PCA和Softmax分类比较—Mnist与人脸数据集

PCA人脸识别中三种方法得到的正确率可达到100%

作为对比，单独使用Softmax回归对人脸40*10*92*112的数据分类正确率为97%。

用PCA对MNIST手写数字10*500*28*28识别，也可以达到相对比较高的正确率，马氏距离h=32时正确率为0.93 （在softmax中为0.85~0.89）。

 # coding:utf8
 import numpy as np
 import os
 import sf
 import pca

 if __name__ == '__main__':
     img=pca.load_img()
     test=img
     print np.mat(img).shape
     label=[a+1 for a in range(40) for j in range(10)]
     index=range(400)
     np.random.shuffle(index)
     label_=[label[i] for i in index]
     test_=np.mat([test[i] for i in index])

     softmax = sf.SoftMax(MAXT=200, step=0.03, landa=0.01)
     softmax.process_train(np.mat(img),np.array(label),40)
     softmax.validate(test_,np.array(label_))
     # correctnum = 390, sumnum = 400, Accuracy:0.97

 #coding:utf8
 import cv2
 import numpy as np
 import matplotlib.pyplot as plt
 import cPickle

 TYPE_NUM=10  #
 SAMPLE_NUM=500  #

 def load_img():
     img=[]
     for i in range(40):
         for j in range(10):
             path='att_faces\\s'+str(i+1)+'\\'+str(j+1)+'.pgm'
             a=cv2.imread(path,0)
             a=a.flatten()/255.0
             img.append(a)
     return img

 def dis(A,B,dis_type=0,s=None):
     if dis_type==1:  # 欧式距离
         return np.sum(np.square(A-B))
     elif dis_type==2:  # 马式距离
         f=np.sqrt(abs(np.dot(np.dot((A-B),s.I),(A-B).T)))  # h增大时会出现负值
         return f.tolist()[0][0]
     else:  # 曼哈顿距离
         return np.sum(abs(A-B))

 def pca(data,h,dis_type=0):
     q,r=np.linalg.qr(data.T)
     u,s,v=np.linalg.svd(r.T)
     fi=np.dot(q,(v[:h]).T)
     y=np.dot(fi.T,data.T)
     ym=[np.mean(np.reshape(x,(TYPE_NUM,SAMPLE_NUM)),axis=1) for x in y]
     ym=np.reshape(ym,(h,TYPE_NUM))
     c=[]
     if dis_type==2:# 计算马氏距离的额外处理"
         yr=[np.reshape(x,(TYPE_NUM,SAMPLE_NUM)) for x in y]
         yr=[[np.array(yr)[j][k] for j in  range(h)]for k in range(TYPE_NUM)]
         for k in yr:
             k=np.reshape(k,(h,SAMPLE_NUM))
             e=np.cov(k)
             c.append(e)
     return fi,ym,c

 def validate(fi,ym,test,label,dis_type=0,c=None):
     ty=np.dot(fi.T,test.T)
     correctnum=0
     testnum=len(test)
     for i in range(testnum):
         if dis_type==2:
             n=len(ym.T)
             dd=[dis(ty.T[i],ym.T[n_],dis_type,np.mat(c[n_])) for n_ in range(n)]
         else:
             dd=[dis(ty.T[i],yy,dis_type) for yy in ym.T]
         if np.argsort(dd)[0]==label[i]:  # mnist中从0开始
             correctnum+=1
     rate = float(correctnum) / testnum
     print "Correctnum = %d, Sumnum = %d" % (correctnum, testnum), "Accuracy:%.2f" % (rate)
     return rate

 if __name__ == '__main__':
     f = open('mnist.pkl', 'rb')
     training_data, validation_data, test_data = cPickle.load(f)
     training_inputs = [np.reshape(x, 784) for x in training_data[0]]
     data = np.array(training_inputs[:10000])
     training_inputs = [np.reshape(x, 784) for x in validation_data[0]]
     vdata = np.array(training_inputs[:5000])
     f.close()
     label=training_data[1][:10000]
     c=np.argsort(label)
     l=[label[x] for x in c]
     d=[data[x] for x in c]
     data_new=[]
     label_new=[]
     temp=-1000
     for i in  range(10):   # 将数据整理为10类各500个样本依次排列
         id= l.index(i)
         if id-temp<500:
             print "<500"
             break
         data_new.append(d[id:id+500])
         label_new.append(l[id:id+500])  # PCA中不需要，用于在Softmax中验证数据
         temp=id
     lb=np.array(label_new).flatten()
     data_=[]
     for j in data_new:
         data_+=j
     x_=[2**i for i in range(9)]
     d_=['Manhattan Distance','Euclidean Metric', 'Mahalanobis Distance']
     for j in range(3):
         y_=[]
         plt.figure()
         for i in range(9):
             fi,ym,c=pca.pca(np.mat(data_),h=x_[i],dis_type=j)
             y_.append(pca.validate(fi,ym,vdata, validation_data[1][:5000],dis_type=j,c=c))
         plt.ylim([0,1.0])
         plt.plot(x_,y_)
         plt.scatter(x_,y_)
         plt.xlabel('h')
         plt.ylabel('Accuracy')
         plt.title(d_[j])
     plt.show()