{ "metadata": { "name": "", "signature": "sha256:b60e51d051fa6c9c3777600a4e6e0401de982cb75bb521366c45044e1941d9e7" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "3. Data Pre-processing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Data pre-processing techniques generally refer to the addition, deletion, or transformation of training set data. Different models have different sensitivities to the type of predictors in the model; *how* the predictors enter the model is also important.\n", "\n", "The need for data pre-processing is determined by the type of model being used. Some procedures, such as tree-based models, are notably insensitive to the characteristics of the predictor data. Others, like linear regression, are not. In this chapter, a wide array of possible methodologies are discussed. \n", "\n", "How the predictors are encoded, called *feature engineering*, can have a significant impact on model performance. Often the most effective encoding of the data is informed by the modeler's understanding of the problem and thus is not derived from any mathematical techniques." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.1 Case Study: Cell Segmentation in High-Content Screening" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check if data exists." ] }, { "cell_type": "code", "collapsed": false, "input": [ "!ls -l ../datasets/segmentationOriginal/" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total 4016\r\n", "-rw-r--r-- 1 leigong staff 2053006 Nov 24 15:58 segmentationOriginal.csv\r\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This dataset is from Hill et al. (2007) that consists of 2019 cells. Of these cells, 1300 were judged to be poorly segmented (PS) and 719 were well segmented (WS); 1009 cells were reserved for the training set." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd\n", "\n", "cell_segmentation = pd.read_csv(\"../datasets/segmentationOriginal/segmentationOriginal.csv\")" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "cell_segmentation.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "(2019, 120)" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A first look at the dataset." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cell_segmentation.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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Unnamed: 0CellCaseClassAngleCh1AngleStatusCh1AreaCh1AreaStatusCh1AvgIntenCh1AvgIntenCh2...VarIntenCh1VarIntenCh3VarIntenCh4VarIntenStatusCh1VarIntenStatusCh3VarIntenStatusCh4WidthCh1WidthStatusCh1XCentroidYCentroid
0 1 207827637 Test PS 143.247705 1 185 0 15.711864 3.954802... 12.474676 7.609035 2.714100 0 2 2 10.642974 2 42 14
1 2 207932307 Train PS 133.752037 0 819 1 31.923274 205.878517... 18.809225 56.715352 118.388139 0 0 0 32.161261 1 215 347
2 3 207932463 Train WS 106.646387 0 431 0 28.038835 115.315534... 17.295643 37.671053 49.470524 0 0 0 21.185525 0 371 252
3 4 207932470 Train PS 69.150325 0 298 0 19.456140 101.294737... 13.818968 30.005643 24.749537 0 0 2 13.392830 0 487 295
4 5 207932455 Test PS 2.887837 2 285 0 24.275735 111.415441... 15.407972 20.504288 45.450457 0 0 0 13.198561 0 283 159
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5 rows \u00d7 120 columns

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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ " Unnamed: 0 Cell Case Class AngleCh1 AngleStatusCh1 AreaCh1 \\\n", "0 1 207827637 Test PS 143.247705 1 185 \n", "1 2 207932307 Train PS 133.752037 0 819 \n", "2 3 207932463 Train WS 106.646387 0 431 \n", "3 4 207932470 Train PS 69.150325 0 298 \n", "4 5 207932455 Test PS 2.887837 2 285 \n", "\n", " AreaStatusCh1 AvgIntenCh1 AvgIntenCh2 ... VarIntenCh1 \\\n", "0 0 15.711864 3.954802 ... 12.474676 \n", "1 1 31.923274 205.878517 ... 18.809225 \n", "2 0 28.038835 115.315534 ... 17.295643 \n", "3 0 19.456140 101.294737 ... 13.818968 \n", "4 0 24.275735 111.415441 ... 15.407972 \n", "\n", " VarIntenCh3 VarIntenCh4 VarIntenStatusCh1 VarIntenStatusCh3 \\\n", "0 7.609035 2.714100 0 2 \n", "1 56.715352 118.388139 0 0 \n", "2 37.671053 49.470524 0 0 \n", "3 30.005643 24.749537 0 0 \n", "4 20.504288 45.450457 0 0 \n", "\n", " VarIntenStatusCh4 WidthCh1 WidthStatusCh1 XCentroid YCentroid \n", "0 2 10.642974 2 42 14 \n", "1 0 32.161261 1 215 347 \n", "2 0 21.185525 0 371 252 \n", "3 2 13.392830 0 487 295 \n", "4 0 13.198561 0 283 159 \n", "\n", "[5 rows x 120 columns]" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This chapter will use the training set samples to demonstrate data pre-processing techniques." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cell_segmentation.groupby('Case').count()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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Unnamed: 0CellClassAngleCh1AngleStatusCh1AreaCh1AreaStatusCh1AvgIntenCh1AvgIntenCh2AvgIntenCh3...VarIntenCh1VarIntenCh3VarIntenCh4VarIntenStatusCh1VarIntenStatusCh3VarIntenStatusCh4WidthCh1WidthStatusCh1XCentroidYCentroid
Case
Test 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010... 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010
Train 1009 1009 1009 1009 1009 1009 1009 1009 1009 1009... 1009 1009 1009 1009 1009 1009 1009 1009 1009 1009
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2 rows \u00d7 119 columns

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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ " Unnamed: 0 Cell Class AngleCh1 AngleStatusCh1 AreaCh1 \\\n", "Case \n", "Test 1010 1010 1010 1010 1010 1010 \n", "Train 1009 1009 1009 1009 1009 1009 \n", "\n", " AreaStatusCh1 AvgIntenCh1 AvgIntenCh2 AvgIntenCh3 ... \\\n", "Case ... \n", "Test 1010 1010 1010 1010 ... \n", "Train 1009 1009 1009 1009 ... \n", "\n", " VarIntenCh1 VarIntenCh3 VarIntenCh4 VarIntenStatusCh1 \\\n", "Case \n", "Test 1010 1010 1010 1010 \n", "Train 1009 1009 1009 1009 \n", "\n", " VarIntenStatusCh3 VarIntenStatusCh4 WidthCh1 WidthStatusCh1 \\\n", "Case \n", "Test 1010 1010 1010 1010 \n", "Train 1009 1009 1009 1009 \n", "\n", " XCentroid YCentroid \n", "Case \n", "Test 1010 1010 \n", "Train 1009 1009 \n", "\n", "[2 rows x 119 columns]" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# separate training and test data\n", "cell_train = cell_segmentation.ix[cell_segmentation['Case'] == 'Train']\n", "cell_test = cell_segmentation.ix[cell_segmentation['Case'] == 'Test']\n", "\n", "cell_train.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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Unnamed: 0CellCaseClassAngleCh1AngleStatusCh1AreaCh1AreaStatusCh1AvgIntenCh1AvgIntenCh2...VarIntenCh1VarIntenCh3VarIntenCh4VarIntenStatusCh1VarIntenStatusCh3VarIntenStatusCh4WidthCh1WidthStatusCh1XCentroidYCentroid
1 2 207932307 Train PS 133.752037 0 819 1 31.923274 205.878517... 18.809225 56.715352 118.388139 0 0 0 32.161261 1 215 347
2 3 207932463 Train WS 106.646387 0 431 0 28.038835 115.315534... 17.295643 37.671053 49.470524 0 0 0 21.185525 0 371 252
3 4 207932470 Train PS 69.150325 0 298 0 19.456140 101.294737... 13.818968 30.005643 24.749537 0 0 2 13.392830 0 487 295
11 12 207932484 Train WS 109.416426 0 256 0 18.828571 125.938776... 13.922937 18.643027 40.331747 0 0 2 17.546861 0 211 495
14 15 207932459 Train PS 104.278654 0 258 0 17.570850 124.368421... 12.324971 17.747143 41.928533 0 0 2 17.660339 0 172 207
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5 rows \u00d7 120 columns

\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ " Unnamed: 0 Cell Case Class AngleCh1 AngleStatusCh1 AreaCh1 \\\n", "1 2 207932307 Train PS 133.752037 0 819 \n", "2 3 207932463 Train WS 106.646387 0 431 \n", "3 4 207932470 Train PS 69.150325 0 298 \n", "11 12 207932484 Train WS 109.416426 0 256 \n", "14 15 207932459 Train PS 104.278654 0 258 \n", "\n", " AreaStatusCh1 AvgIntenCh1 AvgIntenCh2 ... VarIntenCh1 \\\n", "1 1 31.923274 205.878517 ... 18.809225 \n", "2 0 28.038835 115.315534 ... 17.295643 \n", "3 0 19.456140 101.294737 ... 13.818968 \n", "11 0 18.828571 125.938776 ... 13.922937 \n", "14 0 17.570850 124.368421 ... 12.324971 \n", "\n", " VarIntenCh3 VarIntenCh4 VarIntenStatusCh1 VarIntenStatusCh3 \\\n", "1 56.715352 118.388139 0 0 \n", "2 37.671053 49.470524 0 0 \n", "3 30.005643 24.749537 0 0 \n", "11 18.643027 40.331747 0 0 \n", "14 17.747143 41.928533 0 0 \n", "\n", " VarIntenStatusCh4 WidthCh1 WidthStatusCh1 XCentroid YCentroid \n", "1 0 32.161261 1 215 347 \n", "2 0 21.185525 0 371 252 \n", "3 2 13.392830 0 487 295 \n", "11 2 17.546861 0 211 495 \n", "14 2 17.660339 0 172 207 \n", "\n", "[5 rows x 120 columns]" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.2 Data Transformation for Individual Predictors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transformations of predictor variables may be needed for several reasons. Some modeling techniques may have strict requirements, such as the predictors having a commom scale. In other cases, creating a good model may be difficult due to specific characteristics of the data (e.g., outliers)." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Centering and Scaling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To center a predictor variable, the average predictor value is substracted from all the values. As a result of centering, the predictor has a zero mean. Similarly, to scale the data, each value of the predictor variable is divided by its standard deviation. Scaling the data coerce the values to have a common standard deviation of one. These manipulations are generally used to improve the numerical stability of some calculations, such as PLS. The only real downside to these transformation is a loss of interpretability of the individual values." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Transformations to Resolve Skewness" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An un-skewed distribution is one that is roughly symmetric. A rule of thumb to consider is that skewed data whose ratio of the highest value to the lowest value is greater than 20 have significant skewness. The sample skewness statistic is defined $$\\text{skewness} = {\\sum (x_i - \\bar{x})^3 \\over (n - 1) v^{3/2}},$$ where $$v = {\\sum (x_i - \\bar{x})^2 \\over (n - 1)}.$$ Note that the skewness for a normal distribution is zero." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cell segmentation data contain a predictor that measures the standard deviation of the intensity of the pixels in the actin filaments." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "# Some nice default configuration for plots\n", "plt.rcParams['figure.figsize'] = 10, 7.5\n", "plt.rcParams['axes.grid'] = True\n", "plt.gray()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, (ax1, ax2, ax3) = plt.subplots(1, 3)\n", "\n", "ax1.hist(cell_train['VarIntenCh3'].values, bins=20)\n", "ax1.set_xlabel('Natural Units')\n", "ax1.set_ylabel('Count')\n", "\n", "ax2.hist(np.log(cell_train['VarIntenCh3'].values), bins=20)\n", "ax2.set_xlabel('Log Units')\n", "\n", "ax3.hist(np.sqrt(cell_train['VarIntenCh3'].values), bins=20)\n", "ax3.set_xlabel('Square Root Units')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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BfPFq4HH59WOB89x9u7tvBW4GDq2rryJV03gQ2ZkyZiIlTJOnMbN54GJ3P7Cg7WKyD59z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\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram shows a strong right skewness. The log transformation seems to work well for this dataset. The ratio of the smallest to largest value and the sample skewness statistic all agree with the histogram under natural units." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import skew\n", "\n", "r = np.max(cell_train['VarIntenCh3'].values)/np.min(cell_train['VarIntenCh3'].values)\n", "skewness = skew(cell_train['VarIntenCh3'].values)\n", "\n", "print 'Ratio of the smallest to largest value is {0} \\nSample skewness statistic is {1}'.format(r, skewness)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ratio of the smallest to largest value is 870.887247203 \n", "Sample skewness statistic is 2.39518418124\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, statistical models can be used to empirically identify an appropriate transformation. One of the most famous transformations is the Box-Cox family, i.e.\n", "\\begin{equation}\n", "x^* = \\begin{cases} {x^{\\lambda}-1 \\over \\lambda} & \\text{if} \\ \\lambda \\neq 0 \\\\ log(x) & \\text{if} \\ \\lambda = 0 \\end{cases}\n", "\\end{equation}\n", "This family covers the log ($\\lambda = 0$), square ($\\lambda = 2$), square root ($\\lambda = 0.5$), inverse ($\\lambda = -1$), and others in-between. Using the training data, $\\lambda$ can be estimated using maximum likelihood estimation (MLE). This procedure would be applied independently to each predictor data that contain values **greater than 0**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The boxcox() in *scipy.stats* finds the estimated lambda and performs the transformation at the same time." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import boxcox\n", "\n", "print 'Estimated lambda is {0}'.format(boxcox(cell_train['VarIntenCh3'].values)[1])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Estimated lambda is 0.121531937325\n" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take another predictor for example." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.hist(cell_train['PerimCh1'].values, bins=20)\n", "ax1.set_xlabel('Natural Units')\n", "ax1.set_ylabel('Count')\n", "\n", "ax2.hist(boxcox(cell_train['PerimCh1'].values)[0], bins=20)\n", "ax2.set_xlabel('Transformed Data (lambda = {:1.4f})'.format(boxcox(cell_train['PerimCh1'].values)[1]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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O4wEAAPRKVI3bS83sWjN7l5ltqdY9WNKttTa3qvzkbcBSdIBWDKmegL5gTPIc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\nAACAnmDiBgAA0BNM3DC16mjOf1Rb/h0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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.3 Data Transformations for Multiple Predictors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These transformations act on groups of predictors, typically the entire set under consideration. Of primary importance are methods to resolve outliers and reducce the dimension of the data." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Transformations to Resolve Outliers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generally define outliers as samples that are exceptionally far from the mainstream of the data. Even with a thorough understanding of the data, outliers can be hard to define. However, we can often identify an unusual value by looking at a figure. When one or more samples are suspected to be outliers, the first step is to make sure that the values are scientifically valid and that no data recording errors have occured. Great care should be taken not to hastily remove or change values, especially if the sample size is small. With small sample sizes, apparent outliers might be a result of a skewed distribution where there are not yet enough data to see the skewness. Also, the outlying data may be an indication of a special part of the population under study that is just starting to be sampled. Depending on how the data were collected, a \"cluster\" of valid points that reside outside the mainstream of the data might belong to a different population than the other samples, e.g. *extrapolation* and *applicability domain*. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several predictive models that are resistant to outliers, e.g.\n", "- Tree based classification models: creat splits of the training set.\n", "- Support Vector Machines (SVM) for classification: disregard a portion if tge training set that may be far away from the decision boundary." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If a model is considered to be sensitive to outliers, one data transformation that can minimize the problem is the *spatial sign*. Mathematically, each sample is divided by its squared norm: $$x_{ij}^* = {x_{ij} \\over \\sqrt{\\sum_{j=1}^p x_{ij}^2}}.$$ Since the denominator is intended to measure the squared distance to the center of the predictor's distribution, it is **important** to center and scale the predictor data prior to using this transformation. Note that, unlike centering and scaling, this manipulation of the predictors transform them as a group. Removing predictor variables after applying the spatial sign transformation may be problematic." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# toy example\n", "beta0 = -2.3 # intercept\n", "beta1 = 0.8 # slope\n", "n = 1000\n", "x1_true = np.random.normal(4, 2, n)\n", "x2_true = np.zeros(n)\n", "\n", "# generate a random sample\n", "for i in xrange(n):\n", " x2_true[i] = beta0 + beta1*x1_true[i] + np.random.normal(size = 1)\n", " \n", "# generate outliers\n", "x1_outliers = np.random.uniform(-4, -3, 8)\n", "x2_outliers = np.zeros(8)\n", "for i in xrange(8):\n", " x2_outliers[i] = x1_outliers[i] + np.random.normal(size = 1)\n", "\n", "plt.scatter(x1_true, x2_true)\n", "plt.plot(x1_outliers, x2_outliers, 'ro', markersize=8)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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AmfKSTorpqFiLts3rONNsSSE77HoE0JFXTbfKFITDS5VrGuvG4z2689Ztk01w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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.preprocessing import scale\n", "x1 = scale(np.concatenate([x1_true, x1_outliers]))\n", "x2 = scale(np.concatenate([x2_true, x2_outliers]))\n", "x = np.array(zip(x1, x2))\n", "\n", "# spatial sign\n", "dist = x[:, 0]**2 + x[:, 1]**2\n", "x1 = x[:, 0]/np.sqrt(dist)\n", "x2 = x[:, 1]/np.sqrt(dist)\n", "\n", "plt.scatter(x1[:-8], x2[:-8])\n", "plt.plot(x1[-7:], x2[-7:], 'ro', markersize=8)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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uYtcudV7ujeounKeYO08x78xOqiLAfXTMeBVjLzP+dkj2Z1TMU4OSLhmwyspt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\nvYgkPdM0mTOnmEhkAwDPPlvMjh3V7Nq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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *spatial sign* transformation brings the outliers towards the majority of the data." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Data Reduction and Feature Extraction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These methods reduce the data by generating a smaller set of predictors that seek to capture a majority of the information in the original variables. For most data reduction techniques, the new predictors are functions of the original predictors; therefore, all the original predictors are still needed to create the surrogate variables. This class of methods is often called *signal extraction* or *feature extraction* techniques." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Principal component analysis (PCA) seeks to find linear combinations of the predictors, known as principal components (PCs), which capture the most possible variance. The first PC is defined as the linear combination of the predictors that captures the most variability of all possible linear combinations. Then, subsequent PCs are derived such that these linear combinations capture the most remaining variability while also being uncorrelated with all previous PCs. Mathematically, \n", "$$\\text{PC}_j = (a_{j1} \\times \\text{Predictor 1}) + \\cdots + (a_{jP} \\times \\text{Predictor P}).$$\n", "P is the number of predictors. The coefficients $a_{j1}, \\cdots, a_{jP}$ are called component weights and help us understand which predictors are most important to each PC." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us look at an example from the previous dataset." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cell_train_subset = cell_train[['Class', 'FiberWidthCh1', 'EntropyIntenCh1']]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "colors = ['b', 'r']\n", "markers = ['s', 'o']\n", "c = ['PS', 'WS']\n", "for k, m in enumerate(colors):\n", " i = (cell_train_subset['Class'] == c[k])\n", " if k == 0:\n", " plt.scatter(cell_train_subset['FiberWidthCh1'][i], cell_train_subset['EntropyIntenCh1'][i], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='PS')\n", " else:\n", " plt.scatter(cell_train_subset['FiberWidthCh1'][i], cell_train_subset['EntropyIntenCh1'][i], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='WS')\n", "\n", "plt.title('Original Data')\n", "plt.xlabel('Channel 1 Fiber Width')\n", "plt.ylabel('Entropy intensity of Channel 1')\n", "plt.legend(loc='upper right')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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SrfWABEwp1ejpE2qtzymlvg8cB64A67TWGzw9nhBDqdq0iRzD4C6rlcz4eKoO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\nhzG1Od3PxYw8GEx1VqVpv6lj2m5mMZ2vD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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate PCs" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.decomposition import PCA\n", "\n", "pca = PCA()\n", "pca.fit(cell_train_subset[['FiberWidthCh1', 'EntropyIntenCh1']])\n", "print 'variance explained by PCs {0}'.format(pca.explained_variance_ratio_)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "variance explained by PCs [ 0.96900659 0.03099341]\n" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first PC summarizes 97% of the original variability, while the second summarizes 3%. Hence, it is reasonable to use only the first PC for modeling since it accounts for the majority of the information in the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cell_train_subset_pca = pca.transform(cell_train_subset[['FiberWidthCh1', 'EntropyIntenCh1']])\n", "\n", "colors = ['b', 'r']\n", "markers = ['s', 'o']\n", "c = ['PS', 'WS']\n", "for k, m in enumerate(colors):\n", " i = np.where(cell_train_subset['Class'] == c[k])[0]\n", " if k == 0:\n", " plt.scatter(cell_train_subset_pca[i, 0], cell_train_subset_pca[i, 1], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='PS')\n", " else:\n", " plt.scatter(cell_train_subset_pca[i, 0], cell_train_subset_pca[i, 1], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='WS')\n", "\n", "plt.title('Transformed')\n", "plt.xlabel('Principal Component #1')\n", "plt.ylabel('Principal Component #2')\n", "plt.legend(loc='upper right')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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8P/+FG5cdRVFNCWnMSVnMoUPnSEzcSW7urV6e8sv7SK66wtYNjwBQWFBAocEw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\nFosczWhzdjxNOMej8Omdbm1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3fAFlWgunVB0lUQvRZn0Wsy2PRx/d5kpCkpNvza0qv7yP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\n4s03x60o4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vePHTO4xbkVMhHvZ4z4zZ1bKXbzFUPzdcufi/iaGL/pyqIvVlWxY88eTKbE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\nxnXq7f07zZv3xZH73367WyeeNk9rB5dr2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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The primary advantage of PCA is that it creates components that are uncorrelated. PCA preprocessing creates new predictors with desirable characteristics for models that prefer predictors to be uncorrelated." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While PCA delivers new predictors with desirable characteristics, it must be used with understanding and care. PCA seeks predictor-set variation without regard to any further understanding of the predictors (i.e. measurement scales or distributions) or to knowledge of the modeling objectives (i.e. response variable). Hence, without proper guidance, PCA can generate components that summarize characteristics of the data that are irrelevant to the underlying structure of the data and also to the ultimate modeling objectives." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA was applied to the entire set of segmentation data predictors." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cell_train.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ " Unnamed: 0 Cell Case Class AngleCh1 AngleStatusCh1 AreaCh1 \\\n", "1 2 207932307 Train PS 133.752037 0 819 \n", "2 3 207932463 Train WS 106.646387 0 431 \n", "3 4 207932470 Train PS 69.150325 0 298 \n", "11 12 207932484 Train WS 109.416426 0 256 \n", "14 15 207932459 Train PS 104.278654 0 258 \n", "\n", " AreaStatusCh1 AvgIntenCh1 AvgIntenCh2 ... VarIntenCh1 \\\n", "1 1 31.923274 205.878517 ... 18.809225 \n", "2 0 28.038835 115.315534 ... 17.295643 \n", "3 0 19.456140 101.294737 ... 13.818968 \n", "11 0 18.828571 125.938776 ... 13.922937 \n", "14 0 17.570850 124.368421 ... 12.324971 \n", "\n", " VarIntenCh3 VarIntenCh4 VarIntenStatusCh1 VarIntenStatusCh3 \\\n", "1 56.715352 118.388139 0 0 \n", "2 37.671053 49.470524 0 0 \n", "3 30.005643 24.749537 0 0 \n", "11 18.643027 40.331747 0 0 \n", "14 17.747143 41.928533 0 0 \n", "\n", " VarIntenStatusCh4 WidthCh1 WidthStatusCh1 XCentroid YCentroid \n", "1 0 32.161261 1 215 347 \n", "2 0 21.185525 0 371 252 \n", "3 2 13.392830 0 487 295 \n", "11 2 17.546861 0 211 495 \n", "14 2 17.660339 0 172 207 \n", "\n", "[5 rows x 120 columns]" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "cell_train_feature = cell_train.iloc[:, 4:]\n", "cell_train_feature.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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AngleCh1AngleStatusCh1AreaCh1AreaStatusCh1AvgIntenCh1AvgIntenCh2AvgIntenCh3AvgIntenCh4AvgIntenStatusCh1AvgIntenStatusCh2...VarIntenCh1VarIntenCh3VarIntenCh4VarIntenStatusCh1VarIntenStatusCh3VarIntenStatusCh4WidthCh1WidthStatusCh1XCentroidYCentroid
1 133.752037 0 819 1 31.923274 205.878517 69.916880 164.153453 0 0... 18.809225 56.715352 118.388139 0 0 0 32.161261 1 215 347
2 106.646387 0 431 0 28.038835 115.315534 63.941748 106.696602 0 0... 17.295643 37.671053 49.470524 0 0 0 21.185525 0 371 252
3 69.150325 0 298 0 19.456140 101.294737 28.217544 31.028070 0 0... 13.818968 30.005643 24.749537 0 0 2 13.392830 0 487 295
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ " AngleCh1 AngleStatusCh1 AreaCh1 AreaStatusCh1 AvgIntenCh1 \\\n", "1 133.752037 0 819 1 31.923274 \n", "2 106.646387 0 431 0 28.038835 \n", "3 69.150325 0 298 0 19.456140 \n", "11 109.416426 0 256 0 18.828571 \n", "14 104.278654 0 258 0 17.570850 \n", "\n", " AvgIntenCh2 AvgIntenCh3 AvgIntenCh4 AvgIntenStatusCh1 \\\n", "1 205.878517 69.916880 164.153453 0 \n", "2 115.315534 63.941748 106.696602 0 \n", "3 101.294737 28.217544 31.028070 0 \n", "11 125.938776 13.600000 46.800000 0 \n", "14 124.368421 22.461538 71.206478 0 \n", "\n", " AvgIntenStatusCh2 ... VarIntenCh1 VarIntenCh3 \\\n", "1 0 ... 18.809225 56.715352 \n", "2 0 ... 17.295643 37.671053 \n", "3 0 ... 13.818968 30.005643 \n", "11 0 ... 13.922937 18.643027 \n", "14 0 ... 12.324971 17.747143 \n", "\n", " VarIntenCh4 VarIntenStatusCh1 VarIntenStatusCh3 VarIntenStatusCh4 \\\n", "1 118.388139 0 0 0 \n", "2 49.470524 0 0 0 \n", "3 24.749537 0 0 2 \n", "11 40.331747 0 0 2 \n", "14 41.928533 0 0 2 \n", "\n", " WidthCh1 WidthStatusCh1 XCentroid YCentroid \n", "1 32.161261 1 215 347 \n", "2 21.185525 0 371 252 \n", "3 13.392830 0 487 295 \n", "11 17.546861 0 211 495 \n", "14 17.660339 0 172 207 \n", "\n", "[5 rows x 116 columns]" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because PCA seeks linear combinations of predictors that maximize variability, it will naturally first be drawn to summarizing predictors that have more variation. If the original predictors are on measurement scales that differ in orders of magnitude or have skewed distributions, PCA will be focusing its efforts on identifying the data structure based on measurement scales and distributional difference rather than based on the important relationships within the data for the current problem. Hence, it is best to first transform skewed predictors and then center and scale the predictors prior to performing PCA." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Box-Cox transformation on positive predictors\n", "# separate positive and non-positive predictors\n", "pos_indx = np.where(cell_train_feature.apply(lambda x: np.all(x > 0)))[0]\n", "cell_train_feature_pos = cell_train_feature.iloc[:, pos_indx]\n", "print \"# of positive features is {0}\".format(pos_indx.shape[0])\n", "cell_train_feature_nonpos = cell_train_feature.drop(cell_train_feature.columns[pos_indx], axis=1, inplace=False)\n", "print \"# of npn-positive features is {0}\".format(cell_train_feature.shape[1] - pos_indx.shape[0])\n", "\n", "cell_train_feature_pos_tr = cell_train_feature_pos.apply(lambda x: boxcox(x)[0])\n", "\n", "cell_train_feature_tr = np.c_[cell_train_feature_pos_tr, cell_train_feature_nonpos]\n", "print \"The shape before/after transformation is {0} and {1}\".format(cell_train_feature.shape, cell_train_feature_tr.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "# of positive features is 47\n", "# of npn-positive features is 69\n", "The shape before/after transformation is (1009, 116) and (1009, 116)" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "# scale and center predictors\n", "from sklearn.preprocessing import scale\n", "\n", "cell_train_feature_tr = scale(cell_train_feature_tr, with_mean=True, with_std=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second caveat of PCA is that it does not consider the modeling obejective or response variable when summarizing variability -- it is an *unsupervised technique*. If the predictive relationship between the predictors and response is not connected to the predictors' variability, then the derived PCs will not provide a suitable relationship with the response. In this case, a *supervised technique*, like PLS will derive components while simultaneously considering the corresponding response." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To decide how many components to retain after PCA, a heuristic approach is to create a scree plot, which contains the ordered component number (x-axis) and the ammount of summarized variability (y-axis). Generally, the component number prior to the tapering off of variation is the maximal component that is retained. In an automated model building process, the optimal number of components can be determined by cross-validation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# conduct PCA to transformed predictors\n", "from sklearn.decomposition import PCA\n", "\n", "pca = PCA()\n", "pca.fit(cell_train_feature_tr)\n", "\n", "# generate scree plot\n", "plt.plot(pca.explained_variance_ratio_)\n", "plt.xlabel('Percent of Total Variance')\n", "plt.ylabel('Component')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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QMfPyzLw8My/PzOtnag/fe0POcOj4tQsXLmTevHkAzJ07l7333vvJX8TMxVxyCey7b7Xe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\nOzCsXdvvUUqSJIs2PemZz6y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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "print \"The first four components account for {0} of the total variance\".format(pca.explained_variance_ratio_[:4])\n", "print \"All together they account for {0} of the total variance\".format(np.sum(pca.explained_variance_ratio_[:4]))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The first four components account for [ 0.14015262 0.12569721 0.09394676 0.06393814] of the total variance\n", "All together they account for 0.42373472472 of the total variance\n" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visually examining the principal components is a critical step for assessing data quality and gaining intuition for the problem. To do this, the first few PCs can be plotted against each other and the plot symbols can be colored by the relevant characteristics, such as the class labels. If PCA has captured a sufficient amount of the information in the data, this type of plot can demonstrate clusters of samples or outliers that may prompt a closer examination of the individual data points. Note that the scale of the components tend to become smaller as they account for less and less variation in the data. If axes are displayed on separate scales, there is the potential to over-interpret any patterns that might be seen for components that account for small amounts of variation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# look at the first 3 PCs\n", "pca = PCA(n_components=3)\n", "cell_train_feature_pca = pca.fit_transform(cell_train_feature_tr)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "colors = ['b', 'r']\n", "markers = ['s', 'o']\n", "c = ['PS', 'WS']\n", "\n", "fig, axarr = plt.subplots(3, 3, sharex=True, sharey=True)\n", "\n", "# PC1 vs PC3\n", "for k, m in enumerate(colors):\n", " i = np.where(cell_train['Class'] == c[k])[0]\n", " if k == 0:\n", " line1= axarr[0,0].scatter(cell_train_feature_pca[i, 0], cell_train_feature_pca[i, 2], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='PS')\n", " else:\n", " line2= axarr[0,0].scatter(cell_train_feature_pca[i, 0], cell_train_feature_pca[i, 2], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='WS')\n", "\n", "# PC2 vs PC3\n", "for k, m in enumerate(colors):\n", " i = np.where(cell_train['Class'] == c[k])[0]\n", " if k == 0:\n", " axarr[0,1].scatter(cell_train_feature_pca[i, 1], cell_train_feature_pca[i, 2], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='PS')\n", " else:\n", " axarr[0,1].scatter(cell_train_feature_pca[i, 1], cell_train_feature_pca[i, 2], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='WS')\n", "\n", "# PC1 vs PC2\n", "for k, m in enumerate(colors):\n", " i = np.where(cell_train['Class'] == c[k])[0]\n", " if k == 0:\n", " axarr[1,0].scatter(cell_train_feature_pca[i, 0], cell_train_feature_pca[i, 1], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='PS')\n", " else:\n", " axarr[1,0].scatter(cell_train_feature_pca[i, 0], cell_train_feature_pca[i, 1], \n", " c=m, marker=markers[k], alpha=0.4, s=26, label='WS')\n", "\n", "axarr[2,0].text(0.5, -1.0, 'PC1', ha='center', va='center', fontsize=24) \n", "axarr[1,1].text(0.5, -1.0, 'PC2', ha='center', va='center', fontsize=24) \n", "axarr[0,2].text(0.5, -1.0, 'PC3', ha='center', va='center', fontsize=24)\n", "fig.legend([line1, line2], ('PS', 'WS'), loc='upper center', ncol=2, frameon=False)\n", "fig.subplots_adjust(hspace=0.12, wspace=0.1)\n", "fig.text(0.5, 0.06, 'Scatter Plot Matrix', ha='center', va='center', fontsize=18)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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P3TpJxOniOnoYS5wqwtTRRowUpZgQJxvIxCVKguuBFjyk6GcrpmV1P+YS5YvA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\n4hnfzczMzArg3y40GyaPSbGUOf8tVa04T5aZmZlZkpJrZKXSd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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the percentages of variation explained are not large for the first three components, it is important not to over-interpret the resulting image. From this plot, there appears to be some separation between the classes when plotting the first and second components. However, the distribution of the well-segmented cells is roughly contained within the distribution of the poorly identified cells. One conclusion is that the cell types are not easily separated." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another exploratory use of PCA is characterizing which predictors are associated with each component. Recall that each component is a linear combination of the predictors and the coefficient for each predictor is called the loading. Loadings close to zero indicate that the predictor variable did not contribute much to that component." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# loadings\n", "pca.components_.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "(3, 116)" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.4 Dealing with Missing Values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In many cases, some predictors have no values for a given sample. It is important to understand *why* the values are missing. First and foremost, it is important to know if the pattern of missing data is related to the outcome. This is called *informative missingness* since the missing data pattern is instructional on its own. Informative missingness can induce significant bias in the model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Missing data should not be confused with *censored* data where the exact value is missing but something is known about its value. When building traditional statistical models focused on interpretation or inference, the censoring is usually taken in to account in a formal manner by making assumptions about the censoring mechanism. For predictive models, it is more common to treat these data as simple missing data or use the censored value as the observed value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Missing values are more often related to predictive variables than the sample. Because of this, amount of missing data may be concentrated in a subset of predictors rather than occuring randomly across all the predictors. In some cases, the percentage of missing data is substantial enough to remove this predictor from subsequent modeling activities." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are cases where the missing values might be concentrated in specific samples. For large datasets, removal of samples based on missing values is not a problem, assuming that the missingness is not informative. In smaller datasets, there is a steep price in removing samples; some of alternative approaches described below may be more appropriate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we do not remove the missing data, there are two general approaches. First, a few predictive models, especially tree-based techniques, can specifically account for missing data. Alternatively, missing data can be imputed. In this case, we can use information in the training set predictors to, in essence, estimate the values of other predictors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Imputation is just another layer of modeling where we try to estimate values of the predictor variables based on other predictor variables. The most relevant scheme for accomplishing this is to use the training set to built an imputation model for each predictor in the daa set. Prior to model training or the prediction of new samples, missing values are filled in using imputation. Note that this extra layer of models adds uncertainty. If we are using resampling to select tuning parameter values or to estimate performance, the imputation should be incorporated within the resampling. This will increase the computational time for building models, but it will also provide honest estimates of model performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the number of predictors affected by missing values is small, an exploratory analysis of the relationships between the preditors is a good idea. For example, visulization or methods like PCA can be used to determine if there are strong relationships between the predictors. If a variable with missing values is highly correlated with another predictor that has few missing values, a focused model can often be effective for imputation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One popular technique for imputation is a $K$-nearest neighbor model. A new sample is imputed by finding the samples in the training set \"closest\" to it and averages these nearby points to fill in the value. One advantage of this approach is that the imputed data are confined to be within the range of the training set values. One disadvantage is that the entire training set is required every time a missing value needs to be imputed. Also, the number of neighbors is a tuning parameter, as is the method for determining \"closeness\" of two points. However, Troyanskaya et al. (2001) found the nearest neighbor approach to be fairly robust to the tuning parameters, as well as the amount of missing data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# randomly sample 50 test set\n", "import random\n", "cell_test_subset = cell_test.iloc[np.sort(random.sample(range(cell_test.shape[0]), 50))]\n", "\n", "# separate features\n", "cell_test_subset_f = cell_test_subset.iloc[:, 4:].drop('VarIntenCh3', 1)\n", "cell_test_subset_v = cell_test_subset.iloc[:, 4:]['VarIntenCh3']\n", "cell_train_f = cell_train_feature.drop('VarIntenCh3', 1)\n", "cell_train_v = cell_train_feature['VarIntenCh3']" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "# scale and center before imputation\n", "from sklearn.preprocessing import StandardScaler\n", "\n", "# standardize based on training set\n", "sc_f = StandardScaler()\n", "cell_train_f_sc = sc_f.fit_transform(cell_train_f)\n", "cell_test_subset_f_sc = sc_f.transform(cell_test_subset_f)\n", "\n", "sc_v = StandardScaler()\n", "cell_train_v_sc = sc_v.fit_transform(cell_train_v)\n", "cell_test_subset_v_sc = sc_v.transform(cell_test_subset_v)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "# use 5-nearest neighbor\n", "from sklearn.neighbors import NearestNeighbors\n", "\n", "nbrs = NearestNeighbors(n_neighbors = 5)\n", "nbrs.fit(cell_train_f_sc) # based on training set\n", "distance, indices = nbrs.kneighbors(cell_test_subset_f_sc) # neighbors for test set\n", "\n", "# imputation\n", "cell_test_subset_v_pred_knn = np.empty(50)\n", "for idx, i in enumerate(indices):\n", " cell_test_subset_v_pred_knn[idx] = np.mean(cell_train_v_sc[i[1:]])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Find the predictor with highest correlation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats.stats import pearsonr\n", "\n", "print \"corr('VarIntenCh3', 'DiffIntenDensityCh3') is {0}\".format(pearsonr(cell_train_v, cell_train_f['DiffIntenDensityCh3'])[0])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "corr('VarIntenCh3', 'DiffIntenDensityCh3') is 0.894871504785\n" ] } ], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "# use linear model\n", "from sklearn.linear_model import LinearRegression\n", "\n", "lm = LinearRegression()\n", "lm.fit(cell_train_f_sc[:, cell_train_f.columns.get_loc('DiffIntenDensityCh3')][:, np.newaxis],\n", " cell_train_v_sc[:, np.newaxis]) # find the predictor with highest correlation\n", "cell_test_subset_v_pred_lm = \\\n", "lm.predict(cell_test_subset_f_sc[:, cell_train_f.columns.get_loc('DiffIntenDensityCh3')][:, np.newaxis])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Correlation between the real and imputed values" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print \"kNN: {0}\".format(pearsonr(cell_test_subset_v_sc, cell_test_subset_v_pred_knn)[0])\n", "print \"Linear Model: {0}\".format(pearsonr(cell_test_subset_v_sc[:, np.newaxis], cell_test_subset_v_pred_lm)[0][0])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "kNN: 0.869781133553\n", "Linear Model: 0.858789107105\n" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the better performance of linear model is because of the high correlation (0.895) between these two predictors. kNN is generally more robust since it takes all predictors into consideration." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.scatter(cell_test_subset_v_sc, cell_test_subset_v_pred_knn)\n", "ax1.set(xlim=(-1.5, 3), ylim=(-1.5, 3))\n", "ax1.plot(ax1.get_xlim(), ax1.get_ylim(), ls=\"--\", c=\".3\")\n", "ax1.set_title('5NN')\n", "\n", "ax2.scatter(cell_test_subset_v_sc, cell_test_subset_v_pred_lm)\n", "ax2.set(xlim=(-1.5, 3), ylim=(-1.5, 3))\n", "ax2.plot(ax2.get_xlim(), ax2.get_ylim(), ls=\"--\", c=\".3\")\n", "ax2.set_title('Linear Model')\n", "\n", "fig.text(0.5, 0.04, 'Original Value (centered and scaled)', ha='center', va='center')\n", "fig.text(0.06, 0.5, 'Imputed', ha='center', va='center', rotation='vertical')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 33, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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cZv78+QCAiRMn2twS92HNHZG9Kioq8Pzzz2PevHno2LGj3c1xlWj7L14tS66Q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\niUgx5dt/qbgTkURTcScicaUbKspQJcwFSHobFS/e8aQwST8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"text": [ "" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.5 Removing Predictors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are potential advantages to removing predictors prior to modeling. First, fewer predictors means decreased computational time and complexity. Second, if two predictors are highly correlated, this implies that they are measuring the same underlying information. Removing one should not compromise the performance of the model and might lead to a more parsimonious and interpretable model. Third, some models can be crippled by predictors with degenerate distributions, e.g. near-zero variance predictors. In these cases, there can be a significant improvement in model performance and/or stability without the problematic variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A rule of thumb for detecting near-zero variance predictors:\n", "- The fraction of unique values over the sample size is low (say 10%)\n", "- The ratio of the frequency of the most prevalent value to the frequency of the second most prevalent value is large (say around 20)\n", "\n", "If both of these criteria are true and the model in question is susceptible to this type of predictor, it may be advantageous to remove the variable from the model." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Between-Predictor Correlations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Collinearity* is the technical term for the situation where a pair of predictor variables have a substantial correlation with each other. It is also possible to have relationships between multiple predictors at once (called *multicollinearity*)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A direct visualization of the correlation matrix from the training set." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calculate the correlation matrix\n", "corr_dataframe = cell_train_feature.corr()\n", "\n", "# compute hierarchical cluster on both rows and columns for correlation matrix and plot heatmap \n", "def corr_heatmap(corr_dataframe):\n", " import scipy.cluster.hierarchy as sch\n", " \n", " corr_matrix = np.array(corr_dataframe)\n", " col_names = corr_dataframe.columns\n", " \n", " Y = sch.linkage(corr_matrix, 'single', 'correlation')\n", " Z = sch.dendrogram(Y, color_threshold=0, no_plot=True)['leaves']\n", " corr_matrix = corr_matrix[Z, :]\n", " corr_matrix = corr_matrix[:, Z]\n", " col_names = col_names[Z]\n", " im = plt.imshow(corr_matrix, interpolation='nearest', aspect='auto', cmap='bwr')\n", " plt.colorbar()\n", " plt.xticks(range(corr_matrix.shape[0]), col_names, rotation='vertical', fontsize=4)\n", " plt.yticks(range(corr_matrix.shape[0]), col_names[::-1], fontsize=4)\n", " \n", "# plot\n", "corr_heatmap(corr_dataframe)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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/df0DB/QEHTWKxMfBLbfA6uiATEgAfvIT+pz2RLaOHIGcORPq819w+imlhLjR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\nSRS75j2s4IvDxRYano5MdLB7cWILE4k9GCY7ER/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re9MFABdaKXDExpEkRdP2NyezjHCs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\n0aNDuI/OntX1MZY925/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9JiHEeCHEvUKINQOdAyDEdXI9PF3cpcJxCzExXdzfP0RdYjFy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\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rpJSPSSmflVIekFIWSymfYfr/lVKulFK+LqXcZaU/Y6U9LaV8QkpZbf2vRkurttLsMguh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\n49ABbrefDmkEjxzJgXy2+45Dsnx39xPu/iY4IM7IL2fsNpN4VBYQzxPxN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"text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the predictor variables have been grouped using a clustering technique so that collinear groups of predictors are adjacent to one another." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the data set consists of too many predictors to examine visually, techniques such as PCA can be used to characterize the magnitude of the problem. For example, if the first principal component accounts for a large percentage of the variance, this implies that there is at least one group of predictors that represent the same information. The PCA loadings can be used to understand which predictors are associated with each component to tease out this relationship." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, there are good reasons to avoid data with highly correlated predictors. First, redundant predictors frequently add more complexity to the model than information they provide to the model. In situations where obtaining the predictor data is costly, fewer variables is obviously better. Using highly correlated predictors in techniques like linear regression can result in highly unstable models, numerical values, and degraded predictive performances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Classical regression analysis has several tools to diagnose multicollinearity for linear regression. A statistic called the variance inflation factor (VIF) can be used to identify predictors that are impacted. A common rule of thumb is that if VIF > 5, then multicollinearity is high. Note that this method is developed for linear models, it requires more samples than predictor variables and it does not determine which should be removed to resolve the problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A more heuristic approach is to remove the minimum number of predictors to ensure that all pairwise correlation are below a certain threshold. The algorithm is as follows:\n", "- Calculate the correlation matrix of the predictors.\n", "- Determine the two predictors associated with the largest absolute pairwise correlation (A and B).\n", "- Determine the average absolute correlation between A and the other variables. Do the same for predictor B.\n", "- If A has a larger average correlation, remove it; otherwise, remove predictor B.\n", "- Repeat Steps 2-4 until no absolute correlations are above the threshold.\n", "\n", "Suppose we wanted to use a model that is particularly sensitive to between predictor correlations, we might apply a threshold of 0.75." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As previously mentioned, feature extraction methods (e.g., principal components) are another technique for mitigating the effect of strong correlations between predictors. However, these techniques make the connection between the predictors and the outcome more complex. Additionally, since signal extraction methods are usually unsupervised, there is no guarantee that the resulting surrogate preditors have any relationship with the outcome." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.6 Adding Predictors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When a predictor is categorical, it is common to decompose the predictor into a set of more specific variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at the following example for the credit scoring data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "!ls -l ../datasets/GermanCredit/" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total 480\r\n", "-rw-r--r-- 1 leigong staff 244776 Nov 24 15:58 GermanCredit.csv\r\n" ] } ], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "credit_data = pd.read_csv(\"../datasets/GermanCredit/GermanCredit.csv\")\n", "credit_data.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ " Unnamed: 0 Duration Amount InstallmentRatePercentage ResidenceDuration \\\n", "0 1 6 1169 4 4 \n", "1 2 48 5951 2 2 \n", "2 3 12 2096 2 3 \n", "3 4 42 7882 2 4 \n", "4 5 24 4870 3 4 \n", "\n", " Age NumberExistingCredits NumberPeopleMaintenance Telephone \\\n", "0 67 2 1 0 \n", "1 22 1 1 1 \n", "2 49 1 2 1 \n", "3 45 1 2 1 \n", "4 53 2 2 1 \n", "\n", " ForeignWorker ... OtherInstallmentPlans.Bank \\\n", "0 1 ... 0 \n", "1 1 ... 0 \n", "2 1 ... 0 \n", "3 1 ... 0 \n", "4 1 ... 0 \n", "\n", " OtherInstallmentPlans.Stores OtherInstallmentPlans.None Housing.Rent \\\n", "0 0 1 0 \n", "1 0 1 0 \n", "2 0 1 0 \n", "3 0 1 0 \n", "4 0 1 0 \n", "\n", " Housing.Own Housing.ForFree Job.UnemployedUnskilled \\\n", "0 1 0 0 \n", "1 1 0 0 \n", "2 1 0 0 \n", "3 0 1 0 \n", "4 0 1 0 \n", "\n", " Job.UnskilledResident Job.SkilledEmployee \\\n", "0 0 1 \n", "1 0 1 \n", "2 1 0 \n", "3 0 1 \n", "4 0 1 \n", "\n", " Job.Management.SelfEmp.HighlyQualified \n", "0 0 \n", "1 0 \n", "2 0 \n", "3 0 \n", "4 0 \n", "\n", "[5 rows x 63 columns]" ] } ], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "credit_data.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "(1000, 63)" ] } ], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predictor based on how much money was in the applicant's saving account is categorical coded into dummy variables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "credit_data_saving = credit_data[['SavingsAccountBonds.lt.100', 'SavingsAccountBonds.100.to.500', \n", " 'SavingsAccountBonds.500.to.1000', 'SavingsAccountBonds.gt.1000', \n", " 'SavingsAccountBonds.Unknown']]\n", "credit_data_saving.head(10)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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