08_Dimensionality_Reduction.ipynb

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     "source": [
      "# Introduction to data analysis using machine learning #\n",
      "\n",
      "## 08. Dimensionality reduction with Principal Component Analysis (PCA) ##\n",
      "\n",
      "by David Taylor, [www.prooffreader.com](http://www.prooffreader.com) (blog) [www.dtdata.io](http://dtdata.io) (hire me!)\n",
      "\n",
      "For links to more material including a slideshow explaining all this stuff in further detail, please see the front page of [this GitHub repo.](https://github.com/Prooffreader/intro_machine_learning)\n",
      "\n",
      "This is notebook 8 of 8. \n",
      "\n",
      "[[01]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/01_The_Dataset.ipynb) [[02]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/02_Clustering_KMeans.ipynb) [[03]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/03_Clustering_OtherAlgos.ipynb) [[04]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/04_Classification_kNN.ipynb) [[05]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/05_Classification_OtherAlgos.ipynb) [[06]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/06_Classification_Decision_Trees.ipynb) [[07]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/07_Classification_Random_Forest.ipynb) **[08]**\n",
      "***\n",
      "\n",
      "In the [previous notebook](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/07_Classification_Random_Forest.ipynb), we finished our look at Supervised Learning. Now we see a way to address the Curse of Dimensionality by reducing our features using PCA."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### 1. Import libraries and load data #"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "from statsmodels.sandbox.tools.tools_pca import pcasvd\n",
      "from sklearn.ensemble import RandomForestClassifier\n",
      "\n",
      "df = pd.read_csv('fruit.csv')\n",
      "\n",
      "fruitnames = {1: 'Orange', 2: 'Pear', 3: 'Apple'}\n",
      "colors = {1: '#e09028', 2: '#55aa33', 3: '#cc3333'}\n",
      "fruitlist = ['Orange', 'Pear', 'Apple']\n",
      "\n",
      "numerical_columns = ['elongatedness', 'weight', 'sweetness', 'acidity', 'color_id']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### 2. Run PCA #\n",
      "\n",
      "Scikit-learn has a PCA module, but instead I'm using statsmodels's ``pcasvd`` function in order to make a biplot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# code taken from http://okomestudio.net/biboroku/?p=2292\n",
      "\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "\n",
      "\n",
      "def biplot(plt, pca, labels=None, colors=None,\n",
      "           xpc=1, ypc=2, scale=1):\n",
      "    \"\"\"Generate biplot from the result of pcasvd of statsmodels.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    plt : object\n",
      "        An existing pyplot module reference.\n",
      "\n",
      "    pca : tuple\n",
      "        The result from statsmodels.sandbox.tools.tools_pca.pcasvd.\n",
      "\n",
      "    labels : array_like, optional\n",
      "        Labels for each observation.\n",
      "\n",
      "    colors : array_like, optional\n",
      "        Colors for each observation.\n",
      "\n",
      "    xpc, ypc : int, optional\n",
      "        The principal component number for x- and y-axis. Defaults to\n",
      "        (xpc, ypc) = (1, 2).\n",
      "\n",
      "    scale : float\n",
      "        The variables are scaled by lambda ** scale, where lambda =\n",
      "        singular value = sqrt(eigenvalue), and the observations are\n",
      "        scaled by lambda ** (1 - scale). Must be in [0, 1].\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    None.\n",
      "\n",
      "    \"\"\"\n",
      "    xpc, ypc = (xpc - 1, ypc - 1)\n",
      "    xreduced, factors, evals, evecs = pca\n",
      "    singvals = np.sqrt(evals)\n",
      " \n",
      "    # data\n",
      "    xs = factors[:, xpc] * singvals[xpc]**(1. - scale)\n",
      "    ys = factors[:, ypc] * singvals[ypc]**(1. - scale)\n",
      " \n",
      "    colors = 'k' if colors is None else colors\n",
      "    plt.scatter(xs, ys, c=colors, marker='o', alpha=0.4)\n",
      " \n",
      "    # variables\n",
      "    tvars = np.dot(np.eye(factors.shape[0], factors.shape[1]),\n",
      "                   evecs) * singvals**scale\n",
      " \n",
      "    for i, col in enumerate(xreduced.columns.values):\n",
      "        x, y = tvars[i][xpc], tvars[i][ypc]\n",
      "        plt.arrow(0, 0, x, y, color='r',\n",
      "                  width=0.002, head_width=0.05)\n",
      "        plt.text(x* 1.4, y * 1.4, col, color='r', ha='center', va='center')\n",
      "    \n",
      "    plt.title('Principal Component Analysis with biplot')\n",
      "    plt.xlabel('PC{}'.format(xpc + 1))\n",
      "    plt.ylabel('PC{}'.format(ypc + 1))\n",
      " \n",
      "    return xs, ys "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "columns = ['elongatedness', 'weight', 'sweetness', 'acidity', 'color_id']\n",
      "\n",
      "data = df[columns]\n",
      "classes = df['fruit_id']\n",
      "data = (data - data.mean()) / data.std() # pca data must be normalized\n",
      "pca = pcasvd(data, keepdim=0, demean=False)\n",
      "\n",
      "colors = [['#e09028', '#55aa33', '#cc3333'][i-1] for i in classes]\n",
      "\n",
      "plt.figure(1)\n",
      "xs, ys = biplot(plt, pca, labels=classes, colors=colors,\n",
      "       xpc=1, ypc=2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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Ce5Mdg9GA0ceI0+W8QSyK26GhoYGzZ8/idrtJSkq66akWkpOTOXYwlh2Hcgjy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       "text": [
        "<matplotlib.figure.Figure at 0x87a9ef0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### 3. Do 100 runs of Random Forest Classifier using two principal components and show confusion matrix #"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_pca = pd.DataFrame({'PC1': xs,\n",
      "                       'PC2': ys,\n",
      "                       'fruit_id': classes})\n",
      "df_pca.sort('fruit_id', inplace=True)\n",
      "\n",
      "# parameters\n",
      "# I did not make a function because I wanted to preserve the \n",
      "# IPython output of the confusion matrix in the same cell.\n",
      "reps=100\n",
      "features = ['PC1', 'PC2']\n",
      "title_suffix='with two principal components'\n",
      "\n",
      "import time\n",
      "start = time.time()\n",
      "for i in range(reps):\n",
      "    df_pca['is_train'] = np.random.uniform(0, 1, len(df_pca)) <= .75 # randomly assign training and testing set\n",
      "    train, test = df_pca[df_pca['is_train']==True], df_pca[df_pca['is_train']==False]\n",
      "    y, _ = pd.factorize(train['fruit_id'])\n",
      "    clf = RandomForestClassifier(n_jobs=2)\n",
      "    clf = clf.fit(train[features], y)\n",
      "    preds = clf.predict(test[features])\n",
      "    test_result = pd.crosstab(np.array([fruitnames[x] for x in test['fruit_id']]), \n",
      "                          np.array([fruitnames[x+1] for x in preds]), rownames=['actual'], colnames=['predicted'])\n",
      "    if i == 0:\n",
      "        final_result = test_result[:]\n",
      "    else:\n",
      "        final_result += test_result\n",
      "confmatrix = np.array(final_result)\n",
      "correct = 0\n",
      "for i in range(confmatrix.shape[0]):\n",
      "    correct += confmatrix[i,i]\n",
      "accuracy = correct/confmatrix.sum()\n",
      "print('{} runs {}\\nFeatures: {}\\nAccuracy: {}\\ntime: {} sec'.format(reps, title_suffix, features, accuracy, int(time.time()-start)))\n",
      "final_result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 runs with two principal components\n",
        "Features: ['PC1', 'PC2']\n",
        "Accuracy: 0.9665188470066519\n",
        "time: 23 sec\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th>predicted</th>\n",
        "      <th>Apple</th>\n",
        "      <th>Orange</th>\n",
        "      <th>Pear</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>actual</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>Apple</th>\n",
        "      <td> 1146</td>\n",
        "      <td>    8</td>\n",
        "      <td>   92</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Orange</th>\n",
        "      <td>    8</td>\n",
        "      <td> 1481</td>\n",
        "      <td>    1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Pear</th>\n",
        "      <td>   42</td>\n",
        "      <td>    0</td>\n",
        "      <td> 1732</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "predicted  Apple  Orange  Pear\n",
        "actual                        \n",
        "Apple       1146       8    92\n",
        "Orange         8    1481     1\n",
        "Pear          42       0  1732"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}