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[Qiita記事3本目] 確率的主成分分析 #125

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[Qiita記事3本目] 確率的主成分分析 #125

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5ba7fc8
EMアルゴリズムを実装しようとした（挫折）
Jul 14, 2019
30f6898
最尤法を用いた確率的主成分分析のプログラムを追加
Jul 16, 2019
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131 changes: 131 additions & 0 deletions trainee/takano/WorkOut_Report/Qiita3_ppca/.ipynb_checkpoints/Untitled-checkpoint.ipynb
View file
Open in desktop
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{
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'matplotlib.pyplot'",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-12-584a9621a47a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;31m#numpyをインストール\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;31m#グラフを書くやつ\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 7\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mmpl_toolkits\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmplot3d\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mAxes3D\u001b[0m\u001b[1;31m#3次元plotを行うためのツール\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpreprocessing\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mNormalizer\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib.pyplot'"
]
}
],
"source": [
"\n",
"\n",
"#PCA：主成分分析\n",
"# Code source: Gaël Varoquaux\n",
"# License: BSD 3 clause\n",
"\n",
"import numpy as np#numpyをインストール\n",
"import matplotlib.pyplot as plt#グラフを書くやつ\n",
"from mpl_toolkits.mplot3d import Axes3D#3次元plotを行うためのツール\n",
"from sklearn.preprocessing import Normalizer\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn import decomposition#PCAのライブラリ\n",
"from sklearn import datasets#datasetsを取ってくる\n",
"\n",
"\n",
"def Estep(W,X,N,sigma):\n",
" M=np.dot(W,W.T)+sigma*np.eye(N)\n",
" Minv=np.linalg.inv(W)\n",
" Ez_n=np.dot(Minv,W.T)\n",
" Ez_n=np.dot(Ez_n,X)\n",
" Ez_nz_nt=sigma*Minv+np.dot(Ez_n,Ez_n.T)\n",
" return Ez_n,Ez_nz_nt\n",
"def Mstep(Ez_n,Ez_nz_nt,X,N,D):\n",
" a=np.dot(X,Ez_n.T)\n",
" b=np.linalg.inv(sam(Ez_nz_nt))\n",
" Wnew=np.dot(sum(a),b)\n",
" nor = np.dot(X,X.T)\n",
" tenti = np.dot(Ez_n.T,Wnew.T)\n",
" W2 = np.dot(Wnew.T,Wnew)\n",
" hoge = np.dot(Ez_nz_nt,trace)\n",
" tr = hoge.trace()\n",
" sig = nor-2*np.dot(tenti,X)+tr\n",
" signew = sum(sig)/(N*D)\n",
" return Wnew,signew\n",
"n_component=2\n",
"np.set_printoptions(suppress=True)\n",
"#centers = [[1, 1], [-1, -1], [1, -1]]#3次元配列を作ってる\n",
"#print(centers)\n",
"fig = plt.figure(2, figsize=(14, 6))\n",
"iris = datasets.load_iris()\n",
"X = iris.data\n",
"y = iris.target\n",
"N=150\n",
"D=4\n",
"M=2\n",
"W =np.random.randn(4, 2)\n",
"sigma = np.array([[1]])\n",
"for i in range(4):#各データの平均を元のデータから引いている\n",
" mean = np.mean(X[:,i])\n",
" X[:,i]=(X[:,i]-mean)\n",
"for i in range(step):\n",
" Ez_n,Ez_nz_nt = Estep(W,X,N,sigma)\n",
" W,sigma = Mstep(Ez_n,Ez_nz_nt,X,N,D)\n",
" \n",
" \n",
"'''\n",
"X_cov=np.dot(X.T,X)#共分散行列を生成\n",
"w,v=np.linalg.eig(X_cov)#共分散行列の固有値、固有ベクトルを算出(固有値は既に大きさ順に並べられている)\n",
"for i in range(n_component):#固有値の大きい順に固有ベクトルを取り出す\n",
" Xpc[i]=v[:,i]\n",
"Xpc=np.array(Xpc)\n",
"'''\n",
"Xafter=np.dot(W,X.T)#取り出した固有ベクトルでデータを線形写像する\n",
"\n",
"\n",
"pca = decomposition.PCA(n_components=2)\n",
"pca.fit(X)\n",
"Xlib = pca.transform(X) \n",
"\n",
"\n",
"ax1 = fig.add_subplot(121)\n",
"for label in np.unique(y):\n",
" ax1.scatter(Xlib[y == label, 0],\n",
" Xlib[y == label, 1])\n",
"ax1.set_title('library pca')\n",
"ax1.set_xlabel(\"X_axis\")\n",
"ax1.set_ylabel(\"Y_axis\")\n",
"ax2 = fig.add_subplot(122)\n",
"for label in np.unique(y):\n",
" ax2.scatter(Xafter[y == label, 0],\n",
" Xafter[y == label, 1])\n",
"ax2.set_title('original pca')\n",
"ax2.set_xlabel(\"X_axis\")\n",
"ax2.set_ylabel(\"Y_axis\")\n",
"plt.show()\n",
"\n"
]
}
],
"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": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
131 changes: 131 additions & 0 deletions trainee/takano/WorkOut_Report/Qiita3_ppca/Untitled.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,131 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'matplotlib.pyplot'",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-12-584a9621a47a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;31m#numpyをインストール\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;31m#グラフを書くやつ\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 7\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mmpl_toolkits\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmplot3d\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mAxes3D\u001b[0m\u001b[1;31m#3次元plotを行うためのツール\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpreprocessing\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mNormalizer\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib.pyplot'"
]
}
],
"source": [
"\n",
"\n",
"#PCA：主成分分析\n",
"# Code source: Gaël Varoquaux\n",
"# License: BSD 3 clause\n",
"\n",
"import numpy as np#numpyをインストール\n",
"import matplotlib.pyplot as plt#グラフを書くやつ\n",
"from mpl_toolkits.mplot3d import Axes3D#3次元plotを行うためのツール\n",
"from sklearn.preprocessing import Normalizer\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn import decomposition#PCAのライブラリ\n",
"from sklearn import datasets#datasetsを取ってくる\n",
"\n",
"\n",
"def Estep(W,X,N,sigma):\n",
" M=np.dot(W,W.T)+sigma*np.eye(N)\n",
" Minv=np.linalg.inv(W)\n",
" Ez_n=np.dot(Minv,W.T)\n",
" Ez_n=np.dot(Ez_n,X)\n",
" Ez_nz_nt=sigma*Minv+np.dot(Ez_n,Ez_n.T)\n",
" return Ez_n,Ez_nz_nt\n",
"def Mstep(Ez_n,Ez_nz_nt,X,N,D):\n",
" a=np.dot(X,Ez_n.T)\n",
" b=np.linalg.inv(sam(Ez_nz_nt))\n",
" Wnew=np.dot(sum(a),b)\n",
" nor = np.dot(X,X.T)\n",
" tenti = np.dot(Ez_n.T,Wnew.T)\n",
" W2 = np.dot(Wnew.T,Wnew)\n",
" hoge = np.dot(Ez_nz_nt,trace)\n",
" tr = hoge.trace()\n",
" sig = nor-2*np.dot(tenti,X)+tr\n",
" signew = sum(sig)/(N*D)\n",
" return Wnew,signew\n",
"n_component=2\n",
"np.set_printoptions(suppress=True)\n",
"#centers = [[1, 1], [-1, -1], [1, -1]]#3次元配列を作ってる\n",
"#print(centers)\n",
"fig = plt.figure(2, figsize=(14, 6))\n",
"iris = datasets.load_iris()\n",
"X = iris.data\n",
"y = iris.target\n",
"N=150\n",
"D=4\n",
"M=2\n",
"W =np.random.randn(4, 2)\n",
"sigma = np.array([[1]])\n",
"for i in range(4):#各データの平均を元のデータから引いている\n",
" mean = np.mean(X[:,i])\n",
" X[:,i]=(X[:,i]-mean)\n",
"for i in range(step):\n",
" Ez_n,Ez_nz_nt = Estep(W,X,N,sigma)\n",
" W,sigma = Mstep(Ez_n,Ez_nz_nt,X,N,D)\n",
" \n",
" \n",
"'''\n",
"X_cov=np.dot(X.T,X)#共分散行列を生成\n",
"w,v=np.linalg.eig(X_cov)#共分散行列の固有値、固有ベクトルを算出(固有値は既に大きさ順に並べられている)\n",
"for i in range(n_component):#固有値の大きい順に固有ベクトルを取り出す\n",
" Xpc[i]=v[:,i]\n",
"Xpc=np.array(Xpc)\n",
"'''\n",
"Xafter=np.dot(W,X.T)#取り出した固有ベクトルでデータを線形写像する\n",
"\n",
"\n",
"pca = decomposition.PCA(n_components=2)\n",
"pca.fit(X)\n",
"Xlib = pca.transform(X) \n",
"\n",
"\n",
"ax1 = fig.add_subplot(121)\n",
"for label in np.unique(y):\n",
" ax1.scatter(Xlib[y == label, 0],\n",
" Xlib[y == label, 1])\n",
"ax1.set_title('library pca')\n",
"ax1.set_xlabel(\"X_axis\")\n",
"ax1.set_ylabel(\"Y_axis\")\n",
"ax2 = fig.add_subplot(122)\n",
"for label in np.unique(y):\n",
" ax2.scatter(Xafter[y == label, 0],\n",
" Xafter[y == label, 1])\n",
"ax2.set_title('original pca')\n",
"ax2.set_xlabel(\"X_axis\")\n",
"ax2.set_ylabel(\"Y_axis\")\n",
"plt.show()\n",
"\n"
]
}
],
"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": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}