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
215
216
217
218
|
from collections import defaultdict
import numpy as np
from Orange.preprocess import Discretize
from Orange.preprocess.discretize import EqualFreq
def create_sql_contingency(X, columns, m):
def convert(row):
c = len(row) - 1
return [m[columns[i]].get(v) if i != c else v
for i, v in enumerate(row)]
group_by = [a.to_sql() for a in (X.domain[c] for c in columns)]
filters = ['%s IS NOT NULL' % a for a in group_by]
fields = group_by + ['COUNT(%s)' % group_by[0]]
query = X._sql_query(fields, group_by=group_by, filters=filters)
with X._execute_sql_query(query) as cur:
cont = np.array(list(map(convert, cur.fetchall())), dtype='float')
return cont[:, :-1], cont[:, -1:].flatten()
def initialize_random(conts, k):
mu = np.zeros((k, len(conts)))
sigma = np.zeros((k, len(conts)))
for i, (c, cw) in enumerate(conts):
w = np.random.random((len(c), k))
w /= w.sum(axis=1)[:, None]
c = c[:, 0] if i == 0 else c[:, 1]
for j in range(k):
mu1 = np.dot(w[:, j] * cw, c) / (w[:, j] * cw).sum()
cn = c - mu1
sigma1 = np.sum(cn ** 2 * w[:, j] * cw, axis=0) / (w[:, j] * cw).sum()
mu[j, i] = mu1
sigma[j, i] = sigma1
return mu, sigma
def initialize_kmeans(conts, k):
x = []
xm = {}
for i, (c, cw) in enumerate(conts[1:-1]):
oldx, oldxm, x, xm = x, xm, [], {}
if i == 0:
for a, w in zip(c, cw):
x.append((tuple(a), w))
xm.setdefault(tuple(a)[1:], []).append(len(x) - 1)
else:
for a, w in zip(c, cw):
for l in oldxm[tuple(a[:2])]:
olda, oldw = oldx[l]
x.append((olda + (a[2],), oldw+w))
xm.setdefault(tuple(a)[1:], []).append(len(x) - 1)
X = np.array([y[0] for y in x])
import sklearn.cluster as skl_cluster
kmeans = skl_cluster.KMeans(n_clusters=k)
Y = kmeans.fit_predict(X)
means = kmeans.cluster_centers_
covars = np.zeros((k, len(conts)))
for j in range(k):
xn = X[Y == j, :] - means[j]
covars[j] = np.sum(xn ** 2, axis=0) / len(xn)
return means, covars
def lac(conts, k, nsteps=30, window_size=1):
"""
k expected classes,
m data points,
each with dim dimensions
"""
import sys
dim = len(conts)
np.random.seed(42)
# Initialize parameters
priors = np.ones(k) / k
print("Initializing")
sys.stdout.flush()
means, covars = initialize_random(conts, k)
#means, covars = initialize_kmeans(conts, k)
print("Done")
w = [np.empty((k, len(c[0]),)) for c in conts]
active = np.ones(k, dtype=bool)
for i in range(1, nsteps + 1):
for l, (c, cw) in enumerate(conts):
lower = l - window_size if l - window_size >= 0 else None
upper = l + window_size + 1 if l + window_size + 1 <= dim else None
dims = slice(lower, upper)
active_dim = min(l, window_size)
x = c
# E step
for j in range(k):
if any(np.abs(covars[j, dims]) < 1e-15):
active[j] = 0
if active[j]:
det = covars[j, dims].prod()
inv_covars = 1. / covars[j, dims]
xn = x - means[j, dims]
factor = (2.0 * np.pi) ** (x.shape[1]/ 2.0) * det ** 0.5
w[l][j] = \
priors[j] \
* np.exp(np.sum(xn * inv_covars * xn, axis=1) * -.5) \
/ factor
else:
w[l][j] = 0
w[l][active] /= w[l][active].sum(axis=0)
# M step
n = np.sum(w[l], axis=1)
priors = n / np.sum(n)
for j in range(k):
if n[j]:
mu = np.dot(w[l][j, :] * cw, x[:, active_dim]) / (w[l][j, :] * cw).sum()
xn = x[:, active_dim] - mu
sigma = np.sum(xn ** 2 * w[l][j] * cw, axis=0) / (w[l][j, :] * cw).sum()
if np.isnan(mu).any() or np.isnan(sigma).any():
return w, means, covars, priors
else:
active[j] = 0
mu = 0.
sigma = 0.
means[j, l] = mu
covars[j, l] = sigma
# w = np.zeros((k, m))
# for j in range(k):
# if active[j]:
# det = covars[j].prod()
# inv_covars = 1. / covars[j]
# xn = X - means[j]
# factor = (2.0 * np.pi) ** (xn.shape[1] / 2.0) * det ** 0.5
# w[j] = priors[j] * exp(-.5 * np.sum(xn * inv_covars * xn, axis=1)) / factor
# w[active] /= w[active].sum(axis=0)
return w, means, covars, priors
def create_contingencies(X, callback=None):
window_size = 1
dim = len(X.domain.variables)
X_ = Discretize(method=EqualFreq(n=10))(X)
m = get_bin_centers(X_)
from Orange.data.sql.table import SqlTable
if isinstance(X, SqlTable):
conts = []
al = len(X.domain.variables)
if al > 1:
conts.append(create_sql_contingency(X_, [0, 1], m))
if callback:
callback(1, al)
for a1, a2, a3 in zip(range(al), range(1, al), range(2, al)):
conts.append(create_sql_contingency(X_, [a1, a2, a3], m))
if callback:
callback(a3, al)
if al > 2:
conts.append(create_sql_contingency(X_, [al - 2, al - 1], m))
if callback:
callback(al, al)
else:
conts = [defaultdict(float) for i in range(len(X_.domain.variables))]
for i, r in enumerate(X_):
if any(np.isnan(r)):
continue
row = tuple(m[vi].get(v) for vi, v in enumerate(r))
for l in range(len(X_.domain.variables)):
lower = l - window_size if l - window_size >= 0 else None
upper = l + window_size + 1 if l + window_size + 1 <= dim else None
dims = slice(lower, upper)
conts[l][row[dims]] += 1
conts = [zip(*x.items()) for x in conts]
conts = [(np.array(c), np.array(cw)) for c, cw in conts]
# for i, ((c1, cw1), (c2, cw2)) in enumerate(zip(contss, conts)):
# a = np.sort(np.hstack((c1, cw1[:, None])), axis=0)
# b = np.sort(np.hstack((c2, cw2[:, None])), axis=0)
# assert_almost_equal(a, b)
return conts
def get_bin_centers(X_):
m = []
for i, var in enumerate(X_.domain.variables):
cleaned_values = [tuple(map(str.strip, v.strip('[]()<>=≥').split('-')))
for v in var.values]
try:
float_values = [[float(v) for v in vals] for vals in cleaned_values]
bin_centers = {
i: v[0] if len(v) == 1 else v[0] + (v[1] - v[0])
for i, v in enumerate(float_values)
}
except ValueError:
bin_centers = {
i: i
for i, v in enumerate(cleaned_values)
}
m.append(bin_centers)
return m
|
