# -*- coding: utf-8 -*- ''' Created on 2018年1月18日 @author: Jason.F @summary: 特征抽取-PCA方法，無監督、線性 ''' import pandas as pd import numpy as np from sklearn.cross_validation import train_test_split from sklearn.preprocessing import MinMaxScaler from sklearn.preprocessing import StandardScaler from sklearn.linear_model import LogisticRegression import matplotlib.pyplot as plt #第一步:導入數據，對原始d維數據集做標準化處理 df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data',header=None) df_wine.columns=['Class label','Alcohol','Malic acid','Ash','Alcalinity of ash','Magnesium','Total phenols','Flavanoids','Nonflavanoid phenols','Proanthocyanins','Color intensity','Hue','OD280/OD315 of diluted wines','Proline'] print ('class labels:',np.unique(df_wine['Class label'])) #print (df_wine.head(5)) #分割訓練集合測試集 X,y=df_wine.iloc[:,1:].values,df_wine.iloc[:,0].values X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.3,random_state=0) #特征值縮放-標準化 stdsc=StandardScaler() X_train_std=stdsc.fit_transform(X_train) X_test_std=stdsc.fit_transform(X_test) #第二步：構造樣本的協方差矩陣 cov_mat=np.cov(X_train_std.T)#d=13維，構造13X13維的協方差矩陣 eigen_vals,eigen_vecs=np.linalg.eig(cov_mat)#計算線性矩陣的特征值和特征向量 print ('\nEigenvalues \n %s'%eigen_vals) #13個特征值 print (eigen_vecs.shape)#13X13的特征向量矩陣 #計算特征值占比，觀察期方差貢獻率，目標是尋找最大方差的成分 tot=sum(eigen_vals) var_exp=[(i/tot) for i in sorted(eigen_vals,reverse=True)] cum_var_exp=np.cumsum(var_exp) plt.bar(range(1,14),var_exp,alpha=0.5,align='center',label='individual explained variance') plt.step(range(1,14),cum_var_exp,where='mid',label='cumulative explained variance') plt.ylabel('Explained variance ratio') plt.xlabel('Principal components') plt.legend(loc='best') plt.show() #第三部：選擇前k個最大特征值對應的特征向量，構造k個特征項的映射矩陣W eigen_pairs=[(np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals))] eigen_pairs.sort(reverse=True) w=np.hstack((eigen_pairs[0][1][:,np.newaxis],eigen_pairs[1][1][:,np.newaxis]))#選取前2個特征，構建13X2維的映射矩陣W print ('Matrix W:\n',w) #第四步：通過映射矩陣W將d=13維的輸入數據集X轉換到新的k=2維特征子空間 print (X_train_std[0].dot(w)) #轉換一行，一個樣本 X_train_pca=X_train_std.dot(w)#轉換整個樣本集，從13維到2維 X_test_pca=X_test_std.dot(w) print (X_train_pca.shape) #用二維散點圖可視化降維后的樣本 colors=['r','b','g'] markers=['s','x','o'] for l,c,m in zip(np.unique(y_train),colors,markers):plt.scatter(X_train_pca[y_train == l, 0],X_train_pca[y_train == l, 1],c=c, label=l, marker=m) plt.xlabel('PC 1') plt.ylabel('PC 2') plt.legend(loc='lower left') plt.show() #第五步：轉換后的數據集進行線性訓練 lr=LogisticRegression() lr.fit(X_train_pca,y_train) print ('Training accuracy:',lr.score(X_train_pca, y_train)) print ('Test accuracy:',lr.score(X_test_pca, y_test))

結果：

('class labels:', array([1, 2, 3], dtype=int64))Eigenvalues [ 4.8923083 2.46635032 1.42809973 1.01233462 0.84906459 0.601815140.52251546 0.08414846 0.33051429 0.29595018 0.16831254 0.214322120.2399553 ] (13L, 13L) ('Matrix W:\n', array([[ 0.14669811, 0.50417079],[-0.24224554, 0.24216889],[-0.02993442, 0.28698484],[-0.25519002, -0.06468718],[ 0.12079772, 0.22995385],[ 0.38934455, 0.09363991],[ 0.42326486, 0.01088622],[-0.30634956, 0.01870216],[ 0.30572219, 0.03040352],[-0.09869191, 0.54527081],[ 0.30032535, -0.27924322],[ 0.36821154, -0.174365 ],[ 0.29259713, 0.36315461]])) [ 2.59891628 0.00484089] (124L, 2L) ('Training accuracy:', 0.967741935483871) ('Test accuracy:', 0.98148148148148151)

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