{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# LDA/QDA on height/weight data\n", "\n", "We're asked to fit a Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) model to the height/weight data and compute the the misclassification rate. See my implementation of these algorithms on [GitHub](https://github.com/ppham27/MLaPP-solutions/blob/master/chap04/DiscriminantAnalysis.py). The data can be found [here](https://github.com/ppham27/MLaPP-solutions/blob/master/chap04/heightWeightData.txt)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 210 entries, 0 to 209\n", "Data columns (total 3 columns):\n", "gender 210 non-null int64\n", "height 210 non-null int64\n", "weight 210 non-null int64\n", "dtypes: int64(3)\n", "memory usage: 5.0 KB\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " gender height weight\n", "0 1 67 125\n", "1 2 68 140\n", "2 2 67 142\n", "3 2 60 110\n", "4 2 64 97" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from matplotlib.colors import ListedColormap\n", "# benchmark sklearn implementations, these are much faster\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n", "# my own implementation, results are identical but runs much slower\n", "import DiscriminantAnalysis\n", "\n", "raw_data = pd.read_csv(\"heightWeightData.txt\", header=None, names=[\"gender\", \"height\", \"weight\"])\n", "raw_data.info()\n", "raw_data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the data, coloring males blue and females red, too." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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F2KOI2tgni/En2aQoi/FnnZK8iDQkzEz5Wq2twSVwvh3BR/28sqhIsRSVavIi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\nCLmjjneSD402nQlzVBrm9dUzDC+8cGh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "labels = {1: 'Male', 2: 'Female'}\n", "colors = {1: 'blue', 2: 'red'}\n", "def plot_height_weight(title=\"Weight vs Height\", ax=None):\n", " if ax == None:\n", " ax = plt.gca()\n", " for name, group in raw_data.groupby('gender'):\n", " ax.scatter(group.height, group.weight, color=colors[name], label=labels[name])\n", " ax.set_title(title)\n", " ax.set_xlabel('height')\n", " ax.set_ylabel('weight')\n", " ax.legend(loc='upper left')\n", " ax.grid()\n", "plot_height_weight()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's define a few globals to help with the plotting and model fitting." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x_min = 50\n", "x_max = 85\n", "y_min = 50\n", "y_max = 300\n", "X = raw_data[['height', 'weight']].as_matrix()\n", "y = raw_data['gender'].as_matrix()\n", "xx, yy = np.meshgrid(np.linspace(x_min, x_max, num=200, endpoint=True),\n", " np.linspace(y_min, y_max, num=200, endpoint=True))\n", "cmap_light = ListedColormap(['#AAAAFF','#FFAAAA'])\n", "def plot_height_weight_mesh(xx, yy, Z, comment=None, title=None, ax=None):\n", " if ax == None:\n", " ax = plt.gca()\n", " ax.pcolormesh(xx, yy, Z, cmap=cmap_light)\n", " if title == None:\n", " plot_height_weight(ax=ax)\n", " else:\n", " plot_height_weight(ax=ax, title = title)\n", " ax.set_xlim([x_min, x_max])\n", " ax.set_ylim([y_min, y_max])\n", " if comment != None:\n", " ax.text(0.95, 0.05, comment, transform=ax.transAxes,\n", " verticalalignment=\"bottom\", horizontalalignment=\"right\",\n", " fontsize=14)\n", "def decimal_to_percent(x, decimals=2):\n", " return '{0:.2f}%'.format(np.round(100*x, decimals=2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try the QDA model first. We follow the conventions of the `sklearn` implementation. Let $X$ be our data or design matrix and $y$ be our class label. The rows of $X$ consist of the vectors $\\mathbf{x}_i$, which are the individual observations. We let $y_i \\sim \\mathrm{Multinomial}\\left(\\theta_1,\\ldots,\\theta_K\\right)$, where $\\sum_{k=1}^K \\theta_k = 1$. We let $\\mathbf{x}_i \\mid y_i = k \\sim \\mathcal{N}\\left(\\mathbf{\\mu}_k, \\Sigma_k\\right)$, which is a multivariate normal. We use the following estimates for the parameters:\n", "\n", "\\begin{align}\n", "\\hat{\\theta}_k &= \\frac{N_k}{N} \\\\\n", "\\hat{\\mu}_k &= \\frac{1}{N_k}\\sum_{\\{i~:~ y_i = k\\}}\\mathbf{x}_i \\\\\n", "\\hat{\\Sigma}_k &= \\frac{1}{N_k - 1}\\sum_{\\{i~:~y_i = k\\}} \\left(\\mathbf{x}_i - \\hat{\\mu}_k\\right)\\left(\\mathbf{x}_i - \\hat{\\mu}_k\\right)^\\intercal.\n", "\\end{align}\n", "\n", "$N$ is total number of observations, and $N_k$ is the number of observations of class $k$. Thus, for each class $k$, we compute the proportion of observations that are of that class, the sample mean, and the unbiased estimate for covariance." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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21m6Enj8E0hec1ACvZBzWktomGVzPSyn+RKmbUDIuxt634E7C6YI7Ln7++SrK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\nNJIXcZhG8CLlTTl5EYepkxeJDuXkRWRI6thF3KG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# qda = QuadraticDiscriminantAnalysis(store_covariances=True) # sklearn implementation\n", "qda = DiscriminantAnalysis.QDA() # my implementation\n", "qda.fit(X, y)\n", "qda_misclassification = 1 - qda.score(X, y)\n", "qda_Z = qda.predict(np.c_[xx.ravel(), yy.ravel()])\n", "qda_Z = qda_Z.reshape(xx.shape)\n", "plt.figure(figsize=(8,8))\n", "plot_height_weight_mesh(xx, yy, qda_Z, title=\"Weight vs Height: QDA\",\n", " comment=\"Misclassification rate: \" + decimal_to_percent(qda_misclassification))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at LDA now. We compute $\\hat{\\theta}_k$ and $\\hat{\\mu}_k$ in the same manner. However, now we have that all covariances are equal, that is, $\\hat{\\Sigma} = \\hat{\\Sigma}_k$ for all $k$. Let $p$ be the number of features, that is, the number of columns in $X$. First, we note that\n", "\n", "\\begin{align}\n", "\\log p\\left(\\mathcal{D} \\mid \\boldsymbol\\mu, \\Sigma,\\boldsymbol\\theta\\right)\n", "&= \\sum_{i=1}^N \\log p\\left(\\mathbf{x}_i,y_i \\mid \\boldsymbol\\mu, \\Sigma,\\boldsymbol\\theta\\right)\n", "= \\sum_{k = 1}^K \\sum_{\\{i~:~y_i = k\\}} \\log p\\left(\\mathbf{x}_i, y_i = k \\mid \\mu_k, \\Sigma, \\theta_k\\right) \\\\\n", "&= \\sum_{k = 1}^K \\sum_{\\{i~:~y_i = k\\}} \\left[\\log p(y_i = k) + \\log p\\left(\\mathbf{x}_i \\mid \\mu_k, \\Sigma, y_i=k\\right)\\right] \\\\\n", "&= \\sum_{k = 1}^K \\sum_{\\{i~:~y_i = k\\}} \\left[\\log \\theta_k - \\frac{p}{2}\\log 2\\pi - \\frac{1}{2}\\log|\\Sigma|\n", "- \\frac{1}{2}\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\Sigma^{-1}\\left(\\mathbf{x}_i - \\mu_k\\right)\\right] \\\\\n", "&= -\\frac{Np}{2}\\log 2\\pi -\\frac{N}{2}\\log|\\Sigma| + \\sum_{k = 1}^K \\left(N_k\\log\\theta_k - \\frac{1}{2}\\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\Sigma^{-1}\\left(\\mathbf{x}_i - \\mu_k\\right)\\right).\n", "\\end{align}\n", "\n", "Let $\\Lambda = \\Sigma^{-1}$. The MLE is invariant with regard to reparameterization, so after isolating the terms that involve $\\Sigma$ we can focus on maximizing\n", "\n", "\\begin{align}\n", "l(\\Lambda) &= \\frac{N}{2}\\log|\\Lambda| - \\frac{1}{2}\\sum_{k = 1}^K \\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\Lambda\\left(\\mathbf{x}_i - \\mu_k\\right) \\\\\n", "&= \\frac{N}{2}\\log|\\Lambda| - \\frac{1}{2}\\sum_{k = 1}^K \\sum_{\\{i~:~y_i = k\\}}\\operatorname{tr}\\left(\\left(\\mathbf{x}_i - \\mu_k\\right)\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\Lambda\\right),\n", "\\end{align}\n", "\n", "where we have used the fact that $\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\Sigma^{-1}\\left(\\mathbf{x}_i - \\mu_k\\right)$ is a scalar, so we can replace it with the trace, and then, we apply the fact that the trace remains the same after cyclic permutations.\n", "\n", "Now, we note these two identities to help us take the derivative with respect to $\\Lambda$,\n", "\n", "\\begin{align}\n", "\\frac{\\partial}{\\partial\\Lambda}\\log|\\Lambda| &= \\left(\\Lambda^{-1}\\right)^\\intercal \\\\\n", "\\frac{\\partial}{\\partial\\Lambda}\\operatorname{tr}\\left(A\\Lambda\\right) &= A^\\intercal.\n", "\\end{align}\n", "\n", "Thus, we'll have that\n", "\n", "\\begin{align}\n", "l^\\prime(\\Lambda) &= \\frac{N}{2}\\left(\\Lambda^{-1}\\right)^\\intercal - \\frac{1}{2}\\sum_{k=1}^K\\left(\\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\mu_k\\right)\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\right) \\\\\n", "&= \\frac{N}{2}\\Sigma - \\frac{1}{2}\\sum_{k=1}^K\\left(\\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\mu_k\\right)\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\right)\n", "\\end{align}\n", "\n", "since $\\Lambda^{-1} = \\Sigma$ and $\\Sigma$ is symmetric.\n", "\n", "Setting $l^\\prime(\\Lambda) = 0$ and solving for $\\Sigma$, we have that\n", "\n", "\\begin{equation}\n", "\\Sigma = \\frac{1}{N} \\sum_{k=1}^K\\left(\\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\mu_k\\right)\\left(\\mathbf{x}_i - \\mu_k\\right)^\\intercal\\right).\n", "\\end{equation}\n", "\n", "In this manner our estimate is\n", "\n", "\\begin{equation}\n", "\\hat{\\Sigma} = \\frac{1}{N} \\sum_{k=1}^K\\left(\\sum_{\\{i~:~y_i = k\\}}\\left(\\mathbf{x}_i - \\hat{\\mu}_k\\right)\\left(\\mathbf{x}_i - \\hat{\\mu}_k\\right)^\\intercal\\right).\n", "\\end{equation}\n", "\n", "For whatever reason, `sklearn` uses the biased MLE estimate for covariance in LDA, but it uses the unbiased estimate for covariance in QDA." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2iYiIVLJQc/LGmN2B3a21K4wxOwN/Aj4OnAa8bq39njHmG8B4a+25xpgDgZuA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\nPoGUl1T8rnI5dlD8ysn7p05eRMRRSV2AJ8VTTl5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# lda = LinearDiscriminantAnalysis(store_covariance=True) # sklearn implementation\n", "lda = DiscriminantAnalysis.LDA() # my implementation\n", "lda.fit(X, y)\n", "lda_misclassification = 1 - lda.score(X, y)\n", "lda_Z = lda.predict(np.c_[xx.ravel(), yy.ravel()])\n", "lda_Z = lda_Z.reshape(xx.shape)\n", "plt.figure(figsize=(8,8))\n", "plot_height_weight_mesh(xx, yy, lda_Z, title=\"Weight vs Height: LDA\",\n", " comment=\"Misclassification rate: \" + decimal_to_percent(lda_misclassification))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, we see that the two methods give us different decision boundaries. However, for these data, the misclassification rate is the same." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JJQ5QLBK2r34VLr0U9t/fTxr029/Ce9/bc5+99vITOTz6KHzmM91Xk8BfLZo7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,8))\n", "ax1 = fig.add_subplot(1,2,1)\n", "ax2 = fig.add_subplot(1,2,2)\n", "plot_height_weight_mesh(xx, yy, qda_Z, title=\"Weight vs Height: QDA\", ax=ax1,\n", " comment=\"Misclassification rate: \" + decimal_to_percent(qda_misclassification))\n", "plot_height_weight_mesh(xx, yy, lda_Z, title=\"Weight vs Height: LDA\", ax=ax2,\n", " comment=\"Misclassification rate: \" + decimal_to_percent(lda_misclassification))\n", "fig.suptitle('Comparison of QDA and LDA', fontsize=18)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }