!rm -rf ./data/
!lsREADME.md main.ipynb
import os
if not os.path.exists("./data/"):
os.makedirs("./data/")!lsREADME.md �[34mdata�[m�[m main.ipynb
The files are in PGM format, and can conveniently be viewed on UNIX (TM) systems using the 'xv' program. The size of each image is 92x112 pixels, with 256 grey levels per pixel. The images are organised in 40 directories (one for each subject), which have names of the form sX, where X indicates the subject number (between 1 and 40). In each of these directories, there are ten different images of that subject, which have names of the form Y.pgm, where Y is the image number for that subject (between 1 and 10). Source : http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html
from six.moves.urllib import request
request.urlretrieve("http://www.cl.cam.ac.uk/Research/DTG/attarchive/pub/data/att_faces.zip","./data/att_faces.zip")('./data/att_faces.zip', <http.client.HTTPMessage at 0x104ab2eb8>)
!ls -d data/*data/att_faces.zip
import zipfile
zip_ref = zipfile.ZipFile("./data/att_faces.zip", 'r')
zip_ref.extractall("./data/")
zip_ref.close()!ls -d data/*data/README �[34mdata/s18�[m�[m �[34mdata/s28�[m�[m �[34mdata/s38�[m�[m
data/att_faces.zip �[34mdata/s19�[m�[m �[34mdata/s29�[m�[m �[34mdata/s39�[m�[m
�[34mdata/s1�[m�[m �[34mdata/s2�[m�[m �[34mdata/s3�[m�[m �[34mdata/s4�[m�[m
�[34mdata/s10�[m�[m �[34mdata/s20�[m�[m �[34mdata/s30�[m�[m �[34mdata/s40�[m�[m
�[34mdata/s11�[m�[m �[34mdata/s21�[m�[m �[34mdata/s31�[m�[m �[34mdata/s5�[m�[m
�[34mdata/s12�[m�[m �[34mdata/s22�[m�[m �[34mdata/s32�[m�[m �[34mdata/s6�[m�[m
�[34mdata/s13�[m�[m �[34mdata/s23�[m�[m �[34mdata/s33�[m�[m �[34mdata/s7�[m�[m
�[34mdata/s14�[m�[m �[34mdata/s24�[m�[m �[34mdata/s34�[m�[m �[34mdata/s8�[m�[m
�[34mdata/s15�[m�[m �[34mdata/s25�[m�[m �[34mdata/s35�[m�[m �[34mdata/s9�[m�[m
�[34mdata/s16�[m�[m �[34mdata/s26�[m�[m �[34mdata/s36�[m�[m
�[34mdata/s17�[m�[m �[34mdata/s27�[m�[m �[34mdata/s37�[m�[m
!ls -d data/s1/*data/s1/1.pgm data/s1/2.pgm data/s1/4.pgm data/s1/6.pgm data/s1/8.pgm
data/s1/10.pgm data/s1/3.pgm data/s1/5.pgm data/s1/7.pgm data/s1/9.pgm
from PIL import Image
import numpy as np
raw_im = Image.open('./data/s1/1.pgm').convert('L')
array_im = np.array(raw_im)raw_im
print(array_im.shape)
print(array_im)
print(array_im.flatten())(112, 92)
[[48 49 45 ..., 56 56 54]
[45 52 39 ..., 52 50 51]
[45 50 42 ..., 48 53 50]
...,
[50 48 50 ..., 45 46 46]
[45 54 49 ..., 46 47 47]
[51 51 51 ..., 47 46 46]]
[48 49 45 ..., 47 46 46]
Image.fromarray(array_im)
number_of_person = 40
number_of_picture_per_person = 10
number_of_elements = array_im.shape[0] * array_im.shape[1] # 112*92
data = np.zeros((number_of_person * number_of_picture_per_person, number_of_elements))counter = 0
for i in range(number_of_person):
for j in range(number_of_picture_per_person):
data[counter] = np.array(Image.open("data/s{0}/{1}.pgm".format(i+1,j+1)).convert('L')).flatten()
counter += 1mean_vec = np.mean(data, axis=0)
mean_vecarray([ 85.6175, 85.5775, 85.925 , ..., 76.87 , 75.865 , 75.2275])
std_vec = np.std(data, axis=0)
std_vecarray([ 35.78325298, 35.68457641, 35.56268234, ..., 46.90056609,
44.42585705, 43.95748791])
for i in range(counter):
data[i] = (data[i] - mean_vec) / std_vecdataarray([[-1.05125993, -1.02502268, -1.15078496, ..., -0.63687931,
-0.67224364, -0.66490378],
[-0.71590752, -0.71676625, -0.67275578, ..., -0.95670487,
-0.94235661, -0.93789482],
[-1.30277423, -1.16513923, -0.92583005, ..., -1.02066998,
-1.12243192, -1.05164108],
...,
[ 1.10058468, 0.93660913, 1.07064477, ..., -0.87141805,
-0.82980954, -0.8013993 ],
[ 0.93290848, 0.96463244, 0.95816732, ..., 0.25863227,
0.40820822, 0.22231707],
[ 1.10058468, 1.07672569, 1.07064477, ..., -0.87141805,
-0.9198472 , -0.93789482]])
data.shape(400, 10304)
1/400 * data.T @ data # 標本相関行列array([[ 1. , 0.99357094, 0.9924485 , ..., -0.0911466 ,
-0.07055043, -0.03737454],
[ 0.99357094, 1. , 0.9934313 , ..., -0.08966899,
-0.06973336, -0.03728562],
[ 0.9924485 , 0.9934313 , 1. , ..., -0.08892552,
-0.06679533, -0.03649965],
...,
[-0.0911466 , -0.08966899, -0.08892552, ..., 1. ,
0.92613359, 0.86433606],
[-0.07055043, -0.06973336, -0.06679533, ..., 0.92613359,
1. , 0.94076559],
[-0.03737454, -0.03728562, -0.03649965, ..., 0.86433606,
0.94076559, 1. ]])
%matplotlib inline
import numpy as np
import sklearn.decomposition as decomp
import matplotlib.pyplot as pltpca = decomp.PCA()
pca.fit(data)
E = pca.explained_variance_ratio_
print(pca.components_.shape)(400, 10304)
transformed_data = pca.transform(data)
transformed_data.shape(400, 400)
def visualize_face(data):
plt.imshow(Image.fromarray((std_vec * data + mean_vec).reshape(112,92).astype(np.uint8)), cmap='gray')
plt.show()Original Data
visualize_face(data[0])
Image Restoration with limited principal components. It need 325 principal components to restore 95 percent data.
index = 0
for i in np.cumsum(E):
if i > 0.95:
print(index)
break
index += 1191
print("Image Restoration with {0} components. Cumulative contribution ratio is {1}.".format(pca.components_[:index].shape[0], np.cumsum(E)[index]))
visualize_face(transformed_data[0][:index] @ pca.components_[:index])Image Restoration with 191 components. Cumulative contribution ratio is 0.9500663577692849.
for i in range(10):
print("Eigenface {0} with contribution {1}:".format(i+1, E[i]))
visualize_face(transformed_data[0][i] * pca.components_[i])Eigenface 1 with contribution 0.1609679694800078:
Eigenface 2 with contribution 0.1251016457589954:
Eigenface 3 with contribution 0.0812922717481364:
Eigenface 4 with contribution 0.05746099657145736:
Eigenface 5 with contribution 0.0505572444688707:
Eigenface 6 with contribution 0.030648331149216057:
Eigenface 7 with contribution 0.023824003108218368:
Eigenface 8 with contribution 0.02182406916226089:
Eigenface 9 with contribution 0.020734888617777305:
Eigenface 10 with contribution 0.019425488245887648:
kpca = decomp.KernelPCA(n_components = index, kernel="poly", degree=20, fit_inverse_transform=True)
kpca.fit(data)KernelPCA(alpha=1.0, coef0=1, degree=20, eigen_solver='auto',
fit_inverse_transform=True, gamma=None, kernel='poly',
kernel_params=None, max_iter=None, n_components=191,
remove_zero_eig=False, tol=0)
print("第一主成分の寄与率",kpca.lambdas_[0]/np.sum(kpca.lambdas_))
print(kpca.lambdas_) # 固有ベクトルの値第一主成分の寄与率 0.233714304174
[ 6.89899157e+09 5.54779307e+09 2.85525345e+09 1.71391558e+09
1.58150376e+09 1.08549049e+09 9.24325805e+08 8.33428294e+08
8.11098127e+08 6.46012001e+08 6.22190812e+08 5.34228334e+08
5.05358440e+08 4.99593599e+08 4.10489171e+08 3.09014480e+08
3.04262491e+08 2.45201572e+08 2.36757445e+08 2.28990174e+08
2.06891538e+08 1.99742921e+08 1.73493936e+08 1.65767833e+08
1.53831524e+08 1.43245214e+08 9.91219067e+07 8.76940710e+07
8.54300654e+07 7.23747130e+07 6.77426457e+07 5.56196108e+07
5.41073373e+07 4.48185023e+07 4.16523880e+07 3.33183085e+07
3.24109342e+07 3.12116174e+07 3.10549627e+07 3.05598805e+07
2.88286406e+07 2.84738056e+07 2.77554265e+07 2.76931927e+07
2.66561852e+07 2.36743743e+07 2.18453876e+07 2.10965722e+07
2.09072806e+07 2.04842353e+07 1.86025749e+07 1.82852138e+07
1.70686403e+07 1.69783919e+07 1.67372388e+07 1.52513171e+07
1.45029465e+07 1.42472830e+07 1.41623388e+07 1.39975458e+07
1.31355319e+07 1.27305311e+07 1.24289294e+07 1.24165230e+07
1.23419028e+07 1.23353714e+07 1.22332813e+07 1.08475955e+07
1.04858767e+07 1.03470021e+07 9.98450415e+06 9.78766995e+06
9.65206181e+06 9.38418424e+06 9.34778197e+06 9.23301807e+06
8.61280904e+06 8.17955656e+06 7.61581767e+06 7.46945934e+06
6.96523112e+06 6.70851867e+06 6.61042093e+06 6.45979131e+06
5.95549481e+06 5.89915807e+06 5.79094338e+06 5.72694180e+06
5.68035284e+06 5.61655659e+06 5.49995922e+06 5.46503745e+06
5.40442576e+06 5.28975774e+06 5.27094587e+06 5.23996467e+06
5.20307122e+06 5.11623923e+06 5.09705901e+06 4.92174070e+06
4.89023959e+06 4.61581888e+06 4.56581189e+06 4.22861244e+06
4.07227167e+06 4.01403900e+06 3.51103377e+06 3.49201629e+06
3.46750103e+06 3.44142874e+06 3.41514452e+06 3.33222764e+06
3.19344718e+06 3.16030935e+06 3.08926993e+06 3.07606493e+06
3.04975016e+06 3.04360124e+06 2.98805530e+06 2.94636715e+06
2.75988134e+06 2.74388101e+06 2.70919645e+06 2.69430914e+06
2.68474318e+06 2.60425491e+06 2.56732416e+06 2.51667054e+06
2.45246261e+06 2.36071142e+06 2.30550951e+06 2.29433262e+06
2.25402732e+06 2.18448319e+06 2.11479260e+06 2.08448593e+06
2.06406703e+06 2.05099277e+06 1.99957759e+06 1.99255654e+06
1.96974041e+06 1.95680459e+06 1.94666395e+06 1.93308577e+06
1.86225594e+06 1.83967587e+06 1.80637830e+06 1.79005457e+06
1.76168456e+06 1.74436191e+06 1.72773105e+06 1.57782182e+06
1.55852247e+06 1.54158188e+06 1.51901407e+06 1.48751909e+06
1.46711629e+06 1.46390490e+06 1.44385553e+06 1.41651144e+06
1.40011422e+06 1.37936357e+06 1.30500524e+06 1.30317836e+06
1.24932740e+06 1.24265705e+06 1.23226597e+06 1.16985363e+06
1.15938704e+06 1.13681773e+06 1.12416447e+06 1.11298858e+06
1.10792586e+06 1.09616168e+06 1.08492775e+06 1.06231473e+06
1.01870931e+06 9.70559122e+05 9.58666297e+05 9.33422327e+05
9.09608774e+05 8.98249536e+05 8.96355235e+05 8.88058852e+05
8.76109849e+05 8.61818738e+05 8.32648861e+05 8.15449449e+05
7.75758780e+05 7.73609770e+05 7.61068426e+05]
transformed_data = kpca.transform(data)
restored_data = kpca.inverse_transform(transformed_data)With kernel, we can restore 95 percent data with only 29 principal components.
limit = 0
index = 0
for i in kpca.lambdas_:
limit += i/np.sum(kpca.lambdas_)
index +=1
if limit > 0.95:
print(index)
break29
Image restration with 191 principal components and this clearly shows that these principal components are more superior to previous ones.
visualize_face(restored_data[0])
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