/
ppca.py
191 lines (141 loc) · 7.09 KB
/
ppca.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
import numpy as np
import sys
#import utils
class PPCA(object):
def __init__(self,latent_dim=None,method='full',n_iter = 100,keep_past=False):
self.latent_dim = latent_dim
self.method_full = method=='full'
self.num_iter = n_iter
self.keep_hist = keep_past
def fit(self,data):
self.n_samples,self.dim = data.shape
self.mu = np.mean(data,axis=0)
self.std = np.std(data,axis=0)
self.data = data#-self.mu)/self.std
self.S = np.cov(self.data,rowvar=False)
self.likelihood = np.zeros(self.num_iter)
self.sigma2_hist = np.zeros(self.num_iter)
self.sigma2 = np.trace(self.S)/self.dim
self.W = np.random.randn(self.dim,self.latent_dim)
#self.W[:self.latent_dim,:self.latent_dim] = np.eye(self.latent_dim)
for i in range(self.num_iter):
sys.stdout.write('\r%d out of %d'%(i,self.num_iter))
sys.stdout.flush()
if self.keep_hist:
self.sigma2_hist[i] = self.sigma2
for row in range(len(self.X)):
a = np.trace(self.sigma2*self.Minv+ np.outer(self.X[row],self.X[row]))
b = np.sum((self.data[row]-self.mu)**2)/self.sigma2
c = -2*np.dot(self.X[row],self.W.T.dot(self.data[row]-self.mu))/self.sigma2
d = np.trace(self.W.T.dot(self.W).dot(np.outer(self.X[row],self.X[row])))/self.sigma2
self.likelihood[i] += -(self.dim/2*np.log(self.sigma2)+a+b+c+d)/2
self.Minv = np.linalg.inv(self.sigma2*np.eye(self.latent_dim) + np.dot(self.W.T,self.W))
Wnew = self.S.dot(self.W).dot(np.linalg.inv(
self.sigma2*np.eye(self.latent_dim) + self.Minv.dot(np.dot(self.W.T,self.S).dot(self.W))))
self.sigma2 = (np.trace(self.S) - np.trace(self.S.dot(np.dot(np.dot(self.W, self.Minv), Wnew.T))))/self.dim
self.W = Wnew
self.X = self.Minv.dot(self.W.T.dot(self.data.T-self.mu.reshape(-1,1))).T
self.data = None
self.X = None
def transform(self,data):
return self.Minv.dot(self.W.T.dot(data.T-self.mu.reshape(-1,1))).T
"""
class MPPCA(object):
def __init__(self,num_mixtures,latent_dim,niter):
self.num_mixtures = num_mixtures
self.latent_dim = latent_dim
self.niter = niter
def initialize(self):
self.pi, self.mu, self.W, self.sigma2 = utils.Kmeans(x)
def fit(self,data):
self.n_samples,self.dim = data.shape
pi, mu, W, sigma2, niter = utils.Kmeans#
p = len(sigma2)
sigma2hist = np.zeros((p, niter))
M = np.zeros((p, self.latent_dim, self.latent_dim))
Minv = np.zeros((p, self.latent_dim, self.latent_dim))
Cinv = np.zeros((p, self.dim, self.dim))
logR = np.zeros((self.n_samples, p))
R = np.zeros((self.n_samples, p))
L = np.zeros(niter)
for i in range(niter):
print('.', end='')
for c in range(p):
sigma2hist[c, i] = sigma2[c]
# M
M[c, :, :] = sigma2[c]*np.eye(self.latent_dim) + np.dot(W[c, :, :].T, W[c, :, :])
Minv[c, :, :] = np.linalg.inv(M[c, :, :])
# Cinv
Cinv[c, :, :] = (np.eye(self.dim)- np.dot(np.dot(W[c, :, :], Minv[c, :, :]), W[c, :, :].T)) / sigma2[c]
# R_ni
deviation_from_center = data - mu[c, :]
logR[:, c] = ( np.log(pi[c])
+ 0.5*np.log(
np.linalg.det(
np.eye(self.dim) - np.dot(np.dot(W[c, :, :], Minv[c, :, :]), W[c, :, :].T)
)
)
- 0.5*self.dim*np.log(sigma2[c])
- 0.5*(deviation_from_center * np.dot(deviation_from_center, Cinv[c, :, :].T)).sum(1)
)
myMax = logR.max(axis=1).reshape((self.n_samples, 1))
L[i] = (
(myMax.ravel() + np.log(np.exp(logR - myMax).sum(axis=1))).sum(axis=0)
- self.n_samples*self.dim*np.log(2*3.141593)/2.
)
logR = logR - myMax - np.reshape(np.log(np.exp(logR - myMax).sum(axis=1)), (self.n_samples, 1))
myMax = logR.max(axis=0)
logpi = myMax + np.log(np.exp(logR - myMax).sum(axis=0)) - np.log(self.n_samples)
logpi = logpi.T
pi = np.exp(logpi)
R = np.exp(logR)
for c in range(self.num_clusters):
mu[c, :] = (R[:, c].reshape((self.n_samples, 1)) * data).sum(axis=0) / R[:, c].sum()
deviation_from_center = data - mu[c, :].reshape((1, self.dim))
SW = ( (1/(pi[c]*self.n_samples))
* np.dot((R[:, c].reshape((self.n_samples, 1)) * deviation_from_center).T,
np.dot(deviation_from_center, W[c, :, :]))
)
Wnew = np.dot(SW, np.linalg.inv(sigma2[c]*np.eye(self.latent_dim) + np.dot(np.dot(Minv[c, :, :], W[c, :, :].T), SW)))
sigma2[c] = (1/self.dim) * (
(R[:, c].reshape(self.n_samples, 1) * np.power(deviation_from_center, 2)).sum()
/
(self.n_samples*pi[c])
-
np.trace(np.dot(np.dot(SW, Minv[c, :, :]), Wnew.T))
)
W[c, :, :] = Wnew
return pi, mu, W, sigma2, R, L, sigma2hist
def MPPCA_predict(self,X, pi, mu, W, sigma2):
self.n_samples, self.dim = X.shape
p = len(sigma2)
_, self.latent_dim = W[0].shape
M = np.zeros((p, self.latent_dim, self.latent_dim))
Minv = np.zeros((p, self.latent_dim, self.latent_dim))
Cinv = np.zeros((p, self.dim, self.dim))
logR = np.zeros((self.n_samples, p))
R = np.zeros((self.n_samples, p))
for c in range(p):
# M
M[c, :, :] = sigma2[c] * np.eye(self.latent_dim) + np.dot(W[c, :, :].T, W[c, :, :])
Minv[c, :, :] = np.linalg.inv(M[c, :, :])
# Cinv
Cinv[c, :, :] = (np.eye(self.dim)
- np.dot(np.dot(W[c, :, :], Minv[c, :, :]), W[c, :, :].T)
) / sigma2[c]
# R_ni
deviation_from_center = X - mu[c, :]
logR[:, c] = ( np.log(pi[c])
+ 0.5*np.log(
np.linalg.det(
np.eye(self.dim) - np.dot(np.dot(W[c, :, :], Minv[c, :, :]), W[c, :, :].T)
)
)
- 0.5*self.dim*np.log(sigma2[c])
- 0.5*(deviation_from_center * np.dot(deviation_from_center, Cinv[c, :, :].T)).sum(1)
)
myMax = logR.max(axis=1).reshape((self.n_samples, 1))
logR = logR - myMax - np.reshape(np.log(np.exp(logR - myMax).sum(axis=1)), (self.n_samples, 1))
R = np.exp(logR)
return R
"""