Multinomial_Logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load libraries\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load iris dataset"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "#https://archive.ics.uci.edu/ml/datasets/Iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
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       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),\n",
       " 'target_names': array(['setosa', 'versicolor', 'virginica'], dtype='<U10'),\n",
       " 'DESCR': '.. _iris_dataset:\\n\\nIris plants dataset\\n--------------------\\n\\n**Data Set Characteristics:**\\n\\n    :Number of Instances: 150 (50 in each of three classes)\\n    :Number of Attributes: 4 numeric, predictive attributes and the class\\n    :Attribute Information:\\n        - sepal length in cm\\n        - sepal width in cm\\n        - petal length in cm\\n        - petal width in cm\\n        - class:\\n                - Iris-Setosa\\n                - Iris-Versicolour\\n                - Iris-Virginica\\n                \\n    :Summary Statistics:\\n\\n    ============== ==== ==== ======= ===== ====================\\n                    Min  Max   Mean    SD   Class Correlation\\n    ============== ==== ==== ======= ===== ====================\\n    sepal length:   4.3  7.9   5.84   0.83    0.7826\\n    sepal width:    2.0  4.4   3.05   0.43   -0.4194\\n    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\\n    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\\n    ============== ==== ==== ======= ===== ====================\\n\\n    :Missing Attribute Values: None\\n    :Class Distribution: 33.3% for each of 3 classes.\\n    :Creator: R.A. Fisher\\n    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\\n    :Date: July, 1988\\n\\nThe famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\\nfrom Fisher\\'s paper. Note that it\\'s the same as in R, but not as in the UCI\\nMachine Learning Repository, which has two wrong data points.\\n\\nThis is perhaps the best known database to be found in the\\npattern recognition literature.  Fisher\\'s paper is a classic in the field and\\nis referenced frequently to this day.  (See Duda & Hart, for example.)  The\\ndata set contains 3 classes of 50 instances each, where each class refers to a\\ntype of iris plant.  One class is linearly separable from the other 2; the\\nlatter are NOT linearly separable from each other.\\n\\n.. topic:: References\\n\\n   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\\n     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\\n     Mathematical Statistics\" (John Wiley, NY, 1950).\\n   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\\n     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\\n   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\\n     Structure and Classification Rule for Recognition in Partially Exposed\\n     Environments\".  IEEE Transactions on Pattern Analysis and Machine\\n     Intelligence, Vol. PAMI-2, No. 1, 67-71.\\n   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\\n     on Information Theory, May 1972, 431-433.\\n   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\\n     conceptual clustering system finds 3 classes in the data.\\n   - Many, many more ...',\n",
       " 'feature_names': ['sepal length (cm)',\n",
       "  'sepal width (cm)',\n",
       "  'petal length (cm)',\n",
       "  'petal width (cm)'],\n",
       " 'filename': '/anaconda3/lib/python3.6/site-packages/sklearn/datasets/data/iris.csv'}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standardize Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standarize features\n",
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        -1.31544430e+00],\n",
       "       [-1.14301691e+00, -1.31979479e-01, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.38535265e+00,  3.28414053e-01, -1.39706395e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.50652052e+00,  9.82172869e-02, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  1.24920112e+00, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-5.37177559e-01,  1.93979142e+00, -1.16971425e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-1.50652052e+00,  7.88807586e-01, -1.34022653e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-1.02184904e+00,  7.88807586e-01, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.74885626e+00, -3.62176246e-01, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.14301691e+00,  9.82172869e-02, -1.28338910e+00,\n",
       "        -1.44707648e+00],\n",
       "       [-5.37177559e-01,  1.47939788e+00, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.26418478e+00,  7.88807586e-01, -1.22655167e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.26418478e+00, -1.31979479e-01, -1.34022653e+00,\n",
       "        -1.44707648e+00],\n",
       "       [-1.87002413e+00, -1.31979479e-01, -1.51073881e+00,\n",
       "        -1.44707648e+00],\n",
       "       [-5.25060772e-02,  2.16998818e+00, -1.45390138e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.73673948e-01,  3.09077525e+00, -1.28338910e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-5.37177559e-01,  1.93979142e+00, -1.39706395e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-9.00681170e-01,  1.01900435e+00, -1.34022653e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-1.73673948e-01,  1.70959465e+00, -1.16971425e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-9.00681170e-01,  1.70959465e+00, -1.28338910e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-5.37177559e-01,  7.88807586e-01, -1.16971425e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-9.00681170e-01,  1.47939788e+00, -1.28338910e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-1.50652052e+00,  1.24920112e+00, -1.56757623e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-9.00681170e-01,  5.58610819e-01, -1.16971425e+00,\n",
       "        -9.20547742e-01],\n",
       "       [-1.26418478e+00,  7.88807586e-01, -1.05603939e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00, -1.31979479e-01, -1.22655167e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  7.88807586e-01, -1.22655167e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-7.79513300e-01,  1.01900435e+00, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-7.79513300e-01,  7.88807586e-01, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.38535265e+00,  3.28414053e-01, -1.22655167e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.26418478e+00,  9.82172869e-02, -1.22655167e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-5.37177559e-01,  7.88807586e-01, -1.28338910e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-7.79513300e-01,  2.40018495e+00, -1.28338910e+00,\n",
       "        -1.44707648e+00],\n",
       "       [-4.16009689e-01,  2.63038172e+00, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.14301691e+00,  9.82172869e-02, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  3.28414053e-01, -1.45390138e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-4.16009689e-01,  1.01900435e+00, -1.39706395e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.14301691e+00,  1.24920112e+00, -1.34022653e+00,\n",
       "        -1.44707648e+00],\n",
       "       [-1.74885626e+00, -1.31979479e-01, -1.39706395e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-9.00681170e-01,  7.88807586e-01, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  1.01900435e+00, -1.39706395e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-1.62768839e+00, -1.74335684e+00, -1.39706395e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-1.74885626e+00,  3.28414053e-01, -1.39706395e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  1.01900435e+00, -1.22655167e+00,\n",
       "        -7.88915558e-01],\n",
       "       [-9.00681170e-01,  1.70959465e+00, -1.05603939e+00,\n",
       "        -1.05217993e+00],\n",
       "       [-1.26418478e+00, -1.31979479e-01, -1.34022653e+00,\n",
       "        -1.18381211e+00],\n",
       "       [-9.00681170e-01,  1.70959465e+00, -1.22655167e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.50652052e+00,  3.28414053e-01, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-6.58345429e-01,  1.47939788e+00, -1.28338910e+00,\n",
       "        -1.31544430e+00],\n",
       "       [-1.02184904e+00,  5.58610819e-01, -1.34022653e+00,\n",
       "        -1.31544430e+00],\n",
       "       [ 1.40150837e+00,  3.28414053e-01,  5.35408562e-01,\n",
       "         2.64141916e-01],\n",
       "       [ 6.74501145e-01,  3.28414053e-01,  4.21733708e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 1.28034050e+00,  9.82172869e-02,  6.49083415e-01,\n",
       "         3.95774101e-01],\n",
       "       [-4.16009689e-01, -1.74335684e+00,  1.37546573e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 7.95669016e-01, -5.92373012e-01,  4.78571135e-01,\n",
       "         3.95774101e-01],\n",
       "       [-1.73673948e-01, -5.92373012e-01,  4.21733708e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 5.53333275e-01,  5.58610819e-01,  5.35408562e-01,\n",
       "         5.27406285e-01],\n",
       "       [-1.14301691e+00, -1.51316008e+00, -2.60315415e-01,\n",
       "        -2.62386821e-01],\n",
       "       [ 9.16836886e-01, -3.62176246e-01,  4.78571135e-01,\n",
       "         1.32509732e-01],\n",
       "       [-7.79513300e-01, -8.22569778e-01,  8.07091462e-02,\n",
       "         2.64141916e-01],\n",
       "       [-1.02184904e+00, -2.43394714e+00, -1.46640561e-01,\n",
       "        -2.62386821e-01],\n",
       "       [ 6.86617933e-02, -1.31979479e-01,  2.51221427e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 1.89829664e-01, -1.97355361e+00,  1.37546573e-01,\n",
       "        -2.62386821e-01],\n",
       "       [ 3.10997534e-01, -3.62176246e-01,  5.35408562e-01,\n",
       "         2.64141916e-01],\n",
       "       [-2.94841818e-01, -3.62176246e-01, -8.98031345e-02,\n",
       "         1.32509732e-01],\n",
       "       [ 1.03800476e+00,  9.82172869e-02,  3.64896281e-01,\n",
       "         2.64141916e-01],\n",
       "       [-2.94841818e-01, -1.31979479e-01,  4.21733708e-01,\n",
       "         3.95774101e-01],\n",
       "       [-5.25060772e-02, -8.22569778e-01,  1.94384000e-01,\n",
       "        -2.62386821e-01],\n",
       "       [ 4.32165405e-01, -1.97355361e+00,  4.21733708e-01,\n",
       "         3.95774101e-01],\n",
       "       [-2.94841818e-01, -1.28296331e+00,  8.07091462e-02,\n",
       "        -1.30754636e-01],\n",
       "       [ 6.86617933e-02,  3.28414053e-01,  5.92245988e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 3.10997534e-01, -5.92373012e-01,  1.37546573e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 5.53333275e-01, -1.28296331e+00,  6.49083415e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 3.10997534e-01, -5.92373012e-01,  5.35408562e-01,\n",
       "         8.77547895e-04],\n",
       "       [ 6.74501145e-01, -3.62176246e-01,  3.08058854e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 9.16836886e-01, -1.31979479e-01,  3.64896281e-01,\n",
       "         2.64141916e-01],\n",
       "       [ 1.15917263e+00, -5.92373012e-01,  5.92245988e-01,\n",
       "         2.64141916e-01],\n",
       "       [ 1.03800476e+00, -1.31979479e-01,  7.05920842e-01,\n",
       "         6.59038469e-01],\n",
       "       [ 1.89829664e-01, -3.62176246e-01,  4.21733708e-01,\n",
       "         3.95774101e-01],\n",
       "       [-1.73673948e-01, -1.05276654e+00, -1.46640561e-01,\n",
       "        -2.62386821e-01],\n",
       "       [-4.16009689e-01, -1.51316008e+00,  2.38717193e-02,\n",
       "        -1.30754636e-01],\n",
       "       [-4.16009689e-01, -1.51316008e+00, -3.29657076e-02,\n",
       "        -2.62386821e-01],\n",
       "       [-5.25060772e-02, -8.22569778e-01,  8.07091462e-02,\n",
       "         8.77547895e-04],\n",
       "       [ 1.89829664e-01, -8.22569778e-01,  7.62758269e-01,\n",
       "         5.27406285e-01],\n",
       "       [-5.37177559e-01, -1.31979479e-01,  4.21733708e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 1.89829664e-01,  7.88807586e-01,  4.21733708e-01,\n",
       "         5.27406285e-01],\n",
       "       [ 1.03800476e+00,  9.82172869e-02,  5.35408562e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 5.53333275e-01, -1.74335684e+00,  3.64896281e-01,\n",
       "         1.32509732e-01],\n",
       "       [-2.94841818e-01, -1.31979479e-01,  1.94384000e-01,\n",
       "         1.32509732e-01],\n",
       "       [-4.16009689e-01, -1.28296331e+00,  1.37546573e-01,\n",
       "         1.32509732e-01],\n",
       "       [-4.16009689e-01, -1.05276654e+00,  3.64896281e-01,\n",
       "         8.77547895e-04],\n",
       "       [ 3.10997534e-01, -1.31979479e-01,  4.78571135e-01,\n",
       "         2.64141916e-01],\n",
       "       [-5.25060772e-02, -1.05276654e+00,  1.37546573e-01,\n",
       "         8.77547895e-04],\n",
       "       [-1.02184904e+00, -1.74335684e+00, -2.60315415e-01,\n",
       "        -2.62386821e-01],\n",
       "       [-2.94841818e-01, -8.22569778e-01,  2.51221427e-01,\n",
       "         1.32509732e-01],\n",
       "       [-1.73673948e-01, -1.31979479e-01,  2.51221427e-01,\n",
       "         8.77547895e-04],\n",
       "       [-1.73673948e-01, -3.62176246e-01,  2.51221427e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 4.32165405e-01, -3.62176246e-01,  3.08058854e-01,\n",
       "         1.32509732e-01],\n",
       "       [-9.00681170e-01, -1.28296331e+00, -4.30827696e-01,\n",
       "        -1.30754636e-01],\n",
       "       [-1.73673948e-01, -5.92373012e-01,  1.94384000e-01,\n",
       "         1.32509732e-01],\n",
       "       [ 5.53333275e-01,  5.58610819e-01,  1.27429511e+00,\n",
       "         1.71209594e+00],\n",
       "       [-5.25060772e-02, -8.22569778e-01,  7.62758269e-01,\n",
       "         9.22302838e-01],\n",
       "       [ 1.52267624e+00, -1.31979479e-01,  1.21745768e+00,\n",
       "         1.18556721e+00],\n",
       "       [ 5.53333275e-01, -3.62176246e-01,  1.04694540e+00,\n",
       "         7.90670654e-01],\n",
       "       [ 7.95669016e-01, -1.31979479e-01,  1.16062026e+00,\n",
       "         1.31719939e+00],\n",
       "       [ 2.12851559e+00, -1.31979479e-01,  1.61531967e+00,\n",
       "         1.18556721e+00],\n",
       "       [-1.14301691e+00, -1.28296331e+00,  4.21733708e-01,\n",
       "         6.59038469e-01],\n",
       "       [ 1.76501198e+00, -3.62176246e-01,  1.44480739e+00,\n",
       "         7.90670654e-01],\n",
       "       [ 1.03800476e+00, -1.28296331e+00,  1.16062026e+00,\n",
       "         7.90670654e-01],\n",
       "       [ 1.64384411e+00,  1.24920112e+00,  1.33113254e+00,\n",
       "         1.71209594e+00],\n",
       "       [ 7.95669016e-01,  3.28414053e-01,  7.62758269e-01,\n",
       "         1.05393502e+00],\n",
       "       [ 6.74501145e-01, -8.22569778e-01,  8.76433123e-01,\n",
       "         9.22302838e-01],\n",
       "       [ 1.15917263e+00, -1.31979479e-01,  9.90107977e-01,\n",
       "         1.18556721e+00],\n",
       "       [-1.73673948e-01, -1.28296331e+00,  7.05920842e-01,\n",
       "         1.05393502e+00],\n",
       "       [-5.25060772e-02, -5.92373012e-01,  7.62758269e-01,\n",
       "         1.58046376e+00],\n",
       "       [ 6.74501145e-01,  3.28414053e-01,  8.76433123e-01,\n",
       "         1.44883158e+00],\n",
       "       [ 7.95669016e-01, -1.31979479e-01,  9.90107977e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 2.24968346e+00,  1.70959465e+00,  1.67215710e+00,\n",
       "         1.31719939e+00],\n",
       "       [ 2.24968346e+00, -1.05276654e+00,  1.78583195e+00,\n",
       "         1.44883158e+00],\n",
       "       [ 1.89829664e-01, -1.97355361e+00,  7.05920842e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 1.28034050e+00,  3.28414053e-01,  1.10378283e+00,\n",
       "         1.44883158e+00],\n",
       "       [-2.94841818e-01, -5.92373012e-01,  6.49083415e-01,\n",
       "         1.05393502e+00],\n",
       "       [ 2.24968346e+00, -5.92373012e-01,  1.67215710e+00,\n",
       "         1.05393502e+00],\n",
       "       [ 5.53333275e-01, -8.22569778e-01,  6.49083415e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 1.03800476e+00,  5.58610819e-01,  1.10378283e+00,\n",
       "         1.18556721e+00],\n",
       "       [ 1.64384411e+00,  3.28414053e-01,  1.27429511e+00,\n",
       "         7.90670654e-01],\n",
       "       [ 4.32165405e-01, -5.92373012e-01,  5.92245988e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 3.10997534e-01, -1.31979479e-01,  6.49083415e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 6.74501145e-01, -5.92373012e-01,  1.04694540e+00,\n",
       "         1.18556721e+00],\n",
       "       [ 1.64384411e+00, -1.31979479e-01,  1.16062026e+00,\n",
       "         5.27406285e-01],\n",
       "       [ 1.88617985e+00, -5.92373012e-01,  1.33113254e+00,\n",
       "         9.22302838e-01],\n",
       "       [ 2.49201920e+00,  1.70959465e+00,  1.50164482e+00,\n",
       "         1.05393502e+00],\n",
       "       [ 6.74501145e-01, -5.92373012e-01,  1.04694540e+00,\n",
       "         1.31719939e+00],\n",
       "       [ 5.53333275e-01, -5.92373012e-01,  7.62758269e-01,\n",
       "         3.95774101e-01],\n",
       "       [ 3.10997534e-01, -1.05276654e+00,  1.04694540e+00,\n",
       "         2.64141916e-01],\n",
       "       [ 2.24968346e+00, -1.31979479e-01,  1.33113254e+00,\n",
       "         1.44883158e+00],\n",
       "       [ 5.53333275e-01,  7.88807586e-01,  1.04694540e+00,\n",
       "         1.58046376e+00],\n",
       "       [ 6.74501145e-01,  9.82172869e-02,  9.90107977e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 1.89829664e-01, -1.31979479e-01,  5.92245988e-01,\n",
       "         7.90670654e-01],\n",
       "       [ 1.28034050e+00,  9.82172869e-02,  9.33270550e-01,\n",
       "         1.18556721e+00],\n",
       "       [ 1.03800476e+00,  9.82172869e-02,  1.04694540e+00,\n",
       "         1.58046376e+00],\n",
       "       [ 1.28034050e+00,  9.82172869e-02,  7.62758269e-01,\n",
       "         1.44883158e+00],\n",
       "       [-5.25060772e-02, -8.22569778e-01,  7.62758269e-01,\n",
       "         9.22302838e-01],\n",
       "       [ 1.15917263e+00,  3.28414053e-01,  1.21745768e+00,\n",
       "         1.44883158e+00],\n",
       "       [ 1.03800476e+00,  5.58610819e-01,  1.10378283e+00,\n",
       "         1.71209594e+00],\n",
       "       [ 1.03800476e+00, -1.31979479e-01,  8.19595696e-01,\n",
       "         1.44883158e+00],\n",
       "       [ 5.53333275e-01, -1.28296331e+00,  7.05920842e-01,\n",
       "         9.22302838e-01],\n",
       "       [ 7.95669016e-01, -1.31979479e-01,  8.19595696e-01,\n",
       "         1.05393502e+00],\n",
       "       [ 4.32165405e-01,  7.88807586e-01,  9.33270550e-01,\n",
       "         1.44883158e+00],\n",
       "       [ 6.86617933e-02, -1.31979479e-01,  7.62758269e-01,\n",
       "         7.90670654e-01]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "data = [[0, 0], [0, 0], [1, 1], [1, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0], [0, 0], [1, 1], [1, 1]]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance 0.25\n",
      "mean 0.5\n",
      "standard deviation 0.5\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print(\"variance\", np.var([0,0,1,1]))\n",
    "print(\"mean\", np.mean([0,0,1,1]))\n",
    "print(\"standard deviation\", np.std([0,0,1,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0 - 0.5)/0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2 - 0.5)/0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "StandardScaler(copy=True, with_mean=True, with_std=True)\n",
      "[0.5 0.5]\n",
      "[[-1. -1.]\n",
      " [-1. -1.]\n",
      " [ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[[3. 3.]]\n"
     ]
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "print(scaler.fit(data))\n",
    "print(scaler.mean_)\n",
    "print(scaler.transform(data))\n",
    "print(scaler.transform([[2, 2]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standarize features\n",
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Multinomial Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create one-vs-rest logistic regression object\n",
    "LogisticRegression()\n",
    "clf = LogisticRegression(random_state=0, multi_class='multinomial', solver='newton-cg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Multinomial Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train model\n",
    "model = clf.fit(X_std, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Previously Unseen Observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create new observation\n",
    "new_observation = [[.5, .5, .5, .5]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict Observation’s Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict class\n",
    "model.predict(new_observation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.01982536, 0.74491994, 0.2352547 ]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# View predicted probabilities\n",
    "model.predict_proba(new_observation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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