-
Notifications
You must be signed in to change notification settings - Fork 0
/
lnc.py
217 lines (190 loc) · 8.06 KB
/
lnc.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
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
#Written by Shuyang Gao (BiLL), email: [email protected]
from scipy import stats
import numpy as np
import scipy.spatial as ss
from scipy.special import digamma,gamma
import numpy.random as nr
import random
import re
from scipy.stats.stats import pearsonr
import numpy.linalg as la
from numpy.linalg import eig, inv, norm, det
from scipy import stats
from math import log,pi,hypot,fabs,sqrt
class MI:
@staticmethod
def zip2(*args):
#zip2(x,y) takes the lists of vectors and makes it a list of vectors in a joint space
#E.g. zip2([[1],[2],[3]],[[4],[5],[6]]) = [[1,4],[2,5],[3,6]]
return [sum(sublist,[]) for sublist in zip(*args)]
@staticmethod
def avgdigamma(points,dvec):
#This part finds number of neighbors in some radius in the marginal space
#returns expectation value of <psi(nx)>
N = len(points)
tree = ss.cKDTree(points)
avg = 0.
for i in range(N):
dist = dvec[i]
#subtlety, we don't include the boundary point,
#but we are implicitly adding 1 to kraskov def bc center point is included
num_points = len(tree.query_ball_point(points[i],dist-1e-15,p=float('inf')))
avg += digamma(num_points)/N
return avg
@staticmethod
def mi_Kraskov(X,k=5,base=np.exp(1),intens=1e-10):
'''The mutual information estimator by Kraskov et al.
ith row of X represents ith dimension of the data, e.g. X = [[1.0,3.0,3.0],[0.1,1.2,5.4]], if X has two dimensions and we have three samples
'''
#adding small noise to X, e.g., x<-X+noise
x = [];
for i in range(len(X)):
tem = [];
for j in range(len(X[i])):
tem.append([X[i][j] + intens*nr.rand(1)[0]]);
x.append(tem);
points = [];
for j in range(len(x[0])):
tem = [];
for i in range(len(x)):
tem.append(x[i][j][0]);
points.append(tem);
tree = ss.cKDTree(points);
dvec = [];
for i in range(len(x)):
dvec.append([])
for point in points:
#Find k-nearest neighbors in joint space, p=inf means max norm
knn = tree.query(point,k+1,p=float('inf'));
points_knn = [];
for i in range(len(x)):
dvec[i].append(float('-inf'));
points_knn.append([]);
for j in range(k+1):
for i in range(len(x)):
points_knn[i].append(points[knn[1][j]][i]);
#Find distances to k-nearest neighbors in each marginal space
for i in range(k+1):
for j in range(len(x)):
if dvec[j][-1] < fabs(points_knn[j][i]-points_knn[j][0]):
dvec[j][-1] = fabs(points_knn[j][i]-points_knn[j][0]);
ret = 0.
for i in range(len(x)):
ret -= MI.avgdigamma(x[i],dvec[i]);
ret += digamma(k) - (float(len(x))-1.)/float(k) + (float(len(x))-1.) * digamma(len(x[0]));
return ret;
@staticmethod
def mi_LNC(X,k=5,base=np.exp(1),alpha=0.25,intens = 1e-10):
'''The mutual information estimator by PCA-based local non-uniform correction(LNC)
ith row of X represents ith dimension of the data, e.g. X = [[1.0,3.0,3.0],[0.1,1.2,5.4]], if X has two dimensions and we have three samples
alpha is a threshold parameter related to k and d(dimensionality), please refer to our paper for details about this parameter
'''
#N is the number of samples
N = len(X[0]);
#First Step: calculate the mutual information using the Kraskov mutual information estimator
#adding small noise to X, e.g., x<-X+noise
x = [];
for i in range(len(X)):
tem = [];
for j in range(len(X[i])):
tem.append([X[i][j] + intens*nr.rand(1)[0]]);
x.append(tem);
points = [];
for j in range(len(x[0])):
tem = [];
for i in range(len(x)):
tem.append(x[i][j][0]);
points.append(tem);
tree = ss.cKDTree(points);
dvec = [];
for i in range(len(x)):
dvec.append([])
for point in points:
#Find k-nearest neighbors in joint space, p=inf means max norm
knn = tree.query(point,k+1,p=float('inf'));
points_knn = [];
for i in range(len(x)):
dvec[i].append(float('-inf'));
points_knn.append([]);
for j in range(k+1):
for i in range(len(x)):
points_knn[i].append(points[knn[1][j]][i]);
#Find distances to k-nearest neighbors in each marginal space
for i in range(k+1):
for j in range(len(x)):
if dvec[j][-1] < fabs(points_knn[j][i]-points_knn[j][0]):
dvec[j][-1] = fabs(points_knn[j][i]-points_knn[j][0]);
ret = 0.
for i in range(len(x)):
ret -= MI.avgdigamma(x[i],dvec[i]);
ret += digamma(k) - (float(len(x))-1.)/float(k) + (float(len(x))-1.) * digamma(len(x[0]));
#Second Step: Add the correction term (Local Non-Uniform Correction)
e = 0.
tot = -1;
for point in points:
tot += 1;
#Find k-nearest neighbors in joint space, p=inf means max norm
knn = tree.query(point,k+1,p=float('inf'));
knn_points = [];
for i in range(k+1):
tem = [];
for j in range(len(point)):
tem.append(points[knn[1][i]][j]);
knn_points.append(tem);
#Substract mean of k-nearest neighbor points
for i in range(len(point)):
avg = knn_points[0][i];
for j in range(k+1):
knn_points[j][i] -= avg;
#Calculate covariance matrix of k-nearest neighbor points, obtain eigen vectors
covr = [];
for i in range(len(point)):
tem = 0;
covr.append([]);
for j in range(len(point)):
covr[i].append(0);
for i in range(len(point)):
for j in range(len(point)):
avg = 0.
for ii in range(1,k+1):
avg += knn_points[ii][i] * knn_points[ii][j] / float(k);
covr[i][j] = avg;
w, v = la.eig(covr);
#Calculate PCA-bounding box using eigen vectors
V_rect = 0;
cur = [];
for i in range(len(point)):
maxV = 0.
for j in range(0,k+1):
tem = 0.;
for jj in range(len(point)):
tem += v[jj,i] * knn_points[j][jj];
if fabs(tem) > maxV:
maxV = fabs(tem);
cur.append(maxV);
V_rect = V_rect + log(cur[i]);
#Calculate the volume of original box
log_knn_dist = 0.;
for i in range(len(dvec)):
log_knn_dist += log(dvec[i][tot]);
#Perform local non-uniformity checking
if V_rect >= log_knn_dist + log(alpha):
V_rect = log_knn_dist;
#Update correction term
if (log_knn_dist - V_rect) > 0:
e += (log_knn_dist - V_rect)/N;
return (ret + e)/log(base);
@staticmethod
def entropy(x,k=3,base=np.exp(1),intens=1e-10):
""" The classic K-L k-nearest neighbor continuous entropy estimator
x should be a list of vectors, e.g. x = [[1.3],[3.7],[5.1],[2.4]]
if x is a one-dimensional scalar and we have four samples
"""
assert k <= len(x)-1, "Set k smaller than num. samples - 1"
d = len(x[0])
N = len(x)
x = [list(p + intens*nr.rand(len(x[0]))) for p in x]
tree = ss.cKDTree(x)
nn = [tree.query(point,k+1,p=float('inf'))[0][k] for point in x]
const = digamma(N)-digamma(k) + d*log(2)
return (const + d*np.mean(list(map(log,nn))))/log(base)