hiQYGURKxnp3jhsLE4JI\nibhUQaT5QKREnKrg0XQgUhruQQeRpgOR0vDN3mwPZYsmBe1ApDQSLoMYpkYGkRKJ1wKRRgaR\nEkkdkDBpTBApmUgnEGloEKkWiDQ0iFQNPBoZRKoGIo0MIlUEjcYFkQAEQCQAARAJQABEAhAA\nkQAEQCQAARApk+gPrhbLBFqCSFnEPWTlkey4IFIWiARfIFIOcR9EDd4a2foDkXIoIhLjVo8g\nUg6IBN8gUhYFrpH43lKXIFIWiARfIFIm4s+REKlLEEkdeNQjiKQOROoRRFIIGvUHIrUlxhn8\nUgwitSThKVThjCARRGoJIg0DIjUk5k43d8V1g0gNQaRxQKSGINI4IFIljApwjTQMiFSFvQVf\nr6MGGURSDSJVYWvBsiGmkTLZQT6IVIOdNGkeWRoWSA/yQaQabK3ZDki2vgY4wmxPD4hUg3iR\nghxBJD0gUhXsM7sMkWRmhyACIlkykC1Ph0iu7d1JIJIiEMkYX75AV80h0oAgkjF+0QL1ahTq\niGkbvGoDIpnCb8o4pjTDtg0fbWLbYYhqBSKZwq9EiinN0G3924VO2gzjESI1AZFM4QuL5B+5\nEoXgqqkZVUX6+/x0O81P57+lQshw8KjyB7RTW0KkZlQU6eNhufNYJIQUKkUKm+khUhsqinRe\nTn/ebq/eX0/LuUQIOZb7nQYdIoU1jUetqCjSaXn7ff22nEqEKEBMacqV8bElRNJNRZF2dVEi\nRAGUiBQ82qFRGxiRvMSUplwZHy+QGGw0U/ca6fX99qqDayRtOEXCr/bUvP39uNx5+CgSohui\na9/ukW0NetWk7nOk8+050unpWflzpEQOtwccG8ZO02JFYiZYFz7ZkIahRrel6yzkn5W3DSJu\nZTja2q9EpLog0lVqnrUtaPclzYH0HM1NhDcMIiCS1Dxra4WrkBNECtEyYCkUo5VIip4jOSve\nuMxYpcEimTxK/HWG5XtqeFyHSJXRI1LMG7Qk1pjON3qnSO6eJIhk3srZAB7VhamdlEhmQVwB\nhUSyjpyIVBFE8rylmz7wZt4j2I+fVfEeLYZF1n3RqCaI5Lj+iBPJoJI7YLxI5kChHYWCIFKS\nSJa3+9D6/lm7BD1HOjaJSOpApKutlE1l6i3dEvWNRx2ASFaSRArfJjoRRNJMRZGW8POvpDhM\nWforN2hmF2XAZvuIwwj1qCjSS3ciedl1Y3Ff+uxdiAnzsz0SKaXm1O7t5P7JE4EQVTFPuIzr\nNktMUzV/qE0riKSNqtdIb+6v80mEqImQSDFWmDRa74tdrah7s+Fl9W3zQiHqYfZhNwMzbb19\nmSbSfsnhNdSFu3bJxIi0GUh+Xy0b/OEQSS+IlEyESBtfDK/89b/bxZiEwV7pPoMNREpnV9Qm\nddavf5YsFoJihYsU0iqIgUjpmMxJFykk1PG2eoBI2FQDRPLiKMSjRstxYnVY9/M6TSTzGtvr\noNYhH0TyEFaIrpo9rFqPFT9GhbbvzA+R2oFIHoIK0Vm0hjXL5paEucHgNNaLl/WAiEkVQSQ3\nYYXorllHE9al++3jdUCkqiCSG0GRooMeFoa3cMhJzxEdFERyE1iInpI122X7U6r4l/V1GJQF\nkTyEFWLse/9u0+2fgqMIA1ItEMlDaCH+vP1Ht7ocHrOGVn9ANDSqBSJ5KVCId1WMFzIxs8nA\nOFAYRGpBokibZYikCkRqwWJhvYFtp30TQXFEswcDiNQE54Dk2WfzV+BnXaE0iNSEBJG2W8Xt\nJJY32ECkRizbTwn5q31tTvAoVuRWCRhApLaEDxmJIkEdEKk1wTKYPCqaGUSASN1gEKl1SvAL\nIgXRvmiNdxoa5wR3ECkAU9nWLuNNDqs/0EkHiBTAUaTqI8J2EPp9zcikBUTyc5xJ1Z9a7XNY\ntnfPoTWI5MdQxNVNMkfkYkkNiOTHLVKlMjYag0hqQKQArB4ZvkkkH9qUwz6V8HagDIgUwKZa\nNx5Zfw2rTGD3BoHtQAkQKQijRusPna7WCURZLXC3iEhaQKQ4FgvXmHmWs2lTMPde4UknZgZ+\nEMldi7t1No/aiRTRMiIVBJFcNXZY5/Aot1wNuyNSPyCSmEh5VyK7trbL0po8NJTbDNiZXiRX\nsdpre/vzJbt1P3+k5SEvEgNSBRApTSTrc53dZtFpiF8joVEVEClOpMBPucmIJDIlQ6MqTC9S\n3DXSbqWnzYjyNe8R0IoviCUV1BIGkZJF8rd5vwmRnIZfI0+CxUY62IBIUc+Rwlv8LdXAok2p\n7ZCBD5HqgEhFWFVqcNEmaxRkknHPqHjgApGKcBiQChQtImkCkQqx3C+QyhTtEiiSYahDJHkQ\nqTBVRErcVzqlmUGk0jSe2VXNaWIQqTDlZlEpGv1ujUfCIFJhyr35J2n0vQdDkjSIFERy0RW9\nro9tFpHKgUgBZJSdphtk91w0ZTUIiBQAIoEPRPKTVXaSFZvZDiIVBJH8KBEpvyWukcqBSH4y\n378FxyNEUgsiBaCi7ESmY/fdm/dnMBApgF5Fap7zRCCSnVUdGkqydpVGi6RC/2lAJBvuOmxQ\npXEhuTFXF0SyMYpIGo7lBCCSLQVnHbap0vh5HSLVApF2kXe/TKdKpAgWTKrLpCJZymtVeQOJ\npDbJkZhSJGt9rVeou0aKA5HqgkjH5SG//qO+RBmS6jKjSNb62q1wV6D6+kSkmiBSyIpOGa0/\nmkEkw5rARsQTEwePqjGjSJb6ipkJJVVo/ZJGpGog0nZZ+HgUW6FtihqNKjGlSKb6iqrzlIsP\nRoehmVSkY8QoNRJEan7hj8RFQaTviIOLxHhYGET6jhhX58kzO0QaFET6CRlVacpuNtjbXUI+\nOQj5INJPyMhCiy7KcpVsb/l3DSKVBpHuQb8rrmyAMu0iUmsQaRO3x2qzS7Ja02XPegKRNnF7\nLDdE0gAircNuSrKXugsSqZ/udAoircOuCq+jt/CAayQoDSKtwyISJIJIm7h7j6r/4Jb0jmhU\nCUTaxN1fnFt/I6Vc8PS9C2wKoSDSLvIe6yalQpfel+leERBpH/q7zqpfeGRNJiVFOqxEuwAQ\naRc5dEASL66cdiP2NW66+vOwlhEsCETaRb7XmaV6RhFp2S8y/GFcACYQaRfZW5KlRMqp2CSR\nfrde/3VoqVh3BwOR9qG9ZVOqsHLajdj3INLmT0RKBJH2oZuJlHNVnyaSYRBCpEQQ6RjcWzQa\nyyoiJ5dIXCMlMo1I1MId89zO8IdxAZiYRKToahi7dLaH4ziZO2xdMbdOQSSBzftheyW0Xwzp\nzCFS7BXzoCLtbyq0zmckECl/827YizRcBxuCSPmbF6FA9HW3UjqIeA7mECmybtqLlBPfut+q\nWwk9bH1IlDO7SObSaF40AQlYVjv2RKSCTCKSpe5sxVG9aHbB/HXuemew7niY2Xm6uF7ffpTW\nzTQimeNYa6O2Rts00kVy7rlaZdxqu2C7ySQiXS6Xw6sgphZJS3HEi2TdwLPn7wrDVvtFE4p0\n+WLzKhBE2ldH/VoxZBE4IB03Ca/3Zf+dq92O+5Ym8AiRUsOs2C6qE3+fxmGRf5fDRuahxtmK\nOQsNR6Yylx9Wr0KZWqTjd3O0iOQdGMNFcvQoXKRlP3wNCSIlx9nXo6U666SRsItpv6ORlsY9\nXb//OcFgdAORMiJ1KpLjMsmymXfVzx+7Y5GaX49wjZQRSoFIabOmQiJtj0Z4oBH41Sd6QGog\n0svDsjy9Fg0RxbZIeiqZoFxdFuzXfI9H84r0/fQoXqOqIn2diMevc3IuEiKFwUUKvtmwWbT6\nGNFcIt1I8Ki6SOfl/HG9vp+XlxIh0tiWSE8FE5KrU4LDCpNIXb27CBB/p+FaX6TT8vHv9cfy\nUCIEmNiMt/5tv60xKjUFXYh0v7ItEQJcxFxTmZ4jzUIXIv33I9KpRAhwkSHSXKi/Rnp6fnld\n/ny+/Di77zZMePIsCBZyqBk/W0zrkX6RVlevp48SIVLQXCuitRw7xMwrUvR3KK51nyO9vb28\nPD3dbjmcnR7VEUn3dbR8dkeRfE3/5CATf2ym/WTDsqF8vDiWEuntGrO0vV2k9PjoY3iRbFVQ\npFTzOBZ5fZEMg5aWw1OR+Jnd6CJZ62BXqQoqZZ1IqewMiuwaN8s21xQv5V5DM5EqPUcaQ6SS\n8ayfEDIlouAwVaBzkUqcMHt76gpkkwoiNSTpeezgUztHAWgrkG0qv68L5mbq+uGATGgSIhna\nCRRJKFwOFpHKR3QvRKRAxhbJWZDKquM4FNQI6cniZyNdh6ow+q+R/j4/3c7G0/lvqRD7htyn\nX1N1aMnFnIOW7GqgXaSPh9UU4bFICFNT7keOmopDUy57ZhJJ+3Ok83L683Z79f56aveh1blK\nQg6OmZOKIp2Wt9/Xb+2+RjG9SD8XPa3z6ITA0amiSLtL2BIh1u1b2pjqstnAZLfgcgm+Xhpz\nRHIUyuxVhEhRaBTp8xrp9f32SvYaKegm7n7VrGW0LJgUQfgzpZq3vx9Xp/BB6ot9ppJwFsrc\nVYRIUegU6fr3fHuOdHp6lnuOhEhR7EWKOw7THTWlIhUIYdQiSKTMFHtl41HcoZjxwGm8RioS\nwuwMA5IVRIoCkRDJxn1KF3csJj1y+p4jlQlhObnW8z1pORhBJDlGFUlwh3HxqLFEXHlOT/ci\nRd9KohruuI7Fcd30R841yxtApPjWZy6GDSEi3ddPLpL7vsOMIn3HmLckVvivJdfyTH3MEMkY\nYe53Vz9GkWbG82wWkcDIgklbEMkYgALxgUhbEMkYgALxgUg7uEYyBaBA/CzRHyIamuFEEjmv\nFEgYHKcVQz1HEjqzFEho7+c+SsHMKtLsBcIbiTC9iTTexU2bvox2FJuDSG1p1JvRDmN7EKlt\nNSHSIPQmknTlNa6nVgWNSBGM+Q3ZKUQqnxEehRL4ZfPuRIqrMt+2rd+ZjfFrpIRIoYwrUkQz\n3mppLdImxdX/K6SERkGE/iDXiCL9lkhXIv2+ap4TrJhXpENphpiUES+XwziESJpApF5E2iZy\n/5yohqRgXpFWZRhWkUoq9ph364zgxqw3G9b29FSRXpG0dCTwBxOHAZH6Esl4/868tiXBP+E7\nEGM+kPXvuy45e+1pqMoNblWai/RdTSOL5O+XY4thRFq74y+55nVp4jsh63DUMOMff0IvvTvE\n37EZfrMhcBgyb6+KY2bLgkgVQKTbDnFl1rouHagU6XKgTR4F8ffMvcUYIsXWmV6Rjpk18mhT\nMPcaGtUjRPraHpFk2ZWMT6QB1EKk2/axhabVI7dI9dLYl4xzXjfGKGXqxfbvCa+RvEWnViQd\n/wjEQZkpRbK8m5h3H1EkQ+UdC1GnRruZ3LJaUjMJgzUX6z07/6SoEywdc2yxYhCRNmIcKk/v\n+GNiWX9w1fJkqTCXHfvF5o3r5lgG0ygctOMwIq12tl1mZKdVjSbXRWv2Jl22S83btkhUlk1H\nEGlfg42LMoH97K46ZpHs9+zG8GjrDiIhkgCuIWm72TgieXvrYECRDjO51jWZQHuRrjuX7suO\nW4zwHOkfu+4iUt83G65KPDLevDNuUDmtYpimsqH79iVSaGEth5vfrWsyhvXETotI7vWV8yqG\np78uMkRalmJn3NxYRqCONDI9k23GqrAM1dWfSJ5cMzqUIdJLRyL1hIrBaMWPRscC602kgGxb\niHR9Oz3G7x0XYrMwusD0FGMM2kS6YS6wvjwKSzexP1nXSG/LOSVmTIj1wogCW5Z+//lTjSJZ\nxp6+RCo6gObdbHhZ3uRSMYdYLQwuMDVX62koTNxag/1opFqkUsRcIxlKrtzFWxXa5O0ssN6u\nhowg0s9SQ4E5lvUtUuWYvhIbYEAqOxPNFOnh+V0sFUuIzXL3770tm+8ddCpSs/EoXqTeRqmw\nfNN6lCnS5xkv4VLsN123PwfZtUdtRAqY9WxWfv2hWCRLWkEaJfUpU6SPP/+VcClPpK5vNrTJ\nO+7y4bKjcHLxZOTVSKR//H1+kHYpRaTjyy6fIyGSAOl5JfdJ5mbD2+nzzL/ENxURwrblcRj6\nXiyXTVUajaQ5HqkTKSOxtiK9Pt5OvdznHLJF6pg2vRhxQOpMpI/nz+Ho4fXj06an+MaCQri3\njfrRb/1YulG8Z+HFM7JIza6R/v672XD++nyD3KlO/YT3CCK5HjG3yMbAvdiOJadCrAzDG4n0\n7zbDy8fPilN8Y/4QMbupKTVpVIpkKDclY1RWGmk75j5HenpNCBoVAhRe/ykXKW9gTNo39zlS\n/O6xIUCfSLYhSe9l0wZngi3v2omjpWAqYzUFkQTxpIhIveNyRZdHI4uU2gVEUkOiSE3KVv01\nkh2PKYjUO57pm12jFpWLSHsQSQtp10HNKtcWVKNGm5x8pnCN1DlJInVxUdKY/RHiZsPgZAxI\niOQgUqQ2z5EKgUiBXC6o5OF4gIocMERSwI8+CTe4L6jkAZFmIesZESL5OBweo1nZYRCpOZkP\nWzHJg2VA+l0ic/AQqTUJd+t2px2RnCDSHESLdDjxiOTBebSEjt6IIin6UFoA+SL18HkCPSBS\n6L66Pt/pJ80jw5tsieSG43D4EMm273wi6fxgjk6sImW2O4JImyrU9tWdEGLvNCBSOtaZ3fQj\n0s6bHkWKg2ukLGwzO0RCpDYidaquVaS83nQv0kGc4UXS8Ryp41HQ+C6U2xlE6h9EyuFyEVFp\nXJHmMamFSE3kLQQifW2702YqkS4/v3faaEAaTaT07iBSx/ycfESyEZggIn1tvZVmGo+cv8Fd\nL7ZewnNEJNPOs4jUdFTQJJItj4gcuUYy7j6DRh6Ryhb594SyYIRwrAch5o0GkSbGUShlxwtN\no5GQSNnvPIikHccJttfJRCLZdak69UUk3ThLQei9ODEnJSb5x+V/q4pni0i68ZSs/QIJkXYf\nWiicLyKpJrEGZhLJ9V6DSOVD9EFqDZStHFUeRYgUO7DHgEiqQaQQrLmEiSTSHUTSzfYkR5zu\nsoWuSSMXiARfrE+ytoFAOZf7pxBDPJr9i33DsxmPECmUn4N1+b75jUjwjcwJn4XdsXIcNkSa\nDESKIOZgcY00F5vaUOmToqQQqVaIDrmfcJVDk6qk4oZvgbQRqR8QKYLa2SBST9zndaqK9oay\npIYW6e/z0+3Lq0/nv6VCTIG/ZhvUszKRah+DiiJ9PCx3HtNCTPLdVw++mm1S0epEqktFkc7L\n6c/b7dX762k5J4SY5tcYfHhKtk1F9+WRdKYVRTotb7+v35ZTQghE+iZoQGo0JNUNmoh8rhVF\n2hjg1sG8cqJfrPOyroJ9RTSbZPWiUeciZY9Ia5HQ6YdjTUx+teLjskKu1brXSK/vt1eJ10h3\nkRiZ7hhKooJH+jQNzOhy6V6k6+Pqrt3DR0KIX38Q6RdTTRQXSd+IF5yRWaT8ztR9jnS+PUc6\nPT2nPUfaDUiYdDWKVL7M+xXJ6JFEdzr7ZMPvBRIifWN6c600ICkyKTgjRNqsPog0sVT7KjjO\nW0qF7F2k6J1ddCmS5d+NLZyUUmxVgUiuLdN2dtBKpJTnSOu9EenOxXCBVGVuVy5AYBKbP8Iy\nGl+kZU3A/lP+02I3NpN7w8ryZe6OUEUx80AcktBxM4kD1ufUbrf1VCLdz7r5/NeZdzk1qjFa\nHcK4NPIkhEjfWyOScX0b6sSPeLsI2TA/4RFEmuoa6V5B1loKe6MuRJ0BMf7uQumEhvhiHyJ5\ntq6WHSKV3eWGxBf7rDtMohEiXb8H2diZXVRCCel39cU+uMb9BEqld+OqIS8bwneIjhCXVk9f\no4B/HERy/3TDqCLFf9w7PkIMPX2xD764n2QJkYRrvrRI0e2X3+EGI1LHBA9J3ibkkxJs0dT8\nzCJlf7EPdiBSiYTUi5T/xT7Ykj9zKzIRK6jRtca9g6RD0tUX+2BHtgVFRCpLQsLxmysXSVOI\nIZhRpOQRL+4yKbZ1ROqbXAc69MiLsT+lO4pIA5FQKOOJZOkRIkEgiaUylkbNvlyCSMMw3uCS\ngsUYRIJAurxvIA8iVQ4xHIh04+I2qVhcRBoFRPoCkeqGGA88umF9Qyl7bBBpGBDpizbHAZEG\nokeN5HNGpKohQANlir7FGwoiQUPGmY4iErRjoDuNiATtQKTCIFIS3VVkAZFaHQNEGoa0mmwr\nn7RH7QY4RBqGlCJqPbNCpLIgUjxJ06SChRfYrPS8rpVJiDQKKUVUrvDaFDQi1Q8xHIiESC1C\njEf6zE6+8FpVNNdI1UOMh6abDYhUZheFIUYkvoRGE4nnSNVDwBfl7tk1GhoagUhQgmIiabUT\nkaAIZUzSO9AhEhRBi0i1tEOkMdD2Nl3mbkN0q/VGMEQaAX0zHkQqsovCEEOxqRcVRukQqeJd\neETqlnt9rOtFy+Ck4hoJkcqH6J11hQwiUsDmiKQuRO9YRKpYOj7iNQrJO65VrpHiUVE81dgK\ncxiQpMqn4kFNT9qxFyLFouZ9uBIhImUfjpoH1ZazN74nyVr5I1Kf7Ovu99VYIgVkoOTMDyKS\n5HRGPZfVxZBppZRJVQ9qqkhxSZbrDCL1hteUPkUyOhOQQUySJbuDSL3x21FHb4cTyZ4CIsmG\nmM0jT1dlDkflg3oMFTK03jcIPChlOoRInTGwSPYMAoYk8cupSEYRaZrnSKHVEHQ4vBu1Pqgh\nQ9L1dzxCpAYhuiW8GOoMW2UJLv5A44p1GJF6I7QaAqdEykWK7S4i1Q7RMcHjkaNqLiskc/tu\nW7QxMZF4jgTReAqrnEjijQY2Fj4FzE/JACINik2Ty/EjeUUCyzYqFbdccog0KGZNfpYV8egi\n9z2OpP3DxiNEgiiMNXMxkBfD2nRes2XKvdAg/A9EGhXHgFSk3hGpwi4KQ0zAsWAkNdrVu7xH\nBcodkUAESY3M3y2sIFJO48U8QqS5kNPIKlL+HWZXhoZVMeEQCURwihRZYbuGBGt01dTBmX2Y\n2LBlNEKk6bCaFC/Cdo8SIlmsWS8rN8bEgUjTUUgk0Tf7+3hkkMagb3uTEGk+jMWXVJGFC9hq\nzX0pIrUOMTFyIpXANALt/74vV5M2Is2HV6SGdbnJ7JDoUaSriqyviDQlxjfx/Zt8+Rz8qflE\nWmXbemBCpAlpL5Itxm4Muuz+Pnx4/bCoaNYuEGlKjCVnKFLZAJvVISIZnxwZc5TJOgNEmoGY\nApMoSV8L1hgOkUxPZmWzzgKRxieuxJqK5HoEi0gqQ0xEZImJeWRvw7KBwZm1SPvZnXDWeSDS\n8MS+WRcT6XKYsZn3Ml8OeVJqPSQh0vDEl1huObqMMPxh2uDYljeptioh0vA0KLAAT0zjlTnN\n8PwRqUGIiShSX84G9xFDhhXHBoEdaDokIdL4FCgvb5M2jZJECpxsIlKLEFNRYjwKr9gwkfJ9\nR6QWISCDqJIN9AiRCoBIukGkA4gELsxlmSxSwHZJacZnJQ0igR1rYaZcI4VtZbz9HRaH298t\nQoAXxzt8PZFiIiFSgxDgwTMjiyrYkI3DRdpvs/q7lUaIBDZCL22kA1qysG7WchhagUhgZO1R\n+Sq92L4sjkhZIFJt7BVcoUh/whhCHXLYL6g7atpBJLBdiFQXKWQdIikLAStMteirULnadUZC\npBwQqSrGYjTW5+8Cyer1uODJS4dHiAQh32jdbLd7WSq8e2vr341AJAiu5PtWshOqyLY2myrx\nCJHgujPEt9W/LZqKJLavJIgEm/vPjqosJlLGnQvpRJJBJPjHZsZm32Y/t6uYoT+npiAS/LKp\nSkNxbtc6NqwHIrUOMTwJxXWcuxnXb9oXqOOs3ZV4hEiDklRfPpFMNZ9dyJkNIFLjEIOTVl97\nj/wN5E+tJExM31kMRBqSxPr+3aueSGoucjJBpCGJEcG8Yw2RopRVDiINSWB5GjaK88j3kbyg\nHINCaVcNkcYkuDp3W0UOSC4XA/dMNV4ZiDQmMeVp+Oia+Vt21lacsS0NRSlr1jUsvzog0qjE\njAnORbGhtk1Ym4sZ+Y7bqRuiEGliTHUcX6GWGt+LtG8UkRBpGMwzprBJ1O9Sp0iXLYZISSKF\n7lgPRJoZYzVethdI5oq9L3WPFoEixd4VQSQ1IeCGsRY3RSoqknV2Z0vFlJExaGvqi/TysCxP\nr6oZb2cAAAlESURBVEVDQB5GE0xb2D5NdDFMwlw+XnxfhVo3uY6a00tZKoq03HZ8XG6ci4QA\nCTZV7xXJU9NukQ6f7gtPbnKRzsv543p9Py8vJUKABKIieUaQ3YAUfMt+5udIN5FOy8e/1x/L\nQ4kQ4Cao+Hbv906Tgpu1a7KxMeFGuBJqi7Qsqz/EQ4CLuPf83c0Gl0ih0cODZm9Xndoi/fcj\n0qlECHCRJpKtdoWLOTE5NVQV6en55XX58/ny4+y+24BIBYi/DIncTyI7se1qU1WkL24vTx8l\nQoAD3SKFDnGIdL2+vb28PD3dbjmcnR4hUgkihNhupKx2FaWygk82zEOKEJeYW9Mzg0jzEK/D\nzx6o5AWRZiJhPPrWB5E8tBKJ50gdcB+IGJJ8IBIcuew/HpQt0vAOMrWDPb/OiIk0wXCGSLDH\ndGWUpwIiCe0S1OyaMiEghNXoIyTSbjwbUqmqIv19frpp8nT+WyoEZLMp+3vR510gbVoccXSq\nKNLHw2rIeSwSAgS4rBBucfWHTMt6qCjSeTn9ebu9en898aFVvVy8KsWKcPRoOJMqinRa3n5f\nv/E1Cr34RIo3IUakTh2r/psNpj/EQoAMbpOiRdrdaXDt3u1wxYgEey62Hwf6XR1V7but3Tsj\nkp/Pa6TX99srrpEUc9lh3yDtG0QhA1KHJtW8/f24umv3wBf7lLKyxDmzCy3544aOnRApiL/n\n23Ok09Mzz5G04h2QYn9aLsoNRJIFkZqxKmVbPYcPSauRLdCNXj1CJNgSVPdhgsSNXJt9olJW\nQQuR/B+lQ6R2hJZyGZF4jhTTACJp4xJ4V223j3PT+/pO3YgCkcBwgzpiL6tK0WNR1yASJF+Y\nINIdRIL0infuiUjyu+waQCRVIJIA3P4GRBIAkSDj4Y1zz5k8QiRAJAkQCa45T0H3e27+nkYj\nRAJRphqENiDS4FQs69+7C4hUaheFIeagYmFf1tQIqAtEGho1Ig0vFyKNTMUR4uISaYJxCpFG\nppVIlpXls2gHIo2MEpFmuHRCpKFpco1kX1Ujj0Yg0tDUF8mxCpGyd1EYYhYKlW/cDYXxPUIk\nSMAkhoRIHcuGSBCPQQzP9C1Qo+BxS51yiATRmKQRuA4Kb0DhVBGRIBqDNI57dhmtejZNDlUA\nRIJonCJ5ytu+QbhIAqOfOIgE8Thmdr6fMPbekUAkQRBJN4Y6DjDJt0XszA6RNISALA5VHCVS\n7tMmfR4hEsRjrmGfSBefSOE3tRFJTwhIxVrF4QNSvgLKNEIkiEZApJLpNQKRIIjf8nfZ4HYE\nkbJ3URgCYlgJkK7DwBohEgQhIpLCKxs5EAn8bNwZeoaWDCKBH0TygkjgZ6tOtkgjOohIEMDW\nnDyPxhzOEAkCQCQfiARBbEs/b143okmIBHVBpIxdFIaARiBSxi4KQ0ArhvQIkaA2iJS+i8IQ\n0I7xNEIkABEQCUAARAIQAJGgKCNeD5lAJCjImHfoTCASFASRZHdRGAIqMOinGEwgEpQDkYR3\nURgCKoBIwrsoDAE1mMYjRIKSIJLsLgpDQB3m0AiRoCEjSYZI0Iixpn2IBI1AJPksGoSAxgx2\naxyRoA2IhEggACIhEkgwlEeIBK1AJPksGoSA9oyjESIBiIBIAAIgEhRkpMmbG0SCYox1O8EN\nIkExEEl6F4UhIBevIoM9cnWDSJBEgCOIJL6LwhCQByJtQSRIIUiSiTxCJEgCkXYgEqQQOG2b\nRSNEgkRmGm1CQCRIApG2IBIkgkZrEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlA\nAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEECpSACdkVDl8uIoDlsautUVkv1C\nJEnoVlcgklboVlcgklboVlcgklboVlcgklboVlcgklboVlcgklboVlcgklboVlcgklboVlcg\nklboVlcgklboVlcMIBLAWCASgACIBCAAIgEIgEgAAiASgACIBCAAIgEIgEgAAiASgACIBCAA\nIgEIgEgAAiASgACIBCAAIgEIUFOk82k5nT9cC7pk34vk32HXxsu2D2Ocreu+X0Knq+L5frwl\n/OBY0CX7XryNItLbtg9jnK3rvl9Sp6ve+f67nN6ub6flr3VBlxx68bY8tcxHjM8+rYtjjLN1\nPfRL6nTVE+m8vH7+98/ybF3QJYdevHTeoW9elsdNwY1xto79kjpd9UR6Wt6vmzeAw4IuOfTi\nZXlpmI4Yy/m6KbgxztaxX1Knq55I3+nfe3FY0CWHXjwtr/99XpU3S0iIt92ZGeNsHfsldboQ\nKRODSDcem2UkxpAiXQ8iyZwuRMrE0K0/1+vHeYAJ3hQiSZ0uRMrE0ouPAW4UTyHSF/mnq95x\nOe3PxGFBl9h60Xm3/rHpwhhn64apD9n9qn3X7n1/1+698/tAtl4MUHGGu3a9n60bnYv0fHsQ\n8bqcrQu65NCL0/LvYzQjVNymuMY4Wzd2I63M6eKTDZkcenH+V2sfX88v+2bMTzbs+iV1uipO\nQB7u9xm/uvIwxH3ifbc+TrcFA71zj3S2/rHpl9TpqijSx+3jw19Rl92CjjF266H/m997kcY4\nW/849kvgdPV/SQygAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAAB\nEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACR\nAARAJAABEAlAAEQCEACRAARAJAABEAlAAETqmxdOoA44D13zlv3P2oMMnIeeeTshkhI4Dx3z\nsjwikhI4D73xuPz9/O/f5b/Pk3e+IpISOA+98b6cPv97On18zuyuiKQFzkN3vCzP1+flz9cf\niKQEzkN/PC4vy9P3a0RSAuehP96XZXn/fo1ISuA8dMh5Of+8RCQlcB76gxFJIZyH/nj6vEZ6\n/H6NSErgPHTHn8+J3fPy8vUHIimB89AbH6fbc6TvyR0iKYHz0Bv/fX+y4Wtyh0hK4DwACIBI\nAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQg\nACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIgEoAAiAQgACIBCIBIAAIg\nEoAA/wP/J/VB7NzifwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# K-means\n",
    "ex2.k2=kmeans(data.mat,centers=2)\n",
    "plot(data.mat,col=ex2.k2$cluster,pch=16)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.0"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}