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()
