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

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

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

14.23 1.71 2.43 15.6 127 2.8 3.06 .28 2.29 5.64 1.04 3.92 1065
13.2 1.78 2.14 11.2 100 2.65 2.76 .26 1.28 4.38 1.05 3.4 1050
13.16 2.36 2.67 18.6 101 2.8 3.24 .3 2.81 5.68 1.03 3.17 1185
14.37 1.95 2.5 16.8 113 3.85 3.49 .24 2.18 7.8 .86 3.45 1480
13.24 2.59 2.87 21 118 2.8 2.69 .39 1.82 4.32 1.04 2.93 735
14.2 1.76 2.45 15.2 112 3.27 3.39 .34 1.97 6.75 1.05 2.85 1450
14.39 1.87 2.45 14.6 96 2.5 2.52 .3 1.98 5.25 1.02 3.58 1290
14.06 2.15 2.61 17.6 121 2.6 2.51 .31 1.25 5.05 1.06 3.58 1295
14.83 1.64 2.17 14 97 2.8 2.98 .29 1.98 5.2 1.08 2.85 1045
13.86 1.35 2.27 16 98 2.98 3.15 .22 1.85 7.22 1.01 3.55 1045
14.1 2.16 2.3 18 105 2.95 3.32 .22 2.38 5.75 1.25 3.17 1510
14.12 1.48 2.32 16.8 95 2.2 2.43 .26 1.57 5 1.17 2.82 1280
13.75 1.73 2.41 16 89 2.6 2.76 .29 1.81 5.6 1.15 2.9 1320
14.75 1.73 2.39 11.4 91 3.1 3.69 .43 2.81 5.4 1.25 2.73 1150
14.38 1.87 2.38 12 102 3.3 3.64 .29 2.96 7.5 1.2 3 1547
13.63 1.81 2.7 17.2 112 2.85 2.91 .3 1.46 7.3 1.28 2.88 1310
14.3 1.92 2.72 20 120 2.8 3.14 .33 1.97 6.2 1.07 2.65 1280
13.83 1.57 2.62 20 115 2.95 3.4 .4 1.72 6.6 1.13 2.57 1130
14.19 1.59 2.48 16.5 108 3.3 3.93 .32 1.86 8.7 1.23 2.82 1680
13.64 3.1 2.56 15.2 116 2.7 3.03 .17 1.66 5.1 .96 3.36 845
14.06 1.63 2.28 16 126 3 3.17 .24 2.1 5.65 1.09 3.71 780
12.93 3.8 2.65 18.6 102 2.41 2.41 .25 1.98 4.5 1.03 3.52 770
13.71 1.86 2.36 16.6 101 2.61 2.88 .27 1.69 3.8 1.11 4 1035
12.85 1.6 2.52 17.8 95 2.48 2.37 .26 1.46 3.93 1.09 3.63 1015
13.5 1.81 2.61 20 96 2.53 2.61 .28 1.66 3.52 1.12 3.82 845
13.05 2.05 3.22 25 124 2.63 2.68 .47 1.92 3.58 1.13 3.2 830
13.39 1.77 2.62 16.1 93 2.85 2.94 .34 1.45 4.8 .92 3.22 1195
13.3 1.72 2.14 17 94 2.4 2.19 .27 1.35 3.95 1.02 2.77 1285
13.87 1.9 2.8 19.4 107 2.95 2.97 .37 1.76 4.5 1.25 3.4 915
14.02 1.68 2.21 16 96 2.65 2.33 .26 1.98 4.7 1.04 3.59 1035
13.73 1.5 2.7 22.5 101 3 3.25 .29 2.38 5.7 1.19 2.71 1285
13.58 1.66 2.36 19.1 106 2.86 3.19 .22 1.95 6.9 1.09 2.88 1515
13.68 1.83 2.36 17.2 104 2.42 2.69 .42 1.97 3.84 1.23 2.87 990
13.76 1.53 2.7 19.5 132 2.95 2.74 .5 1.35 5.4 1.25 3 1235
13.51 1.8 2.65 19 110 2.35 2.53 .29 1.54 4.2 1.1 2.87 1095
13.48 1.81 2.41 20.5 100 2.7 2.98 .26 1.86 5.1 1.04 3.47 920
13.28 1.64 2.84 15.5 110 2.6 2.68 .34 1.36 4.6 1.09 2.78 880
13.05 1.65 2.55 18 98 2.45 2.43 .29 1.44 4.25 1.12 2.51 1105
13.07 1.5 2.1 15.5 98 2.4 2.64 .28 1.37 3.7 1.18 2.69 1020
14.22 3.99 2.51 13.2 128 3 3.04 .2 2.08 5.1 .89 3.53 760
13.56 1.71 2.31 16.2 117 3.15 3.29 .34 2.34 6.13 .95 3.38 795
13.41 3.84 2.12 18.8 90 2.45 2.68 .27 1.48 4.28 .91 3 1035
13.88 1.89 2.59 15 101 3.25 3.56 .17 1.7 5.43 .88 3.56 1095
13.24 3.98 2.29 17.5 103 2.64 2.63 .32 1.66 4.36 .82 3 680
13.05 1.77 2.1 17 107 3 3 .28 2.03 5.04 .88 3.35 885
14.21 4.04 2.44 18.9 111 2.85 2.65 .3 1.25 5.24 .87 3.33 1080
14.38 3.59 2.28 16 102 3.25 3.17 .27 2.19 4.9 1.04 3.44 1065
13.9 1.68 2.12 16 101 3.1 3.39 .21 2.14 6.1 .91 3.33 985
14.1 2.02 2.4 18.8 103 2.75 2.92 .32 2.38 6.2 1.07 2.75 1060
13.94 1.73 2.27 17.4 108 2.88 3.54 .32 2.08 8.90 1.12 3.1 1260
13.05 1.73 2.04 12.4 92 2.72 3.27 .17 2.91 7.2 1.12 2.91 1150
13.83 1.65 2.6 17.2 94 2.45 2.99 .22 2.29 5.6 1.24 3.37 1265
13.82 1.75 2.42 14 111 3.88 3.74 .32 1.87 7.05 1.01 3.26 1190
13.77 1.9 2.68 17.1 115 3 2.79 .39 1.68 6.3 1.13 2.93 1375
13.74 1.67 2.25 16.4 118 2.6 2.9 .21 1.62 5.85 .92 3.2 1060
13.56 1.73 2.46 20.5 116 2.96 2.78 .2 2.45 6.25 .98 3.03 1120
14.22 1.7 2.3 16.3 118 3.2 3 .26 2.03 6.38 .94 3.31 970
13.29 1.97 2.68 16.8 102 3 3.23 .31 1.66 6 1.07 2.84 1270
13.72 1.43 2.5 16.7 108 3.4 3.67 .19 2.04 6.8 .89 2.87 1285
12.37 .94 1.36 10.6 88 1.98 .57 .28 .42 1.95 1.05 1.82 520
12.33 1.1 2.28 16 101 2.05 1.09 .63 .41 3.27 1.25 1.67 680
12.64 1.36 2.02 16.8 100 2.02 1.41 .53 .62 5.75 .98 1.59 450
13.67 1.25 1.92 18 94 2.1 1.79 .32 .73 3.8 1.23 2.46 630
12.37 1.13 2.16 19 87 3.5 3.1 .19 1.87 4.45 1.22 2.87 420
12.17 1.45 2.53 19 104 1.89 1.75 .45 1.03 2.95 1.45 2.23 355
12.37 1.21 2.56 18.1 98 2.42 2.65 .37 2.08 4.6 1.19 2.3 678
13.11 1.01 1.7 15 78 2.98 3.18 .26 2.28 5.3 1.12 3.18 502
12.37 1.17 1.92 19.6 78 2.11 2 .27 1.04 4.68 1.12 3.48 510
13.34 .94 2.36 17 110 2.53 1.3 .55 .42 3.17 1.02 1.93 750
12.21 1.19 1.75 16.8 151 1.85 1.28 .14 2.5 2.85 1.28 3.07 718
12.29 1.61 2.21 20.4 103 1.1 1.02 .37 1.46 3.05 .906 1.82 870
13.86 1.51 2.67 25 86 2.95 2.86 .21 1.87 3.38 1.36 3.16 410
13.49 1.66 2.24 24 87 1.88 1.84 .27 1.03 3.74 .98 2.78 472
12.99 1.67 2.6 30 139 3.3 2.89 .21 1.96 3.35 1.31 3.5 985
11.96 1.09 2.3 21 101 3.38 2.14 .13 1.65 3.21 .99 3.13 886
11.66 1.88 1.92 16 97 1.61 1.57 .34 1.15 3.8 1.23 2.14 428
13.03 .9 1.71 16 86 1.95 2.03 .24 1.46 4.6 1.19 2.48 392
11.84 2.89 2.23 18 112 1.72 1.32 .43 .95 2.65 .96 2.52 500
12.33 .99 1.95 14.8 136 1.9 1.85 .35 2.76 3.4 1.06 2.31 750
12.7 3.87 2.4 23 101 2.83 2.55 .43 1.95 2.57 1.19 3.13 463
12 .92 2 19 86 2.42 2.26 .3 1.43 2.5 1.38 3.12 278
12.72 1.81 2.2 18.8 86 2.2 2.53 .26 1.77 3.9 1.16 3.14 714
12.08 1.13 2.51 24 78 2 1.58 .4 1.4 2.2 1.31 2.72 630
13.05 3.86 2.32 22.5 85 1.65 1.59 .61 1.62 4.8 .84 2.01 515
11.84 .89 2.58 18 94 2.2 2.21 .22 2.35 3.05 .79 3.08 520
12.67 .98 2.24 18 99 2.2 1.94 .3 1.46 2.62 1.23 3.16 450
12.16 1.61 2.31 22.8 90 1.78 1.69 .43 1.56 2.45 1.33 2.26 495
11.65 1.67 2.62 26 88 1.92 1.61 .4 1.34 2.6 1.36 3.21 562
11.64 2.06 2.46 21.6 84 1.95 1.69 .48 1.35 2.8 1 2.75 680
12.08 1.33 2.3 23.6 70 2.2 1.59 .42 1.38 1.74 1.07 3.21 625
12.08 1.83 2.32 18.5 81 1.6 1.5 .52 1.64 2.4 1.08 2.27 480
12 1.51 2.42 22 86 1.45 1.25 .5 1.63 3.6 1.05 2.65 450
12.69 1.53 2.26 20.7 80 1.38 1.46 .58 1.62 3.05 .96 2.06 495
12.29 2.83 2.22 18 88 2.45 2.25 .25 1.99 2.15 1.15 3.3 290
11.62 1.99 2.28 18 98 3.02 2.26 .17 1.35 3.25 1.16 2.96 345
12.47 1.52 2.2 19 162 2.5 2.27 .32 3.28 2.6 1.16 2.63 937
11.81 2.12 2.74 21.5 134 1.6 .99 .14 1.56 2.5 .95 2.26 625
12.29 1.41 1.98 16 85 2.55 2.5 .29 1.77 2.9 1.23 2.74 428
12.37 1.07 2.1 18.5 88 3.52 3.75 .24 1.95 4.5 1.04 2.77 660
12.29 3.17 2.21 18 88 2.85 2.99 .45 2.81 2.3 1.42 2.83 406
12.08 2.08 1.7 17.5 97 2.23 2.17 .26 1.4 3.3 1.27 2.96 710
12.6 1.34 1.9 18.5 88 1.45 1.36 .29 1.35 2.45 1.04 2.77 562
12.34 2.45 2.46 21 98 2.56 2.11 .34 1.31 2.8 .8 3.38 438
11.82 1.72 1.88 19.5 86 2.5 1.64 .37 1.42 2.06 .94 2.44 415
12.51 1.73 1.98 20.5 85 2.2 1.92 .32 1.48 2.94 1.04 3.57 672
12.42 2.55 2.27 22 90 1.68 1.84 .66 1.42 2.7 .86 3.3 315
12.25 1.73 2.12 19 80 1.65 2.03 .37 1.63 3.4 1 3.17 510
12.72 1.75 2.28 22.5 84 1.38 1.76 .48 1.63 3.3 .88 2.42 488
12.22 1.29 1.94 19 92 2.36 2.04 .39 2.08 2.7 .86 3.02 312
11.61 1.35 2.7 20 94 2.74 2.92 .29 2.49 2.65 .96 3.26 680
11.46 3.74 1.82 19.5 107 3.18 2.58 .24 3.58 2.9 .75 2.81 562
12.52 2.43 2.17 21 88 2.55 2.27 .26 1.22 2 .9 2.78 325
11.76 2.68 2.92 20 103 1.75 2.03 .6 1.05 3.8 1.23 2.5 607
11.41 .74 2.5 21 88 2.48 2.01 .42 1.44 3.08 1.1 2.31 434
12.08 1.39 2.5 22.5 84 2.56 2.29 .43 1.04 2.9 .93 3.19 385
11.03 1.51 2.2 21.5 85 2.46 2.17 .52 2.01 1.9 1.71 2.87 407
11.82 1.47 1.99 20.8 86 1.98 1.6 .3 1.53 1.95 .95 3.33 495
12.42 1.61 2.19 22.5 108 2 2.09 .34 1.61 2.06 1.06 2.96 345
12.77 3.43 1.98 16 80 1.63 1.25 .43 .83 3.4 .7 2.12 372
12 3.43 2 19 87 2 1.64 .37 1.87 1.28 .93 3.05 564
11.45 2.4 2.42 20 96 2.9 2.79 .32 1.83 3.25 .8 3.39 625
11.56 2.05 3.23 28.5 119 3.18 5.08 .47 1.87 6 .93 3.69 465
12.42 4.43 2.73 26.5 102 2.2 2.13 .43 1.71 2.08 .92 3.12 365
13.05 5.8 2.13 21.5 86 2.62 2.65 .3 2.01 2.6 .73 3.1 380
11.87 4.31 2.39 21 82 2.86 3.03 .21 2.91 2.8 .75 3.64 380
12.07 2.16 2.17 21 85 2.6 2.65 .37 1.35 2.76 .86 3.28 378
12.43 1.53 2.29 21.5 86 2.74 3.15 .39 1.77 3.94 .69 2.84 352
11.79 2.13 2.78 28.5 92 2.13 2.24 .58 1.76 3 .97 2.44 466
12.37 1.63 2.3 24.5 88 2.22 2.45 .4 1.9 2.12 .89 2.78 342
12.04 4.3 2.38 22 80 2.1 1.75 .42 1.35 2.6 .79 2.57 580
12.86 1.35 2.32 18 122 1.51 1.25 .21 .94 4.1 .76 1.29 630
12.88 2.99 2.4 20 104 1.3 1.22 .24 .83 5.4 .74 1.42 530
12.81 2.31 2.4 24 98 1.15 1.09 .27 .83 5.7 .66 1.36 560
12.7 3.55 2.36 21.5 106 1.7 1.2 .17 .84 5 .78 1.29 600
12.51 1.24 2.25 17.5 85 2 .58 .6 1.25 5.45 .75 1.51 650
12.6 2.46 2.2 18.5 94 1.62 .66 .63 .94 7.1 .73 1.58 695
12.25 4.72 2.54 21 89 1.38 .47 .53 .8 3.85 .75 1.27 720
12.53 5.51 2.64 25 96 1.79 .6 .63 1.1 5 .82 1.69 515
13.49 3.59 2.19 19.5 88 1.62 .48 .58 .88 5.7 .81 1.82 580
12.84 2.96 2.61 24 101 2.32 .6 .53 .81 4.92 .89 2.15 590
12.93 2.81 2.7 21 96 1.54 .5 .53 .75 4.6 .77 2.31 600
13.36 2.56 2.35 20 89 1.4 .5 .37 .64 5.6 .7 2.47 780
13.52 3.17 2.72 23.5 97 1.55 .52 .5 .55 4.35 .89 2.06 520
13.62 4.95 2.35 20 92 2 .8 .47 1.02 4.4 .91 2.05 550
12.25 3.88 2.2 18.5 112 1.38 .78 .29 1.14 8.21 .65 2 855
13.16 3.57 2.15 21 102 1.5 .55 .43 1.3 4 .6 1.68 830
13.88 5.04 2.23 20 80 .98 .34 .4 .68 4.9 .58 1.33 415
12.87 4.61 2.48 21.5 86 1.7 .65 .47 .86 7.65 .54 1.86 625
13.32 3.24 2.38 21.5 92 1.93 .76 .45 1.25 8.42 .55 1.62 650
13.08 3.9 2.36 21.5 113 1.41 1.39 .34 1.14 9.40 .57 1.33 550
13.5 3.12 2.62 24 123 1.4 1.57 .22 1.25 8.60 .59 1.3 500
12.79 2.67 2.48 22 112 1.48 1.36 .24 1.26 10.8 .48 1.47 480
13.11 1.9 2.75 25.5 116 2.2 1.28 .26 1.56 7.1 .61 1.33 425
13.23 3.3 2.28 18.5 98 1.8 .83 .61 1.87 10.52 .56 1.51 675
12.58 1.29 2.1 20 103 1.48 .58 .53 1.4 7.6 .58 1.55 640
13.17 5.19 2.32 22 93 1.74 .63 .61 1.55 7.9 .6 1.48 725
13.84 4.12 2.38 19.5 89 1.8 .83 .48 1.56 9.01 .57 1.64 480
12.45 3.03 2.64 27 97 1.9 .58 .63 1.14 7.5 .67 1.73 880
14.34 1.68 2.7 25 98 2.8 1.31 .53 2.7 13 .57 1.96 660
13.48 1.67 2.64 22.5 89 2.6 1.1 .52 2.29 11.75 .57 1.78 620
12.36 3.83 2.38 21 88 2.3 .92 .5 1.04 7.65 .56 1.58 520
13.69 3.26 2.54 20 107 1.83 .56 .5 .8 5.88 .96 1.82 680
12.85 3.27 2.58 22 106 1.65 .6 .6 .96 5.58 .87 2.11 570
12.96 3.45 2.35 18.5 106 1.39 .7 .4 .94 5.28 .68 1.75 675
13.78 2.76 2.3 22 90 1.35 .68 .41 1.03 9.58 .7 1.68 615
13.73 4.36 2.26 22.5 88 1.28 .47 .52 1.15 6.62 .78 1.75 520
13.45 3.7 2.6 23 111 1.7 .92 .43 1.46 10.68 .85 1.56 695
12.82 3.37 2.3 19.5 88 1.48 .66 .4 .97 10.26 .72 1.75 685
13.58 2.58 2.69 24.5 105 1.55 .84 .39 1.54 8.66 .74 1.8 750
13.4 4.6 2.86 25 112 1.98 .96 .27 1.11 8.5 .67 1.92 630
12.2 3.03 2.32 19 96 1.25 .49 .4 .73 5.5 .66 1.83 510
12.77 2.39 2.28 19.5 86 1.39 .51 .48 .64 9.899999 .57 1.63 470
14.16 2.51 2.48 20 91 1.68 .7 .44 1.24 9.7 .62 1.71 660
13.71 5.65 2.45 20.5 95 1.68 .61 .52 1.06 7.7 .64 1.74 740
13.4 3.91 2.48 23 102 1.8 .75 .43 1.41 7.3 .7 1.56 750
13.27 4.28 2.26 20 120 1.59 .69 .43 1.35 10.2 .59 1.56 835
13.17 2.59 2.37 20 120 1.65 .68 .53 1.46 9.3 .6 1.62 840
14.13 4.1 2.74 24.5 96 2.05 .76 .56 1.35 9.2 .61 1.6 560

handle face data

# 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

Written on January 21, 2020