PCA
题目：PCA模型实验
目标：实现一个PCA模型，能够对给定数据进行降维（即找到其中的主成分）
测试：
（1）首先人工生成一些数据（如三维数据），让它们主要分布在低维空间中，如首先让某个维度的方差远小于其它唯独，然后对这些数据旋转。生成这些数据后，用你的PCA方法进行主成分提取。
（2）找一个人脸数据（小点样本量），用你实现PCA方法对该数据降维，找出一些主成分，然后用这些主成分对每一副人脸图像进行重建，比较一些它们与原图像有多大差别（用信噪比衡量）。
handle my data
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import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D # 空间三维画图
def three_dimension_generator(tdg_number,loc_0=1,scales_0=0.7):
'''
返回3列tgd_number行的矩阵,第一列数据方差小于其余两列
:param tdg_number:
:param loc_0:
:param scales_0:
:return:
'''
tdg_x = np.random.normal(loc=loc_0, scale=scales_0 / 4,
size=tdg_number).transpose()
tdg_y = np.random.normal(loc=loc_0, scale=scales_0,
size=tdg_number).transpose()
tdg_z = np.random.normal(loc=loc_0, scale=scales_0,
size=tdg_number).transpose()
tdg_ending = np.c_[tdg_x,tdg_y]
tdg_ending = np.c_[tdg_ending, tdg_z]
return tdg_ending
def reverse(r_data):
r_temp = np.copy(r_data)#!!!np.coy才能获得副本,否则就直接在原来数据上修改了
for r_i in range(r_data.shape[0]):
r_temp[r_i][0] = - r_temp[r_i][0]
return r_temp
def pca(pca_data,expection_dimension=3):
print(pca_data.shape)
#返回结果是!!!列!!!向量的矩阵!!!
pca_size = pca_data.shape[0]
for pca_i in range(pca_size):
if pca_i == 0:
pca_mu = pca_data[0]
else:
pca_mu = pca_mu + pca_data[pca_i]
pca_mu = pca_mu / pca_size
for pca_i in range(pca_data.shape[0]):
pca_data[pca_i] = pca_data[pca_i] - pca_mu
pca_cov = np.dot(pca_data.transpose(),pca_data)
pca_eigenvalues, pca_featurevector = np.linalg.eig(pca_cov)
pca_eigenvalues_2 = np.sort(pca_eigenvalues)
pca_featurevector = np.mat(pca_featurevector)
for pca_i in range(expection_dimension):
for pca_j in range(len(pca_eigenvalues)):
if pca_eigenvalues_2[pca_data.shape[1] - pca_i - 1] == pca_eigenvalues[pca_j]:
if pca_i == 0:
pca_ending = pca_featurevector[:,pca_j]
else:
pca_ending = np.c_[pca_ending,pca_featurevector[:,pca_j]]
print(pca_ending)
return pca_ending
data_size = 100
original_data = three_dimension_generator(data_size)
reverse_data = reverse(original_data)
#print(reverse_data)
vectors = pca(reverse_data,2)
two_dimension_data = np.mat(np.dot(reverse_data,vectors))
print('vectors : ')
print(vectors)
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(original_data[:,0], original_data[:,1], original_data[:,2], c='r', label='original_data')
ax.scatter(reverse_data[:,0], reverse_data[:,1], reverse_data[:,2], c='g', label='reverse_data')
ax.scatter(two_dimension_data[:,0], two_dimension_data[:,1], np.mat(np.zeros(data_size)).transpose(), c='y', label='ending')
ax.legend(loc='best')
plt.show()
handle uci data
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import numpy as np
from matplotlib import pyplot as plt
def reverse(r_data):
r_temp = np.copy(r_data)#!!!np.coy才能获得副本,否则就直接在原来数据上修改了
for r_i in range(r_data.shape[0]):
r_temp[r_i][0] = - r_temp[r_i][0]
return r_temp
def pca(pca_data,expection_dimension=3):
#返回结果是!!!列!!!向量的矩阵!!!
pca_size = pca_data.shape[0]
for pca_i in range(pca_size):
if pca_i == 0:
pca_mu = pca_data[0]
else:
pca_mu = pca_mu + pca_data[pca_i]
pca_mu = pca_mu / pca_size
for pca_i in range(pca_data.shape[0]):
pca_data[pca_i] = pca_data[pca_i] - pca_mu
pca_cov = np.dot(pca_data.transpose(),pca_data)
pca_eigenvalues, pca_featurevector = np.linalg.eig(pca_cov)
pca_eigenvalues_2 = np.sort(pca_eigenvalues)
pca_featurevector = np.mat(pca_featurevector)
for pca_i in range(expection_dimension):
for pca_j in range(len(pca_eigenvalues)):
if pca_eigenvalues_2[pca_data.shape[1] - pca_i - 1] == pca_eigenvalues[pca_j]:
if pca_i == 0:
pca_ending = pca_featurevector[:,pca_j]
else:
pca_ending = np.c_[pca_ending,pca_featurevector[:,pca_j]]
return pca_ending
filename = "wine_4.txt"
original_data = np.loadtxt(filename,dtype=np.float32)
matrix_data = np.mat(original_data)
lables = matrix_data[:, 0]#提取矩阵某一列
train_data = np.delete(matrix_data,0,1)#删除矩阵第一列
for i_1 in range(train_data.shape[0]):
for i_2 in range(train_data.shape[1]):
train_data[i_1, i_2] = train_data[i_1, i_2]
vectors = pca(train_data,2)
two_dimension_data = np.mat(np.dot(train_data,vectors))
X = two_dimension_data[:,0]
Y = two_dimension_data[:,1]
plt.subplot(111)
plt.plot(X[0:59],Y[0:59],"ro")#列矩阵分片的方法!!!
plt.plot(X[59:130],Y[59:130],"yo")
plt.plot(X[130:178],Y[130:178],"co")
plt.title("wine data in two dimension")
plt.xlabel('x')
plt.ylabel('y')
plt.show()
uci data : wine_4.txt
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1 14.23 1.71 2.43 15.6 127 2.8 3.06 .28 2.29 5.64 1.04 3.92 1065
1 13.2 1.78 2.14 11.2 100 2.65 2.76 .26 1.28 4.38 1.05 3.4 1050
1 13.16 2.36 2.67 18.6 101 2.8 3.24 .3 2.81 5.68 1.03 3.17 1185
1 14.37 1.95 2.5 16.8 113 3.85 3.49 .24 2.18 7.8 .86 3.45 1480
1 13.24 2.59 2.87 21 118 2.8 2.69 .39 1.82 4.32 1.04 2.93 735
1 14.2 1.76 2.45 15.2 112 3.27 3.39 .34 1.97 6.75 1.05 2.85 1450
1 14.39 1.87 2.45 14.6 96 2.5 2.52 .3 1.98 5.25 1.02 3.58 1290
1 14.06 2.15 2.61 17.6 121 2.6 2.51 .31 1.25 5.05 1.06 3.58 1295
1 14.83 1.64 2.17 14 97 2.8 2.98 .29 1.98 5.2 1.08 2.85 1045
1 13.86 1.35 2.27 16 98 2.98 3.15 .22 1.85 7.22 1.01 3.55 1045
1 14.1 2.16 2.3 18 105 2.95 3.32 .22 2.38 5.75 1.25 3.17 1510
1 14.12 1.48 2.32 16.8 95 2.2 2.43 .26 1.57 5 1.17 2.82 1280
1 13.75 1.73 2.41 16 89 2.6 2.76 .29 1.81 5.6 1.15 2.9 1320
1 14.75 1.73 2.39 11.4 91 3.1 3.69 .43 2.81 5.4 1.25 2.73 1150
1 14.38 1.87 2.38 12 102 3.3 3.64 .29 2.96 7.5 1.2 3 1547
1 13.63 1.81 2.7 17.2 112 2.85 2.91 .3 1.46 7.3 1.28 2.88 1310
1 14.3 1.92 2.72 20 120 2.8 3.14 .33 1.97 6.2 1.07 2.65 1280
1 13.83 1.57 2.62 20 115 2.95 3.4 .4 1.72 6.6 1.13 2.57 1130
1 14.19 1.59 2.48 16.5 108 3.3 3.93 .32 1.86 8.7 1.23 2.82 1680
1 13.64 3.1 2.56 15.2 116 2.7 3.03 .17 1.66 5.1 .96 3.36 845
1 14.06 1.63 2.28 16 126 3 3.17 .24 2.1 5.65 1.09 3.71 780
1 12.93 3.8 2.65 18.6 102 2.41 2.41 .25 1.98 4.5 1.03 3.52 770
1 13.71 1.86 2.36 16.6 101 2.61 2.88 .27 1.69 3.8 1.11 4 1035
1 12.85 1.6 2.52 17.8 95 2.48 2.37 .26 1.46 3.93 1.09 3.63 1015
1 13.5 1.81 2.61 20 96 2.53 2.61 .28 1.66 3.52 1.12 3.82 845
1 13.05 2.05 3.22 25 124 2.63 2.68 .47 1.92 3.58 1.13 3.2 830
1 13.39 1.77 2.62 16.1 93 2.85 2.94 .34 1.45 4.8 .92 3.22 1195
1 13.3 1.72 2.14 17 94 2.4 2.19 .27 1.35 3.95 1.02 2.77 1285
1 13.87 1.9 2.8 19.4 107 2.95 2.97 .37 1.76 4.5 1.25 3.4 915
1 14.02 1.68 2.21 16 96 2.65 2.33 .26 1.98 4.7 1.04 3.59 1035
1 13.73 1.5 2.7 22.5 101 3 3.25 .29 2.38 5.7 1.19 2.71 1285
1 13.58 1.66 2.36 19.1 106 2.86 3.19 .22 1.95 6.9 1.09 2.88 1515
1 13.68 1.83 2.36 17.2 104 2.42 2.69 .42 1.97 3.84 1.23 2.87 990
1 13.76 1.53 2.7 19.5 132 2.95 2.74 .5 1.35 5.4 1.25 3 1235
1 13.51 1.8 2.65 19 110 2.35 2.53 .29 1.54 4.2 1.1 2.87 1095
1 13.48 1.81 2.41 20.5 100 2.7 2.98 .26 1.86 5.1 1.04 3.47 920
1 13.28 1.64 2.84 15.5 110 2.6 2.68 .34 1.36 4.6 1.09 2.78 880
1 13.05 1.65 2.55 18 98 2.45 2.43 .29 1.44 4.25 1.12 2.51 1105
1 13.07 1.5 2.1 15.5 98 2.4 2.64 .28 1.37 3.7 1.18 2.69 1020
1 14.22 3.99 2.51 13.2 128 3 3.04 .2 2.08 5.1 .89 3.53 760
1 13.56 1.71 2.31 16.2 117 3.15 3.29 .34 2.34 6.13 .95 3.38 795
1 13.41 3.84 2.12 18.8 90 2.45 2.68 .27 1.48 4.28 .91 3 1035
1 13.88 1.89 2.59 15 101 3.25 3.56 .17 1.7 5.43 .88 3.56 1095
1 13.24 3.98 2.29 17.5 103 2.64 2.63 .32 1.66 4.36 .82 3 680
1 13.05 1.77 2.1 17 107 3 3 .28 2.03 5.04 .88 3.35 885
1 14.21 4.04 2.44 18.9 111 2.85 2.65 .3 1.25 5.24 .87 3.33 1080
1 14.38 3.59 2.28 16 102 3.25 3.17 .27 2.19 4.9 1.04 3.44 1065
1 13.9 1.68 2.12 16 101 3.1 3.39 .21 2.14 6.1 .91 3.33 985
1 14.1 2.02 2.4 18.8 103 2.75 2.92 .32 2.38 6.2 1.07 2.75 1060
1 13.94 1.73 2.27 17.4 108 2.88 3.54 .32 2.08 8.90 1.12 3.1 1260
1 13.05 1.73 2.04 12.4 92 2.72 3.27 .17 2.91 7.2 1.12 2.91 1150
1 13.83 1.65 2.6 17.2 94 2.45 2.99 .22 2.29 5.6 1.24 3.37 1265
1 13.82 1.75 2.42 14 111 3.88 3.74 .32 1.87 7.05 1.01 3.26 1190
1 13.77 1.9 2.68 17.1 115 3 2.79 .39 1.68 6.3 1.13 2.93 1375
1 13.74 1.67 2.25 16.4 118 2.6 2.9 .21 1.62 5.85 .92 3.2 1060
1 13.56 1.73 2.46 20.5 116 2.96 2.78 .2 2.45 6.25 .98 3.03 1120
1 14.22 1.7 2.3 16.3 118 3.2 3 .26 2.03 6.38 .94 3.31 970
1 13.29 1.97 2.68 16.8 102 3 3.23 .31 1.66 6 1.07 2.84 1270
1 13.72 1.43 2.5 16.7 108 3.4 3.67 .19 2.04 6.8 .89 2.87 1285
2 12.37 .94 1.36 10.6 88 1.98 .57 .28 .42 1.95 1.05 1.82 520
2 12.33 1.1 2.28 16 101 2.05 1.09 .63 .41 3.27 1.25 1.67 680
2 12.64 1.36 2.02 16.8 100 2.02 1.41 .53 .62 5.75 .98 1.59 450
2 13.67 1.25 1.92 18 94 2.1 1.79 .32 .73 3.8 1.23 2.46 630
2 12.37 1.13 2.16 19 87 3.5 3.1 .19 1.87 4.45 1.22 2.87 420
2 12.17 1.45 2.53 19 104 1.89 1.75 .45 1.03 2.95 1.45 2.23 355
2 12.37 1.21 2.56 18.1 98 2.42 2.65 .37 2.08 4.6 1.19 2.3 678
2 13.11 1.01 1.7 15 78 2.98 3.18 .26 2.28 5.3 1.12 3.18 502
2 12.37 1.17 1.92 19.6 78 2.11 2 .27 1.04 4.68 1.12 3.48 510
2 13.34 .94 2.36 17 110 2.53 1.3 .55 .42 3.17 1.02 1.93 750
2 12.21 1.19 1.75 16.8 151 1.85 1.28 .14 2.5 2.85 1.28 3.07 718
2 12.29 1.61 2.21 20.4 103 1.1 1.02 .37 1.46 3.05 .906 1.82 870
2 13.86 1.51 2.67 25 86 2.95 2.86 .21 1.87 3.38 1.36 3.16 410
2 13.49 1.66 2.24 24 87 1.88 1.84 .27 1.03 3.74 .98 2.78 472
2 12.99 1.67 2.6 30 139 3.3 2.89 .21 1.96 3.35 1.31 3.5 985
2 11.96 1.09 2.3 21 101 3.38 2.14 .13 1.65 3.21 .99 3.13 886
2 11.66 1.88 1.92 16 97 1.61 1.57 .34 1.15 3.8 1.23 2.14 428
2 13.03 .9 1.71 16 86 1.95 2.03 .24 1.46 4.6 1.19 2.48 392
2 11.84 2.89 2.23 18 112 1.72 1.32 .43 .95 2.65 .96 2.52 500
2 12.33 .99 1.95 14.8 136 1.9 1.85 .35 2.76 3.4 1.06 2.31 750
2 12.7 3.87 2.4 23 101 2.83 2.55 .43 1.95 2.57 1.19 3.13 463
2 12 .92 2 19 86 2.42 2.26 .3 1.43 2.5 1.38 3.12 278
2 12.72 1.81 2.2 18.8 86 2.2 2.53 .26 1.77 3.9 1.16 3.14 714
2 12.08 1.13 2.51 24 78 2 1.58 .4 1.4 2.2 1.31 2.72 630
2 13.05 3.86 2.32 22.5 85 1.65 1.59 .61 1.62 4.8 .84 2.01 515
2 11.84 .89 2.58 18 94 2.2 2.21 .22 2.35 3.05 .79 3.08 520
2 12.67 .98 2.24 18 99 2.2 1.94 .3 1.46 2.62 1.23 3.16 450
2 12.16 1.61 2.31 22.8 90 1.78 1.69 .43 1.56 2.45 1.33 2.26 495
2 11.65 1.67 2.62 26 88 1.92 1.61 .4 1.34 2.6 1.36 3.21 562
2 11.64 2.06 2.46 21.6 84 1.95 1.69 .48 1.35 2.8 1 2.75 680
2 12.08 1.33 2.3 23.6 70 2.2 1.59 .42 1.38 1.74 1.07 3.21 625
2 12.08 1.83 2.32 18.5 81 1.6 1.5 .52 1.64 2.4 1.08 2.27 480
2 12 1.51 2.42 22 86 1.45 1.25 .5 1.63 3.6 1.05 2.65 450
2 12.69 1.53 2.26 20.7 80 1.38 1.46 .58 1.62 3.05 .96 2.06 495
2 12.29 2.83 2.22 18 88 2.45 2.25 .25 1.99 2.15 1.15 3.3 290
2 11.62 1.99 2.28 18 98 3.02 2.26 .17 1.35 3.25 1.16 2.96 345
2 12.47 1.52 2.2 19 162 2.5 2.27 .32 3.28 2.6 1.16 2.63 937
2 11.81 2.12 2.74 21.5 134 1.6 .99 .14 1.56 2.5 .95 2.26 625
2 12.29 1.41 1.98 16 85 2.55 2.5 .29 1.77 2.9 1.23 2.74 428
2 12.37 1.07 2.1 18.5 88 3.52 3.75 .24 1.95 4.5 1.04 2.77 660
2 12.29 3.17 2.21 18 88 2.85 2.99 .45 2.81 2.3 1.42 2.83 406
2 12.08 2.08 1.7 17.5 97 2.23 2.17 .26 1.4 3.3 1.27 2.96 710
2 12.6 1.34 1.9 18.5 88 1.45 1.36 .29 1.35 2.45 1.04 2.77 562
2 12.34 2.45 2.46 21 98 2.56 2.11 .34 1.31 2.8 .8 3.38 438
2 11.82 1.72 1.88 19.5 86 2.5 1.64 .37 1.42 2.06 .94 2.44 415
2 12.51 1.73 1.98 20.5 85 2.2 1.92 .32 1.48 2.94 1.04 3.57 672
2 12.42 2.55 2.27 22 90 1.68 1.84 .66 1.42 2.7 .86 3.3 315
2 12.25 1.73 2.12 19 80 1.65 2.03 .37 1.63 3.4 1 3.17 510
2 12.72 1.75 2.28 22.5 84 1.38 1.76 .48 1.63 3.3 .88 2.42 488
2 12.22 1.29 1.94 19 92 2.36 2.04 .39 2.08 2.7 .86 3.02 312
2 11.61 1.35 2.7 20 94 2.74 2.92 .29 2.49 2.65 .96 3.26 680
2 11.46 3.74 1.82 19.5 107 3.18 2.58 .24 3.58 2.9 .75 2.81 562
2 12.52 2.43 2.17 21 88 2.55 2.27 .26 1.22 2 .9 2.78 325
2 11.76 2.68 2.92 20 103 1.75 2.03 .6 1.05 3.8 1.23 2.5 607
2 11.41 .74 2.5 21 88 2.48 2.01 .42 1.44 3.08 1.1 2.31 434
2 12.08 1.39 2.5 22.5 84 2.56 2.29 .43 1.04 2.9 .93 3.19 385
2 11.03 1.51 2.2 21.5 85 2.46 2.17 .52 2.01 1.9 1.71 2.87 407
2 11.82 1.47 1.99 20.8 86 1.98 1.6 .3 1.53 1.95 .95 3.33 495
2 12.42 1.61 2.19 22.5 108 2 2.09 .34 1.61 2.06 1.06 2.96 345
2 12.77 3.43 1.98 16 80 1.63 1.25 .43 .83 3.4 .7 2.12 372
2 12 3.43 2 19 87 2 1.64 .37 1.87 1.28 .93 3.05 564
2 11.45 2.4 2.42 20 96 2.9 2.79 .32 1.83 3.25 .8 3.39 625
2 11.56 2.05 3.23 28.5 119 3.18 5.08 .47 1.87 6 .93 3.69 465
2 12.42 4.43 2.73 26.5 102 2.2 2.13 .43 1.71 2.08 .92 3.12 365
2 13.05 5.8 2.13 21.5 86 2.62 2.65 .3 2.01 2.6 .73 3.1 380
2 11.87 4.31 2.39 21 82 2.86 3.03 .21 2.91 2.8 .75 3.64 380
2 12.07 2.16 2.17 21 85 2.6 2.65 .37 1.35 2.76 .86 3.28 378
2 12.43 1.53 2.29 21.5 86 2.74 3.15 .39 1.77 3.94 .69 2.84 352
2 11.79 2.13 2.78 28.5 92 2.13 2.24 .58 1.76 3 .97 2.44 466
2 12.37 1.63 2.3 24.5 88 2.22 2.45 .4 1.9 2.12 .89 2.78 342
2 12.04 4.3 2.38 22 80 2.1 1.75 .42 1.35 2.6 .79 2.57 580
3 12.86 1.35 2.32 18 122 1.51 1.25 .21 .94 4.1 .76 1.29 630
3 12.88 2.99 2.4 20 104 1.3 1.22 .24 .83 5.4 .74 1.42 530
3 12.81 2.31 2.4 24 98 1.15 1.09 .27 .83 5.7 .66 1.36 560
3 12.7 3.55 2.36 21.5 106 1.7 1.2 .17 .84 5 .78 1.29 600
3 12.51 1.24 2.25 17.5 85 2 .58 .6 1.25 5.45 .75 1.51 650
3 12.6 2.46 2.2 18.5 94 1.62 .66 .63 .94 7.1 .73 1.58 695
3 12.25 4.72 2.54 21 89 1.38 .47 .53 .8 3.85 .75 1.27 720
3 12.53 5.51 2.64 25 96 1.79 .6 .63 1.1 5 .82 1.69 515
3 13.49 3.59 2.19 19.5 88 1.62 .48 .58 .88 5.7 .81 1.82 580
3 12.84 2.96 2.61 24 101 2.32 .6 .53 .81 4.92 .89 2.15 590
3 12.93 2.81 2.7 21 96 1.54 .5 .53 .75 4.6 .77 2.31 600
3 13.36 2.56 2.35 20 89 1.4 .5 .37 .64 5.6 .7 2.47 780
3 13.52 3.17 2.72 23.5 97 1.55 .52 .5 .55 4.35 .89 2.06 520
3 13.62 4.95 2.35 20 92 2 .8 .47 1.02 4.4 .91 2.05 550
3 12.25 3.88 2.2 18.5 112 1.38 .78 .29 1.14 8.21 .65 2 855
3 13.16 3.57 2.15 21 102 1.5 .55 .43 1.3 4 .6 1.68 830
3 13.88 5.04 2.23 20 80 .98 .34 .4 .68 4.9 .58 1.33 415
3 12.87 4.61 2.48 21.5 86 1.7 .65 .47 .86 7.65 .54 1.86 625
3 13.32 3.24 2.38 21.5 92 1.93 .76 .45 1.25 8.42 .55 1.62 650
3 13.08 3.9 2.36 21.5 113 1.41 1.39 .34 1.14 9.40 .57 1.33 550
3 13.5 3.12 2.62 24 123 1.4 1.57 .22 1.25 8.60 .59 1.3 500
3 12.79 2.67 2.48 22 112 1.48 1.36 .24 1.26 10.8 .48 1.47 480
3 13.11 1.9 2.75 25.5 116 2.2 1.28 .26 1.56 7.1 .61 1.33 425
3 13.23 3.3 2.28 18.5 98 1.8 .83 .61 1.87 10.52 .56 1.51 675
3 12.58 1.29 2.1 20 103 1.48 .58 .53 1.4 7.6 .58 1.55 640
3 13.17 5.19 2.32 22 93 1.74 .63 .61 1.55 7.9 .6 1.48 725
3 13.84 4.12 2.38 19.5 89 1.8 .83 .48 1.56 9.01 .57 1.64 480
3 12.45 3.03 2.64 27 97 1.9 .58 .63 1.14 7.5 .67 1.73 880
3 14.34 1.68 2.7 25 98 2.8 1.31 .53 2.7 13 .57 1.96 660
3 13.48 1.67 2.64 22.5 89 2.6 1.1 .52 2.29 11.75 .57 1.78 620
3 12.36 3.83 2.38 21 88 2.3 .92 .5 1.04 7.65 .56 1.58 520
3 13.69 3.26 2.54 20 107 1.83 .56 .5 .8 5.88 .96 1.82 680
3 12.85 3.27 2.58 22 106 1.65 .6 .6 .96 5.58 .87 2.11 570
3 12.96 3.45 2.35 18.5 106 1.39 .7 .4 .94 5.28 .68 1.75 675
3 13.78 2.76 2.3 22 90 1.35 .68 .41 1.03 9.58 .7 1.68 615
3 13.73 4.36 2.26 22.5 88 1.28 .47 .52 1.15 6.62 .78 1.75 520
3 13.45 3.7 2.6 23 111 1.7 .92 .43 1.46 10.68 .85 1.56 695
3 12.82 3.37 2.3 19.5 88 1.48 .66 .4 .97 10.26 .72 1.75 685
3 13.58 2.58 2.69 24.5 105 1.55 .84 .39 1.54 8.66 .74 1.8 750
3 13.4 4.6 2.86 25 112 1.98 .96 .27 1.11 8.5 .67 1.92 630
3 12.2 3.03 2.32 19 96 1.25 .49 .4 .73 5.5 .66 1.83 510
3 12.77 2.39 2.28 19.5 86 1.39 .51 .48 .64 9.899999 .57 1.63 470
3 14.16 2.51 2.48 20 91 1.68 .7 .44 1.24 9.7 .62 1.71 660
3 13.71 5.65 2.45 20.5 95 1.68 .61 .52 1.06 7.7 .64 1.74 740
3 13.4 3.91 2.48 23 102 1.8 .75 .43 1.41 7.3 .7 1.56 750
3 13.27 4.28 2.26 20 120 1.59 .69 .43 1.35 10.2 .59 1.56 835
3 13.17 2.59 2.37 20 120 1.65 .68 .53 1.46 9.3 .6 1.62 840
3 14.13 4.1 2.74 24.5 96 2.05 .76 .56 1.35 9.2 .61 1.6 560
handle face data
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# encoding:utf-8
import numpy as np
import math
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
def psnr(img1, img2):
'''
根据原图像和现图像计算信噪比
:param source: 原图
:param target: 现图
:return: 信噪比
'''
mse = np.mean((img1 / 255. - img2 / 255.) ** 2)
if mse < 1.0e-10:
return 100
PIXEL_MAX = 1
return 20 * math.log10(PIXEL_MAX / math.sqrt(mse))
def reverse(r_data):
r_temp = np.copy(r_data) # !!!np.coy才能获得副本,否则就直接在原来数据上修改了
for r_i in range(r_data.shape[0]):
r_temp[r_i][0] = - r_temp[r_i][0]
return r_temp
def pca(pca_data, pc_number):
# 将矩阵按列取均值
row_mean = np.mean(pca_data, axis=0)
data = pca_data - row_mean
cov_matrix = np.cov(data, rowvar=0)
# 求特征值,特征向量
pca_eigenvalues, pca_featurevector = np.linalg.eigh(np.mat(cov_matrix))
# 根据特征值大小进行排序，并取前N大的特征向量
temp_vectors = np.argsort(pca_eigenvalues)
temp_vectors = temp_vectors[:-(pc_number + 1):-1]
#重组特征向量
new_featurevector = pca_featurevector[:, temp_vectors]
# 矩阵生成
pca_ending = (data * new_featurevector * new_featurevector.T) + row_mean
pca_ending = pca_ending.real
return pca_ending
def show(s_image, start, step, number):
position = 2
side = 0
if s_image.shape[0] > s_image.shape[1]:
side = s_image.shape[1]
else:
side = s_image.shape[0]
for s_i in range(number):
plt.subplot(330 + position)
temp_image = pca(s_image, start + step * s_i)
plt.imshow(temp_image)
plt.axis("off")
s_str = str(start + s_i * step) + " dimension"
plt.title(s_str)
s_i = s_i + 1
position = position + 1
print("PSNR of " + s_str + " is " + str(psnr(s_image[0:side, 0:side], temp_image[0:side, 0:side])))
temp_image = mpimg.imread('faces/s4/1.jpg')
print("原图形尺寸 : " + str(temp_image.shape))
temp_image = np.mat(temp_image)
# 生成指定形状的全0矩阵,后面是两个括号
image_matrix = np.zeros((temp_image.shape[0], temp_image.shape[1]))
image_matrix = np.mat(image_matrix)
for i in range(temp_image.shape[0]):
for j in range(temp_image.shape[1]):
image_matrix[i, j] = temp_image[i, j]
plt.subplot(331)
plt.imshow(temp_image) # 显示图片
plt.axis('off') # 不显示坐标轴
plt.title("Original image")
show(image_matrix, 1, 2, 8)
plt.show()
face data下载地址:
https://raw.githubusercontent.com/ac-ancheon/ac-ancheon.github.io/master/images/faces.rar
This post is licensed under CC BY 4.0 by the author.