0024 Gaussian Naive Bayes Classification in Python.ipynb

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     "input": [
      "%matplotlib inline\n",
      "import sys\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from __future__ import print_function\n",
      "\n",
      "# turn of data table rendering\n",
      "pd.set_option('display.notebook_repr_html', False)\n",
      "sns.set_palette(['#00A99D', '#F5CA0C', '#B6129F', '#76620C', '#095C57'])\n",
      "sys.version"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "text": [
        "'3.4.1 |Anaconda 2.1.0 (64-bit)| (default, Sep 24 2014, 18:32:42) [MSC v.1600 64 bit (AMD64)]'"
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      "## Supervised Classification\n",
      "In this type of machine learing we tell the system the correct answer to a set a features. The system should be thaught so well that it is later capable of accurately classifying data it did not encounter before. Some examples of applications are; recognize someone in a picture from a set of tagged photos, spam filtering and recommender systems (music, movies, customers who buy this product also bought...)"
     ]
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     "cell_type": "markdown",
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     "source": [
      "### Features and Labels\n",
      "We can describe a hidden object based on its features. A piece of music, for instance, can have continuous features like the song lenght, tempo, dynamics, intensity. Labels are the classes an object can belong to. In this case a class could be whether a song is liked or disliked by someone.\n",
      "\n",
      "A classifier algorithm defines a decision surface (DS) to separate one class from another. If we know on which side of the boundary a new data point falls, we can predict what class it belongs to. The example below is a linear decision surface. The scatterplot shows two features (a, b) and the purple descision boundary separates two classes (1, 2)."
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     "cell_type": "code",
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     "input": [
      "# Create and plot a linear descision surface\n",
      "df = pd.DataFrame({'feature_a': np.random.rand(100) * 6, \n",
      "                   'feature_b': np.random.rand(100) * 4.2, \n",
      "                   'class': 1})\n",
      "df = df.append(pd.DataFrame({\n",
      "                   'feature_a': np.random.rand(100) * 6 + 1.7, \n",
      "                   'feature_b': np.random.rand(100) * np.random.randint(5,6) + 3.8, \n",
      "                   'class': 2}))\n",
      "\n",
      "sns.lmplot(\"feature_a\", \"feature_b\", df, hue='class', \n",
      "           markers=[\"x\", \"o\"], scatter_kws={\"s\": 30}, fit_reg=False);\n",
      "\n",
      "plt.plot([9.5,0.5], [1.5,6.5], color='#B6129F')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "display_data",
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LeswhsKv9Nk3TYnpcU1XVTmAspDuW8wiGniz/Z8fHbOgMdIEsLSjFblFY39ES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\n/gERZTjH//uiSwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa756da0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Gaussian Naive Bayes Classifier\n",
      "Naive Bayes Classifiers are a set of supervised machine learning classifiers based on applying [Bayes' Theorem](http://unsupervised-learning.com/bayes-theorem-conditional-probability/). The reason it is called naive is mainly because the algorithms assume independence between features. For example, a solely naive Bayes spam filter only looks at the words separately and doesn't take the word order into account.\n",
      "\n",
      "In the example below we use the training set from the example above to train a [Gaussian Naive Bayes Classifier](http://scikit-learn.org/stable/modules/naive_bayes.html#naive-bayes) found in scikit-learn called [GaussianNB](http://scikit-learn.org/stable/modules/generated/sklearn.naive_bayes.GaussianNB.html#sklearn.naive_bayes.GaussianNB). The likelihood of the chosen features in the data is assumed to folow the [Bell curve](http://en.wikipedia.org/wiki/The_Bell_Curve)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# First shuffle the labeled dataframe\n",
      "def shuffle(data, n):\n",
      "    ind = data.index\n",
      "    for i in range(n):\n",
      "       sampler = np.random.permutation(data.shape[0])\n",
      "       new_vals = data.take(sampler).values\n",
      "       data = pd.DataFrame(new_vals, index=ind)\n",
      "    return data\n",
      "\n",
      "df = shuffle(df, 1)\n",
      "df.columns = ['class', 'feature_a', 'feature_b']\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   class  feature_a  feature_b\n",
        "0      2   5.798872   7.596082\n",
        "1      2   1.775559   7.201435\n",
        "2      2   5.421547   4.152468\n",
        "3      1   5.044245   3.089780\n",
        "4      2   4.518854   6.674273"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a training set of 3/4 of the data\n",
      "train_n = 150\n",
      "\n",
      "train_features = df[['feature_a', 'feature_b']][:train_n]\n",
      "train_labels = df['class'][:train_n]\n",
      "train_features.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "        feature_a   feature_b\n",
        "count  150.000000  150.000000\n",
        "mean     3.947905    4.160631\n",
        "std      1.913207    2.479593\n",
        "min      0.218355    0.036516\n",
        "25%      2.349316    2.017435\n",
        "50%      3.951341    4.042921\n",
        "75%      5.199696    6.341548\n",
        "max      7.691394    8.766121"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a test set of 1/4 of the data to evaluate the classifier\n",
      "test_features = df[['feature_a', 'feature_b']][train_n:]\n",
      "test_labels = df['class'][train_n:]\n",
      "test_features.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "       feature_a  feature_b\n",
        "count  50.000000  50.000000\n",
        "mean    4.273527   4.430639\n",
        "std     1.707272   2.572468\n",
        "min     0.957064   0.158048\n",
        "25%     3.024620   2.181059\n",
        "50%     4.138659   4.750336\n",
        "75%     5.357447   6.236545\n",
        "max     7.686878   8.765652"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Train a Gaussian Naive Bayes Classifier\n",
      "from sklearn.naive_bayes import GaussianNB\n",
      "clf = GaussianNB()\n",
      "clf.fit(train_features, train_labels)\n",
      "clf.predict([4.8, 4.2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([ 2.])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Query the accuracy of the model with the test set\n",
      "accuracy = clf.score(test_features, test_labels)\n",
      "print(accuracy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.98\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Another, more generic, way to calculate accuracy in scikit-learn\n",
      "from sklearn.metrics import accuracy_score\n",
      "print(accuracy_score(clf.predict(test_features), test_labels))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.98\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_decision_surface(clf, features, labels, title):\n",
      "    x_min = 0.0; x_max = 8.0\n",
      "    y_min = 0.0; y_max = 8.0\n",
      "\n",
      "    # Plot the decision boundary. For that, we will assign a color to each\n",
      "    # point in the mesh [x_min, m_max]x[y_min, y_max].\n",
      "    h = .01  # step size in the mesh\n",
      "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
      "    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])   \n",
      "    z_min, z_max = -np.abs(Z).max(), np.abs(Z).max()\n",
      "    \n",
      "    # set title\n",
      "    f, ax = plt.subplots()\n",
      "    ax.set_title(title)\n",
      "\n",
      "    # Put the result into a color plot\n",
      "    Z = Z.reshape(xx.shape)\n",
      "    plt.xlim(xx.min(), xx.max())\n",
      "    plt.ylim(yy.min(), yy.max())\n",
      "    plt.pcolormesh(xx, yy, Z, cmap='gray', vmin=.2, vmax=2.4)  # \n",
      "\n",
      "    # Plot the points\n",
      "    class_1_x = [features[ii][0] for ii in range(0, len(features)) if labels[ii]==1]\n",
      "    class_1_y = [features[ii][1] for ii in range(0, len(features)) if labels[ii]==1]\n",
      "    class_2_x = [features[ii][0] for ii in range(0, len(features)) if labels[ii]==2]\n",
      "    class_2_y = [features[ii][1] for ii in range(0, len(features)) if labels[ii]==2]\n",
      "\n",
      "    plt.scatter(class_1_x, class_1_y, color = '#F5CA0C', label=\"1\", s=40)\n",
      "    plt.scatter(class_2_x, class_2_y, color = '#00A99D', label=\"2\", s=40)\n",
      "   \n",
      "    plt.xlabel(\"feature_a\")\n",
      "    plt.ylabel(\"feature_b\")\n",
      "    plt.legend(('class 1', 'class 2'), frameon=True)\n",
      "    \n",
      "    \n",
      "# Plot the decision surface and data point for training and tests data\n",
      "plot_decision_surface(clf, train_features.values, train_labels.values, \n",
      "                      'Training data')\n",
      "plot_decision_surface(clf, test_features.values, test_labels.values,\n",
      "                      'Test data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aW0QiVcv8cBLmxmuR9o1fJDwKztIw34twfG9fFtUzP1zL3Ljvy8OysPGLhEPBWRriexGO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\nFhER8cz/B+clMcm/zHC8AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbfd5d30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xbfd5dd8>"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}