zhzgithub
diff --git a/‎PCA/PCA.py‎
Lines changed: 94 additions & 17 deletions b/‎PCA/PCA.py‎
Lines changed: 94 additions & 17 deletions
diff --git a/‎PCA/data1.mat‎
995 Bytes b/‎PCA/data1.mat‎
995 Bytes
@@ -4,37 +4,76 @@
 import numpy as np
 from matplotlib import pyplot as plt
 from scipy import io as spio
+from sklearn.decomposition import pca
 
 '''
-主成分分析运行方法
+主成分分析_2维数据降维1维演示函数
 '''
-def PCA():
+def PCA_2D():
     data_2d = spio.loadmat("data.mat")
     X = data_2d['X']
     m = X.shape[0]
-    plt = plot_data_2d(X) # 显示二维的数据
+    plt = plot_data_2d(X,'bo') # 显示二维的数据
     plt.show()
 
     X_copy = X.copy()
     X_norm,mu,sigma = featureNormalize(X_copy)    # 归一化数据
-    plot_data_2d(X_norm)    # 显示归一化后的数据
+    #plot_data_2d(X_norm)    # 显示归一化后的数据
+    #plt.show()
 
-    Sigma = np.dot(np.transpose(X_norm),X_norm)/m
-    U,S,V = np.linalg.svd(Sigma)
+    Sigma = np.dot(np.transpose(X_norm),X_norm)/m  # 求Sigma
+    U,S,V = np.linalg.svd(Sigma)       # 求Sigma的奇异值分解
 
-    plt = plot_data_2d(X_norm)
-    plt.plot(mu.reshape(-1,1),mu.reshape(-1,1)+S[0]*(U[:,0].reshape(-1,1)),'k-')
+    plt = plot_data_2d(X,'bo') # 显示原本数据
+    drawline(plt, mu, mu+S[0]*(U[:,0]), 'r-')  # 线，为投影的方向
+
+    plt.axis('square')
     plt.show()
 
-    K = 1
-    Z = projectData(X_norm,U,K)
-    print Z[0]
-    
+    K = 1  # 定义降维多少维（本来是2维的，这里降维1维）
+    '''投影之后数据（降维之后）'''
+    Z = projectData(X_norm,U,K)   # 投影
+    '''恢复数据'''
+    X_rec = recoverData(Z,U,K)    # 恢复
+    '''作图-----原数据与恢复的数据'''
+    plt = plot_data_2d(X_norm,'bo')
+    plot_data_2d(X_rec,'ro')
+    for i in range(X_norm.shape[0]):
+        drawline(plt, X_norm[i,:], X_rec[i,:], '--k')
+    plt.axis('square')
+    plt.show()
 
 
+'''主成分分析_PCA图像数据降维'''    
+def PCA_faceImage():
+    print (u'加载图像数据.....')
+    data_image = spio.loadmat('data_faces.mat')
+    X = data_image['X']
+    display_imageData(X[0:100,:])
+    m = X.shape[0]  # 数据条数
+    
+    print (u'运行PCA....')
+    X_norm,mu,sigma = featureNormalize(X)  # 归一化
+    
+    Sigma = np.dot(np.transpose(X_norm),X_norm)/m  # 求Sigma
+    U,S,V = np.linalg.svd(Sigma)                   # 奇异值分解
+    display_imageData(np.transpose(U[:,0:36]))     # 显示U的数据
+    
+    print (u'对face数据降维.....')
+    K = 100     # 降维100维(原先是32*32=1024维的)
+    Z = projectData(X_norm, U, K)
+    print (u'投影之后Z向量的大小：%d %d' %Z.shape)
+    
+    print (u'显示降维之后的数据......')
+    X_rec = recoverData(Z, U, K) # 恢复数据
+    display_imageData(X_rec[0:100,:])
+    
+    
+      
+    
 # 可视化二维数据
-def plot_data_2d(X):
-    plt.plot(X[:,0],X[:,1],'bo')
+def plot_data_2d(X,marker):
+    plt.plot(X[:,0],X[:,1],marker) 
     return plt
 
 # 归一化数据
@@ -55,10 +94,48 @@ def featureNormalize(X):
 def projectData(X_norm,U,K):
     Z = np.zeros((X_norm.shape[0],K))
 
-    U_reduce = U[:,0:K]
-    Z = np.dot(X_norm,U_reduce)
+    U_reduce = U[:,0:K]          # 取前K个
+    Z = np.dot(X_norm,U_reduce) 
     return Z
 
+# 画一条线
+def drawline(plt,p1,p2,line_type):
+    plt.plot(np.array([p1[0],p2[0]]),np.array([p1[1],p2[1]]),line_type)  
+
+
+# 恢复数据
+def recoverData(Z,U,K):
+    X_rec = np.zeros((Z.shape[0],U.shape[0]))
+    U_recude = U[:,0:K]
+    X_rec = np.dot(Z,np.transpose(U_recude))  # 还原数据（近似）
+    return X_rec
+
+# 显示图片
+def display_imageData(imgData):
+    sum = 0
+    '''
+    显示100个数（若是一个一个绘制将会非常慢，可以将要画的图片整理好，放到一个矩阵中，显示这个矩阵即可）
+    - 初始化一个二维数组
+    - 将每行的数据调整成图像的矩阵，放进二维数组
+    - 显示即可
+    '''
+    m,n = imgData.shape
+    width = np.int32(np.round(np.sqrt(n)))
+    height = np.int32(n/width);
+    rows_count = np.int32(np.floor(np.sqrt(m)))
+    cols_count = np.int32(np.ceil(m/rows_count))
+    pad = 1
+    display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad)))
+    for i in range(rows_count):
+        for j in range(cols_count):
+            max_val = np.max(np.abs(imgData[sum,:]))
+            display_array[pad+i*(height+pad):pad+i*(height+pad)+height,pad+j*(width+pad):pad+j*(width+pad)+width] = imgData[sum,:].reshape(height,width,order="F")/max_val    # order=F指定以列优先，在matlab中是这样的，python中需要指定，默认以行
+            sum += 1
+            
+    plt.imshow(display_array,cmap='gray')   #显示灰度图像
+    plt.axis('off')
+    plt.show()
 
 if __name__ == "__main__":
-    PCA()
+    PCA_2D()
+    PCA_faceImage()