{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 7. Dimensionality Reduction with PCA(Principal Component Analysis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## motivated by\n", " \n", "- first. mitigate problems caused by the curse of dimensionality\n", "- second. dimensionality reduction can be used to compress data wile minimizing the amount of information that is lost\n", "- third. understanding the structure of data with hundreds of dimensions can be difficult" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##thus.\n", "- high-dimensional dataset >> two or three dimensions\n", "- more dimension -> more sample required exponentially, more memory, more processing power" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## 응용\n", " - 신호처리 분야 : 이산 카루넨-뢰브 변환(Karhunen-Loève transform 또는 KLT)\n", " - 다변수 품질 관리에서는 호텔링 변환\n", " - 기계공학에서는 적합 직교 분해(POD)\n", " - 선형대수학에서는 특이 값 분해(Singular Value Decomposition; SVD) 또는 고유 값 분해(Eigen Value Decomposition; EVD), 인자 분석(주성분 분석과 인자 분석의 차이점에 관한 논의는 [2]의 7장을 보면 된다.)\n", " - 심리측정학의 Eckart–Young 이론 (Harman, 1960) 또는 Schmidt–Mirsky 이론\n", " - 기상 과학의 실증 직교 함수(EOF), \n", " - 소음과 진동의 실증적 고유 함수 분해(Sirovich, 1987)와 실증적 요소 분석(Lorenz, 1956), 준조화모드(Brooks et al., 1988), 스펙트럼 분해, \n", " - 구조 동역학의 실증적 모델 분석\n", " \n", " [출처] https://ko.wikipedia.org/wiki/%EC%A3%BC%EC%84%B1%EB%B6%84_%EB%B6%84%EC%84%9D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA is most useful when the variance in a data set is distributed unevenly across the dimensions. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 주요 용어\n", "\n", "\n", "- Variance(분산) : how a set of values are spread out\n", "- Covariance(공분산) : how much two variables change together(Covariance measure linear dependence)\n", " - Cov(X,Y) = 0 ≠> independent\n", "- eigen vector, eigen value (eigen pair) -- Important but using SVD(SVD is more faster)\n", "\n", " <img src='https://upload.wikimedia.org/math/7/f/6/7f68feea2e8797ebcfe2d7619fde3d08.png' align=left>\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " - Eigenvectors and eigenvalues can only be derived from square matrices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###선형대수 이론(다크프로그래머)\n", "- <a href='http://darkpgmr.tistory.com/103'>[선형대수학 #1] 주요용어 및 기본공식</a>\n", "- <a href='http://darkpgmr.tistory.com/104'>[선형대수학 #2] 역행렬과 행렬식(determinant)</a>\n", "- <a href='http://darkpgmr.tistory.com/105'>[선형대수학 #3] 고유값과 고유벡터 (eigenvalue & eigenvector)</a>\n", "- <a href='http://darkpgmr.tistory.com/106'>[선형대수학 #4] 특이값 분해(Singular Value Decomposition, SVD)의 활용</a>\n", "- <a href='http://darkpgmr.tistory.com/108'>[선형대수학 #5] 선형연립방정식 풀이</a>\n", "- <a href='http://darkpgmr.tistory.com/110'>[선형대수학 #6] 주성분분석(PCA)의 이해와 활용</a>\n", "\n", "###대학강의\n", "- <a href='http://www.kocw.net/home/search/kemView.do?kemId=1043234'>선형대수(한양대학교, 유경렬)</a>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###First example(covariance)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.04916667 0.01416667 0.01916667]\n", " [ 0.01416667 0.00916667 -0.00583333]\n", " [ 0.01916667 -0.00583333 0.04916667]]\n" ] } ], "source": [ "import numpy as np\n", "X = [[2, 0, -1.4],\n", " [2.2, 0.2, -1.5],\n", " [2.4, 0.1, -1],\n", " [1.9, 0, -1.2]]\n", "print np.cov(np.array(X).T)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "###Second Example(Eigenvectors and eigenvalues)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "eigenvalues(w) : \n", "[-0.99999998 -1.00000002] \n", "\n", "eigenvectors(v) :\n", "[[ 0.70710678 0.70710678]\n", " [ 0.70710678 0.70710678]]\n" ] } ], "source": [ "import numpy as np\n", "w, v = np.linalg.eig(np.array([[1, -2], [2, -3]]))\n", "w; v\n", "print 'eigenvalues(w) : \\n',w,'\\n\\neigenvectors(v) :\\n', v" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####Rotatin Matrix\n", "<img src='https://upload.wikimedia.org/math/3/8/f/38f4b1b17056c57ea7cb7f2188c9a81a.png' align=left>\n", "<img src='https://upload.wikimedia.org/math/7/5/2/752fd6396a9c9d026f10eccb39ddca15.png' align=mid>\n", "<img src='https://upload.wikimedia.org/math/f/3/3/f338c036c7b38d2541d15ca1601e8803.png' align=left>" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "###Third Example(Dimensionality reduction with PCA)\n", "\n", "- 공분산행렬의 고유벡터가 데이터 분포의 분산 방향\n", "- 고유값이 그 분산의 크기" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "COV\n", "[[ 0.68677778 0.60666667]\n", " [ 0.60666667 0.59777778]]\n", "\n", "Eigenvalue\n", "[ 1.25057433 0.03398123] \n", "\n", "EigenVector\n", "[[ 0.73251454 -0.68075138]\n", " [ 0.68075138 0.73251454]]\n", "0.732514541884 -0.680751383347 0.680751383347 0.732514541884\n" ] }, { "data": { "image/png": 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"text/plain": [ "<matplotlib.figure.Figure at 0xcd3aa90>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.decomposition import PCA\n", "from sklearn.datasets import load_iris\n", "\n", "# Origin value\n", "x1 = [0.9, 2.4, 1.2, 0.5, 0.3, 1.8, 0.5, 0.3, 2.5, 1.3]\n", "x2 = [1, 2.6, 1.7, 0.7, 0.7, 1.4, 0.6, 0.6, 2.6, 1.1]\n", "c = np.cov(x1, x2)\n", "print \"COV\\n\", c\n", "\n", "w, v = np.linalg.eig(np.array(c))\n", "print \"\\nEigenvalue\\n\",w, \"\\n\\nEigenVector\\n\", v\n", "\n", "# Origin value - Mean\n", "x, y = [],[]\n", "x_1, y_1 = [],[]\n", "\n", "print v[0][0], v[0][1],v[1][0],v[1][1]\n", "for i in range(10):\n", " x.append((x1[i]-1.17))\n", " y.append((x2[i]-1.3))\n", " x_1.append((x1[i]-1.17)*v[0][0]+(x2[i]-1.3)*v[1][0])\n", " y_1.append((x1[i]-1.17)*v[0][1]+(x2[i]-1.3)*v[1][1]) \n", "\n", "# PCA transform * eigenvalue\n", "z1 = [-0.40200434,1.78596968,0.29427599,-0.89923557,-1.04573848,\n", " 0.52955,-0.96731071,-1.11381362,1.85922113,-0.04092339]\n", "z2 = [0,0,0,0,0,0,0,0,0,0]\n", "\n", "plt.scatter(x, y, c='b', marker='x', label='origin-mean')\n", "plt.scatter(x_1, y_1, c='r', marker='x', label='rotate')\n", "plt.scatter(z1, z2, c='g', marker='.', label='reduction with PCA')\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Fourth Example(Dimensionality reduction with PCA)\n", "\n", "<a href='https://en.wikipedia.org/wiki/Iris_flower_data_set'>Iris flower dataset</a>\n", "\n", "<a href='http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html'>scikit-learn iris example</a>" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Automatically created module for IPython interactive environment\n" ] }, { "data": { "image/png": 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ODTKNE4UCCSeCyBOJlgBJlEaLRqMIBoPCMha5MF1LxyMVRQDg8/k6pdGkqTWiuMilMd1o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\nfb34+a1bt8aff/4JAOjRowcOHjyIiooKAMCJEydQX1+Pjh07QiaT4bfff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"text/plain": [ "<matplotlib.figure.Figure at 0xd16e490>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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dkc56eSbiIrZiaksbCIKATdGZMGveBRt+2FJuPG/3xlgUaIs+Hg4oUmnQa8cl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\n7du3T+Hh4Sf9a4CahTtIAQDgMRZIAQDgE8oWAAC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"text/plain": [ "<matplotlib.figure.Figure at 0xd062990>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "print(__doc__)\n", "\n", "\n", "# Code source: Gaël Varoquaux\n", "# Modified for documentation by Jaques Grobler\n", "# License: BSD 3 clause\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from sklearn import datasets\n", "from sklearn.decomposition import PCA\n", "\n", "# import some data to play with\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2] # we only take the first two features.\n", "Y = iris.target\n", "\n", "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n", "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n", "\n", "plt.figure(2, figsize=(8, 6))\n", "plt.clf()\n", "\n", "# Plot the training points\n", "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)\n", "plt.xlabel('Sepal length')\n", "plt.ylabel('Sepal width')\n", "\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(y_min, y_max)\n", "plt.xticks(())\n", "plt.yticks(())\n", "\n", "# To getter a better understanding of interaction of the dimensions\n", "# plot the first three PCA dimensions\n", "fig = plt.figure(1, figsize=(8, 6))\n", "ax = Axes3D(fig, elev=-150, azim=110)\n", "X_reduced = PCA(n_components=3).fit_transform(iris.data)\n", "ax.scatter(X_reduced[:, 0], X_reduced[:, 1], X_reduced[:, 2], c=Y,\n", " cmap=plt.cm.Paired)\n", "ax.set_title(\"First three PCA directions\")\n", "ax.set_xlabel(\"1st eigenvector\")\n", "ax.w_xaxis.set_ticklabels([])\n", "ax.set_ylabel(\"2nd eigenvector\")\n", "ax.w_yaxis.set_ticklabels([])\n", "ax.set_zlabel(\"3rd eigenvector\")\n", "ax.w_zaxis.set_ticklabels([])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gP1u2bFER0W3btkV9zz7iEXoLrzSyjkgGPgVKxxDpgKlUj6LNllQHX331FXX1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\nb6iyGSX0roj+P+CTdNvi4UZV/ZGqHgo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"text/plain": [ "<matplotlib.figure.Figure at 0x5e05710>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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TJ47iwQfviil8snUE0b6ur3+mDQSLgLq6Ov7617/y6quvJrzuUFMJDh8+nPnz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\nVFpYuxZOPdUZRQvNoZf+naw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"text/plain": [ "<matplotlib.figure.Figure at 0xcdf88b0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline \n", "\n", "import matplotlib.pyplot as plt\n", "from sklearn.decomposition import PCA\n", "from sklearn.datasets import load_iris\n", "\n", "data = load_iris()\n", "y=data.target\n", "x=data.data\n", "target_names = data.target_names\n", "pca=PCA(n_components=2)\n", "reduced_X=pca.fit_transform(x)\n", "\n", "#Mastering Machine Learning with scikit-learn 예제\n", "red_x, red_y = [], []\n", "blue_x, blue_y = [], []\n", "green_x, green_y = [], []\n", "for i in range(len(reduced_X)):\n", " if y[i] == 0:\n", " red_x.append(reduced_X[i][0])\n", " red_y.append(reduced_X[i][1])\n", " elif y[i] == 1:\n", " blue_x.append(reduced_X[i][0])\n", " blue_y.append(reduced_X[i][1])\n", " else:\n", " green_x.append(reduced_X[i][0])\n", " green_y.append(reduced_X[i][1])\n", "plt.figure(1)\n", "plt.scatter(red_x, red_y, c='r', marker='x', label=target_names[0])\n", "plt.scatter(blue_x, blue_y, c='b', marker='D', label=target_names[1])\n", "plt.scatter(green_x, green_y, c='g', marker='.', label=target_names[2])\n", "plt.legend()\n", "plt.title('PCA of IRIS dataset(book example)')\n", "\n", "#scikit-learn 예제\n", "plt.figure(2)\n", "for c, m, i, target_name in zip(\"rbg\", \"xD.\", [0, 1, 2], target_names):\n", " plt.scatter(reduced_X[y == i, 0], reduced_X[y == i, 1],marker=m, c=c, label=target_name)\n", "\n", "plt.legend()\n", "plt.title('PCA of IRIS dataset(scikit-learn.org example)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Fifth Example(Dimensionality reduction with PCA)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from os import walk, path\n", "import numpy as np\n", "import mahotas as mh\n", "from sklearn.cross_validation import train_test_split\n", "from sklearn.cross_validation import cross_val_score\n", "from sklearn.preprocessing import scale\n", "from sklearn.decomposition import PCA\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.metrics import classification_report\n", "X = []\n", "y = []\n", "for dir_path, dir_names, file_names in walk('data/att-faces'):\n", " for fn in file_names:\n", " if fn[-3:] == 'pgm':\n", " image_filename = path.join(dir_path, fn)\n", " X.append(scale(mh.imread(image_filename, as_grey=True).reshape(10304).astype('float32')))\n", " y.append(dir_path)\n", "X = np.array(X)\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "300 100 300 100\n" ] } ], "source": [ "# We then randomly split the images into training and test sets, and fit the PCA object on the training set:\n", "X_train, X_test, y_train, y_test = train_test_split(X, y)\n", "pca = PCA(n_components=150)\n", "\n", "print len(X_train), len(X_test), len(y_train), len(y_test)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The original dimensions of the training data were (300, 10304)\n", "The reduced dimensions of the training data are (300, 150)\n", "Cross validation accuracy: 0.787721624212 [ 0.78632479 0.7628866 0.81395349]\n", " precision recall f1-score support\n", "\n", "data/att-faces\\s1 1.00 1.00 1.00 2\n", "data/att-faces\\s10 1.00 1.00 1.00 2\n", "data/att-faces\\s11 1.00 1.00 1.00 3\n", "data/att-faces\\s12 1.00 1.00 1.00 2\n", "data/att-faces\\s13 1.00 1.00 1.00 4\n", "data/att-faces\\s14 1.00 0.67 0.80 3\n", "data/att-faces\\s16 0.75 1.00 0.86 3\n", "data/att-faces\\s17 1.00 1.00 1.00 2\n", "data/att-faces\\s18 1.00 1.00 1.00 2\n", "data/att-faces\\s19 1.00 0.50 0.67 2\n", "data/att-faces\\s2 0.75 1.00 0.86 3\n", "data/att-faces\\s21 1.00 1.00 1.00 4\n", "data/att-faces\\s22 0.67 1.00 0.80 2\n", "data/att-faces\\s23 1.00 0.75 0.86 4\n", "data/att-faces\\s24 1.00 1.00 1.00 3\n", "data/att-faces\\s25 1.00 1.00 1.00 3\n", "data/att-faces\\s26 1.00 1.00 1.00 1\n", "data/att-faces\\s27 1.00 0.83 0.91 6\n", "data/att-faces\\s28 0.75 1.00 0.86 3\n", "data/att-faces\\s29 1.00 1.00 1.00 3\n", "data/att-faces\\s3 1.00 1.00 1.00 3\n", "data/att-faces\\s30 1.00 1.00 1.00 2\n", "data/att-faces\\s31 0.50 1.00 0.67 1\n", "data/att-faces\\s32 1.00 1.00 1.00 2\n", "data/att-faces\\s33 1.00 1.00 1.00 3\n", "data/att-faces\\s34 1.00 1.00 1.00 3\n", "data/att-faces\\s35 1.00 1.00 1.00 2\n", "data/att-faces\\s36 1.00 1.00 1.00 1\n", "data/att-faces\\s37 1.00 0.80 0.89 5\n", "data/att-faces\\s38 1.00 1.00 1.00 3\n", "data/att-faces\\s39 1.00 1.00 1.00 3\n", "data/att-faces\\s4 1.00 1.00 1.00 3\n", "data/att-faces\\s40 1.00 0.67 0.80 3\n", "data/att-faces\\s5 1.00 1.00 1.00 3\n", "data/att-faces\\s6 1.00 1.00 1.00 4\n", "data/att-faces\\s8 0.50 1.00 0.67 1\n", "data/att-faces\\s9 1.00 1.00 1.00 1\n", "\n", "avg / total 0.96 0.94 0.94 100\n", "\n" ] } ], "source": [ "#We reduce all of the instances to 150 dimensions and train a logistic regression \n", "#classifier. The data set contains forty classes; scikit-learn automatically creates \n", "#binary classifiers using the one versus all strategy behind the scenes:\n", "X_train_reduced = pca.fit_transform(X_train)\n", "X_test_reduced = pca.transform(X_test)\n", "print 'The original dimensions of the training data were', X_train.shape\n", "print 'The reduced dimensions of the training data are', X_train_reduced.shape\n", "\n", "\n", "classifier = LogisticRegression()\n", "accuracies = cross_val_score(classifier, X_train_reduced, y_train)\n", "#Finally, we evaluate the performance of the classifier using cross-validation and a \n", "#test set. The average per-class F1 score of the classifier trained on the full data was \n", "#0.94, but required significantly more time to train and could be prohibitively slow in \n", "#an application with more training instances:\n", "print 'Cross validation accuracy:', np.mean(accuracies), accuracies\n", "\n", "\n", "classifier.fit(X_train_reduced, y_train)\n", "predictions = classifier.predict(X_test_reduced)\n", "print classification_report(y_test, predictions)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }