-
Notifications
You must be signed in to change notification settings - Fork 0
/
ssif.py
622 lines (510 loc) · 22.1 KB
/
ssif.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
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
import numpy as np
import pandas as pd
import sys
import random as rn
from collections import Counter
import os
import warnings
import threading
from multiprocessing import Pool
import seaborn as sb
from joblib import Parallel, delayed
import matplotlib.pyplot as plt
import scipy
import warnings
warnings.filterwarnings('ignore')
def compute_labeled_component(X, Y, X_axis, ul):
"""
This function computes the labeled component.
Parameters
----------
X : numpy array of shape (n_labeled_samples, n_features)
The labeled samples at that splitting step.
Y : numpy array of shape (n_samples)
The corresponding labels.
X_axis : numpy array of shape (n_thresholds)
The thresholds for which the unlabeled component has to be estimated.
ul : numpy array of shape (n_unlabeled_samples, n_features)
The unlabeled samples at that splitting step.
Returns
-------
labeled_component : numpy array of shape (n_thresholds)
The estimated labeled component.
"""
if Y[Y==1].size == 0:
min_normal = X[Y==-1].min()
max_normal = X[Y==-1].max()
dist_l = np.abs(min_normal - X_axis)
dist_r = np.abs(max_normal - X_axis)
dist = np.min(np.array([dist_r, dist_l]),axis=0)
dist[np.logical_or(dist <= max_normal, dist >= min_normal)] = 0
return dist
elif Y[Y==-1].size == 0:
anomalies = X[Y==1]
normals = ul
an_index = np.sort(np.searchsorted(X_axis, anomalies, side='right'))
nor_index = np.sort(np.searchsorted(X_axis, normals, side='right'))
an_left = np.searchsorted(an_index, range(len(X_axis)),side='right')
nor_left = np.searchsorted(nor_index,range(len(X_axis)), side='right')
an_right = len(anomalies) - an_left
nor_right = len(normals) - nor_left
p_al = np.nan_to_num(an_left/(an_left+nor_left), nan=0, posinf=0, neginf=0)
p_nl = 1 - p_al
p_ar = np.nan_to_num(an_right/(an_right+nor_right), nan=0, posinf=0, neginf=0)
p_nr = 1 - p_ar
p_n = len(normals) / len(X)
p_a = 1 - p_n
c_l = (an_left + nor_left) / len(X)
c_r = 1 - c_l
en_l = np.nan_to_num(- p_al * np.log2(p_al) - (p_nl) * np.log2(p_nl),nan=0,posinf=0,neginf=0)
en_r = np.nan_to_num(- p_ar * np.log2(p_ar) - (p_nr) * np.log2(p_nr),nan=0,posinf=0,neginf=0)
en_in = np.nan_to_num(- p_a * np.log2(p_a) - (p_n) * np.log2(p_n),nan=0,posinf=0,neginf=0)
return (en_in - c_l * en_l - c_r * en_r)
else:
anomalies = X[Y==1]
normals = X[Y==-1]
an_index = np.sort(np.searchsorted(X_axis, anomalies, side='right'))
nor_index = np.sort(np.searchsorted(X_axis, normals, side='right'))
an_left = np.searchsorted(an_index, range(len(X_axis)),side='right')
nor_left = np.searchsorted(nor_index,range(len(X_axis)), side='right')
an_right = len(anomalies) - an_left
nor_right = len(normals) - nor_left
p_al = np.nan_to_num(an_left/(an_left+nor_left), nan=0, posinf=0, neginf=0)
p_nl = 1 - p_al
p_ar = np.nan_to_num(an_right/(an_right+nor_right), nan=0, posinf=0, neginf=0)
p_nr = 1 - p_ar
p_n = len(normals) / len(X)
p_a = 1 - p_n
c_l = (an_left + nor_left) / len(X)
c_r = 1 - c_l
en_l = np.nan_to_num(- p_al * np.log2(p_al) - (p_nl) * np.log2(p_nl),nan=0,posinf=0,neginf=0)
en_r = np.nan_to_num(- p_ar * np.log2(p_ar) - (p_nr) * np.log2(p_nr),nan=0,posinf=0,neginf=0)
en_in = np.nan_to_num(- p_a * np.log2(p_a) - (p_n) * np.log2(p_n),nan=0,posinf=0,neginf=0)
return (en_in - c_l * en_l - c_r * en_r)
def compute_unlabeled_component(X,X_axis):
"""
This function computes the unlabeled component.
Parameters
----------
X : numpy array of shape (n_unlabeled_samples, n_features)
The unlabeled samples at that splitting step.
X_axis : numpy array of shape (n_thresholds)
The thresholds for which the unlabeled component has to be estimated.
Returns
-------
unlabeled_component : numpy array of shape (n_thresholds)
The estimated unlabeled component.
"""
ul_index = np.sort(np.searchsorted(X_axis, X, side='right'))
X_left = np.searchsorted(ul_index, range(len(X_axis)),side='right')
X_right = len(X) - X_left
matrix = np.repeat(X.reshape((len(X),1)), len(X_axis), axis=1)
left = np.where(matrix < X_axis, matrix, np.nan)
right = np.where(matrix >= X_axis, matrix, np.nan)
var_left = np.nanvar(left, axis=0)
var_right = np.nanvar(right, axis=0)
var_left[np.isnan(var_left)] = 0
var_right[np.isnan(var_right)] = 0
wb = X_left / X.size
wf = 1 - wb
V2w = wb * (var_left) + wf * (var_right)
t1 = np.nan_to_num(wb*np.log(wb), nan=0,posinf=0, neginf=0)
t2 = np.nan_to_num(wf*np.log(wf), nan=0,posinf=0, neginf=0)
t3 = np.nan_to_num(np.log(np.sqrt(V2w)), nan=0,posinf=0, neginf=0)
return t1 +t2 - t3
def compute_split_distribution(X,Y,X_axis):
"""
This function computes the split distribution for a feature.
Parameters
----------
X : numpy array of shape (n_samples,)
The labeled samples along a given feature at that splitting step.
Y : numpy array of shape (n_samples)
The corresponding labels.
X_axis : numpy array of shape (n_thresholds,)
The thresholds for which the split distribution has to be estimated.
Returns
-------
split_distribution : scipy.stats.rv_histogram
The estimated split distribution.
split_scores : numpy array of shape (n_thresholds-1,)
The quality of the thresholds for which the split distribution is estimated.
"""
X_norm = np.nan_to_num((X - X.min()) / (X.max() - X.min()), nan=0.5)
pp = Y[Y!=0].size/Y.size
unlabeled_component = compute_unlabeled_component(X_norm[Y==0],X_axis) if Y[Y==0].size > 0 else np.zeros((X_axis.size))
labeled_component = compute_labeled_component(X_norm[Y!=0], Y[Y!=0], X_axis, X_norm[Y==0]) if Y[Y!=0].size > 0 else np.zeros((X_axis.size))
unlabeled_component = np.nan_to_num((unlabeled_component - unlabeled_component.min()) / (unlabeled_component.max() - unlabeled_component.min()),nan=0)
labeled_component = np.nan_to_num((labeled_component - labeled_component.min()) / (labeled_component.max() - labeled_component.min()),nan=0)
split_scores = (1-pp)*unlabeled_component + (1+pp)*labeled_component
if split_scores.max() != split_scores.min():
split_distribution = scipy.stats.rv_histogram((split_scores,np.append(X_axis,1)), density=True)
split_scores = (split_scores - split_scores.min()) / (split_scores.max() - split_scores.min())
else:
split_distribution = scipy.stats.uniform()
split_scores[0:split_scores.size] = 1
return split_distribution, split_scores
def c_factor(n) :
if(n<2):
n=2
return 2.0*(np.log(n-1)+0.5772156649) - (2.0*(n-1.)/(n*1.0))
class SSIF(object):
"""
SSIF class
The algorithm first constructs an ensemble of SSiTree.
Then, it computes the anomaly scores based on the (expected) path lengths in the ensemble.
Parameters
----------
ntrees : int, optional
The number of SSiTree in the ensemble.
sample : float, optional
The proportion of samples to draw from X to train each SSiTree.
If sample is larger than 1, all samples will be used for all trees (no sampling).
nattr : float, optional
The proportion of features for which the split distribution is computed.
If nattr is larger than 1, the split distribution will be computed for all feautres.
max_depth : float, optional
The height limit at which the tree construction phase stops given as a factor of the deafult value.
seed : int, optional
random_state is the seed used by the random number generator;
If None, it is set to 9 by default
"""
def __init__(self, contamination=0.1, max_depth=None, ntrees=100, seed=9, sample=None, nattr=None):
self.ntrees = ntrees
self.sample = sample
self.max_depth = max_depth
self.nattr = nattr
self.ntrees = ntrees
self.forest_seed = np.random.RandomState(seed=seed)
self.contamination = contamination
self.Trees = []
def fit(self, Xtrain, ytrain, n_jobs=-1):
"""
The SSIF algorithm first constructs an ensemble of SSiTree. Then, it computes the anomaly scores based on the (expected) path lengths in the ensemble.
Parameters
----------
Xtrain : numpy array of shape (n_samples, n_features)
The input samples.
ytrain : numpy array of shape (n_samples)
The input labels.
n_jobs : int, optional
The number of jobs to run in parallel for the `fit` method.
If -1, then the number of jobs is set to the number of cores.
"""
self.X = Xtrain
self.Y = ytrain
if self.sample != None:
self.sample = int(self.sample*Xtrain.shape[0])
else:
self.sample = min(max(128,int(Xtrain.shape[0]/3)), Xtrain.shape[0])
self.c = c_factor(self.sample)
if self.max_depth != None:
self.max_depth = int(np.ceil(self.max_depth*2*max(np.log2(self.sample), 2)))
else:
self.max_depth = int(np.ceil(2*max(np.log2(self.sample), 2)))
if self.nattr != None:
self.nattr = int(max(1,self.nattr))
else:
self.nattr = min(Xtrain.shape[1],max(3,int(Xtrain.shape[1]/5)))
self.Trees = Parallel(n_jobs=n_jobs)(delayed(self.buildTree)(self.forest_seed.randint(0,100000)) for i in range(self.ntrees))
self.decision_scores_ = self.compute_anomaly_scores(Xtrain)
self.min_score = np.min(self.decision_scores_)
self.max_score = np.max(self.decision_scores_)
self.decision_scores_ = (self.decision_scores_ - self.min_score) / (self.max_score - self.min_score)
self.t_ = np.percentile(self.decision_scores_, q=int((1.0 - self.contamination) * 100))
def predict(self, X):
"""
Predict the labels for the input samples.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The input samples.
Returns
-------
labels : numpy array of shape (n_samples,)
The predicted labels.
"""
test_probs = self.predict_proba(X)
return np.where(test_probs[:,1] >= 0.5, 1, -1)
def predict_proba(self, X):
"""
Predict the probabilities for the input samples.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The input samples.
Returns
-------
probs : numpy array of shape (n_samples, 2)
The probabilities of being normal and anomalous for the input samples.
"""
scores = self.compute_anomaly_scores(X)
scores = np.clip((scores - self.min_score) / (self.max_score - self.min_score), 0, 1)
probs = 1.0 - np.exp(np.log(0.5) * np.power(scores / self.t_, 2))
return np.vstack([1-probs, probs]).T
def buildTree(self, seed):
"""
Wrapper funtion used for the parallel computation of the SSiTrees.
Parameters
----------
i : int
Index of the tree.
seed: int
Seed of the tree.
Returns
-------
t : SSiTree
The constructed SSiTree.
"""
tree_seed = np.random.RandomState(seed=seed)
ix = tree_seed.choice(range(len(self.X)), self.sample, replace=False)
X_p = self.X[ix]
Y_p = self.Y[ix]
t = SSiTree(X_p, Y_p, 0, self.max_depth, self.nattr, tree_seed)
return t
def compute_anomaly_scores(self, X):
"""
Predict raw anomaly score of X using the fitted detector.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
Returns
-------
anomaly_scores : numpy array of shape (n_samples,)
The anomaly score of the input samples.
"""
S = np.zeros(len(X))
for i in range(len(X)):
paths = np.zeros(self.ntrees)
for j in range(self.ntrees):
pf = PathFactor(X[i], self.Trees[j], self.max_depth)
paths[j] = pf.path
S[i] = 2**(-np.mean(paths)/self.c)
return S
class Node(object):
"""
This class is used to represent the nodes of the SSiTree.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The samples contained in the node.
y : numpy array of shape (n_samples)
The corresponding labels.
q : int
The feature used to split the data in the node. It is set to -1 if the node is a leaf.
p : int
The split values used to split the data in the node. It is set to -1 if the node is a leaf.
e : int
The height of the node in the tree.
score : float
The quality of the selected feature q and split value p.
left : Node
The left child of the node.
right : Node
The right child of the node.
node_type : str, optional
If the node is a leaf or an internal node.
"""
def __init__(self, X, Y, q, p, e, score, left, right, node_type = '' ):
self.e = e
self.size = len(X)
self.X = X #
self.Y = Y
self.q = q
self.p = p
self.left = left
self.right = right
self.ntype = node_type
self.score = score
if Y.size > 0:
self.perc_anomaly = Y[Y==1].size / Y.size
self.perc_normal = Y[Y==-1].size / Y.size
else:
self.perc_anomaly = self.perc_normal = 0
class SSiTree(object):
"""
This class is used to represent an SSiTree.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The samples contained in the tree.
y : numpy array of shape (n_samples)
The corresponding labels.
e : int
The height of the tree.
l : int
The height limit of the tree.
nattr : int
The number of features for which the split distribution is estimated.
seed : int
The seed of the tree.
"""
def __init__(self,X,Y,e,l, nattr, seed):
self.e = e # depth
self.X = X
self.Y = Y
self.height = 0
self.size = len(X) # n objects
self.l = l # depth inferior limit
self.p = None
self.q = None
self.exnodes = -1
self.eps = 10**-4
self.nattr = nattr
self.tree_seed = seed
self.root = self.make_tree(X,Y,e,l)
def make_tree(self,X,Y,e,l):
"""
This function is used to recursively build the trees.
Parameters
----------
X : numpy array of shape (n_samples,n_features)
The samples at that splitting step.
Y : numpy array of shape (n_samples)
The corresponding labels.
e : int
The current height in the tree
l : int
The depth limit of the tree.
Returns
-------
n : Node
The built node.
"""
self.e = e
seed = self.tree_seed
if Y[Y!=1].size == 0 or len(np.unique(X, axis=0)) <= 1 or e >= l:
if e > self.height:
self.height = e
left = None
right = None
self.exnodes += 1
return Node(X, Y, self.q, self.p, e, 1, left, right, node_type = 'exNode')
else:
num_bin = max(5, int(len(X)/10))
X_axis = np.linspace(self.eps, 1-self.eps, num_bin-1)
attr = np.array([len(np.unique(X[:,k])) for k in range(X.shape[1])], dtype=int)
attr = np.where(attr > 1)[0].tolist()
attr_morethanone = attr.copy()
if Y[Y==1].size > 0:
for i in attr.copy():
max_us = X[:, i][Y!=1].max()
min_us = X[:, i][Y!=1].min()
max_ss = X[:, i][Y==1].max()
min_ss = X[:, i][Y==1].min()
if max_ss <= max_us and min_us <= min_ss:
attr.remove(i)
else:
max_al = X[:, i][Y==1].max()
min_al = X[:, i][Y==1].min()
max_nl = X[:, i][Y!=1].max()
min_nl = X[:, i][Y!=1].min()
norm_max_al = (max_al - X[:,i].min()) / (X[:,i].max() - X[:,i].min())
norm_min_al = (min_al - X[:,i].min()) / (X[:,i].max() - X[:,i].min())
norm_max_nl = (max_nl - X[:,i].min()) / (X[:,i].max() - X[:,i].min())
norm_min_nl = (min_nl - X[:,i].min()) / (X[:,i].max() - X[:,i].min())
if norm_max_al > norm_max_nl and norm_max_nl > X_axis[num_bin-2]:
X_axis = np.insert(X_axis, num_bin-1, (norm_max_nl + norm_max_al) / 2)
X_axis = np.insert(X_axis, num_bin-1, norm_max_nl)
num_bin += 2
elif norm_max_al > norm_max_nl and norm_max_nl != 0:
X_axis = np.insert(X_axis, num_bin-1, norm_max_nl-self.eps)
X_axis = np.sort(X_axis)
num_bin += 1
if norm_min_al < norm_min_nl and norm_min_nl < X_axis[0]:
X_axis = np.insert(X_axis, 0, (norm_min_nl + norm_min_al) / 2)
X_axis = np.insert(X_axis, 1, norm_min_nl)
num_bin += 2
elif norm_min_al < norm_min_nl and norm_min_nl != 1:
X_axis = np.insert(X_axis, num_bin-1, norm_min_nl+self.eps)
X_axis = np.sort(X_axis)
num_bin += 1
if len(attr) >= self.nattr:
values = seed.choice(attr, self.nattr, replace=False)
elif len(attr) > 0:
values = seed.choice(attr, len(attr), replace=False)
else:
values = seed.choice(attr_morethanone, min(self.nattr,len(attr_morethanone)), replace=False)
Y_axis={}
for idx in values:
Y_axis[idx] = []
Y_axis[idx], _ = compute_split_distribution(X[:,idx], Y, X_axis)
uniform = scipy.stats.uniform()
KL_values = np.zeros((X.shape[1],))
for idx in Y_axis.keys():
p1 = Y_axis[idx].cdf(X_axis)
p1 = p1[1:] - p1[:-1]
u1 = uniform.cdf(X_axis)
u1 = u1[1:] - u1[:-1]
kl = np.sum(scipy.special.kl_div(p1,u1))
KL_values[idx] = kl
if KL_values.sum() <= 0:
KL_values[values] = 1
KL_norm = np.nan_to_num((KL_values - KL_values.min()) / (KL_values.max() - KL_values.min()),nan=1)
KL_values /= KL_values.sum()
cdf_kl = np.nan_to_num(np.cumsum(KL_values), nan=0)
u = seed.uniform(0,1)
self.q = np.searchsorted(cdf_kl, u) if sum(cdf_kl) != 0 else seed.choice(list(Y_axis.keys()),1,replace=False)[0]
u = seed.uniform(0,1)
split_value = Y_axis[self.q].ppf(u)
self.p = split_value*(X[:,self.q].max() - X[:,self.q].min()) + X[:,self.q].min()
w = np.where(X[:,self.q] < self.p,True,False)
return Node(X, Y, self.q, self.p, e,1, left=self.make_tree(X[w],Y[w],e+1,l), right=self.make_tree(X[~w],Y[~w],e+1,l), node_type = 'inNode' )
def get_node(self, path):
node = self.root
for p in path:
if p == 'L' : node = node.left
if p == 'R' : node = node.right
return node
class PathFactor(object):
"""
This class is used to find for a tree the height of the leaf where a sample ends up .
Parameters
----------
x : numpy array of shape (n_features)
The considered sample.
tree : SSiTree
The considered tree.
depth_limit : int
The height limit of the tree.
"""
def __init__(self,x, ssitree, depth_limit):
self.path_list=[]
self.x = x
self.limit = depth_limit
self.path = self.find_path(ssitree.root)
def find_path(self, T, e=0, score=0):
"""
This class is used to recursively find the leaf in the tree and modify the height depending on the available labels and on the splits quality.
Parameters
----------
T : Node
The node at that point in the recursion.
e : int
The actual height in the tree.
score : float
The average quality of the splits traversed in the tree.
Returns
-------
height : float
The modified height of the sample.
"""
if T.ntype == 'exNode':
self.e = e
self.score = score / e
if self.e < self.limit:
self.e = e
else:
self.e = e + c_factor(T.size)
if self.e >= self.limit:
return self.e
else:
return self.e*(1 + T.perc_normal - T.perc_anomaly)
else:
a = T.q
if self.x[a] < T.p:
self.path_list.append('L')
return self.find_path(T.left, e+1, score+T.score)
else:
self.path_list.append('R')
return self.find_path(T.right, e+1, score+T.score)