-
-
Notifications
You must be signed in to change notification settings - Fork 1.3k
/
loci.py
248 lines (199 loc) · 7.98 KB
/
loci.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
# -*- coding: utf-8 -*-
"""Local Correlation Integral (LOCI).
Part of the codes are adapted from https://github.com/Cloudy10/loci
"""
# Author: Winston Li <jk_zhengli@hotmail.com>
# License: BSD 2 clause
from __future__ import division
from __future__ import print_function
import numpy as np
from numba import njit
from sklearn.utils import check_array
from sklearn.utils.validation import check_is_fitted
from scipy.spatial.distance import pdist, squareform
from .base import BaseDetector
@njit
def _get_critical_values(dist_matrix, alpha, p_ix, r_max,
r_min=0): # pragma: no cover
"""Computes the critical values of a given distance matrix.
Parameters
----------
dist_matrix : array-like, shape (n_samples, n_features)
The distance matrix w.r.t. to the training samples.
p_ix : int
Subsetting index
alpha : int, default = 0.5
The neighbourhood parameter measures how large of a neighbourhood
should be considered "local".
r_max : int
Maximum neighbourhood radius
r_min : int, default = 0
Minimum neighbourhood radius
Returns
-------
cv : array, shape (n_critical_val, )
Returns a list of critical values.
"""
distances = dist_matrix[p_ix, :]
mask = (r_min < distances) & (distances <= r_max)
cv = np.sort(
np.concatenate((distances[mask], distances[mask] / alpha)))
return cv
@njit
def _get_sampling_N(dist_matrix, p_ix, r): # pragma: no cover
"""Computes the set of r-neighbours.
Parameters
----------
dist_matrix : array-like, shape (n_samples, n_features)
The distance matrix w.r.t. to the training samples.
p_ix : int
Subsetting index
r : int
Neighbourhood radius
Returns
-------
sample : array, shape (n_sample, )
Returns a list of neighbourhood data points.
"""
p_distances = dist_matrix[p_ix, :]
sample = np.nonzero(p_distances <= r)[0]
return sample
class LOCI(BaseDetector):
"""Local Correlation Integral.
LOCI is highly effective for detecting outliers and groups of
outliers ( a.k.a.micro-clusters), which offers the following advantages
and novelties: (a) It provides an automatic, data-dictated cut-off to
determine whether a point is an outlier—in contrast, previous methods
force users to pick cut-offs, without any hints as to what cut-off value
is best for a given dataset. (b) It can provide a LOCI plot for each
point; this plot summarizes a wealth of information about the data in
the vicinity of the point, determining clusters, micro-clusters, their
diameters and their inter-cluster distances. None of the existing
outlier-detection methods can match this feature, because they output
only a single number for each point: its outlierness score.(c) It can
be computed as quickly as the best previous methods
Read more in the :cite:`papadimitriou2003loci`.
Parameters
----------
contamination : float in (0., 0.5), optional (default=0.1)
The amount of contamination of the data set, i.e.
the proportion of outliers in the data set. Used when fitting to
define the threshold on the decision function.
alpha : int, default = 0.5
The neighbourhood parameter measures how large of a neighbourhood
should be considered "local".
k: int, default = 3
An outlier cutoff threshold for determine whether or not a point
should be considered an outlier.
Attributes
----------
decision_scores_ : numpy array of shape (n_samples,)
The outlier scores of the training data.
The higher, the more abnormal. Outliers tend to have higher
scores. This value is available once the detector is fitted.
threshold_ : float
The threshold is based on ``contamination``. It is the
``n_samples * contamination`` most abnormal samples in
``decision_scores_``. The threshold is calculated for generating
binary outlier labels.
labels_ : int, either 0 or 1
The binary labels of the training data. 0 stands for inliers
and 1 for outliers/anomalies. It is generated by applying
``threshold_`` on ``decision_scores_``.
Examples
--------
>>> from pyod.models.loci import LOCI
>>> from pyod.utils.data import generate_data
>>> n_train = 50
>>> n_test = 50
>>> contamination = 0.1
>>> X_train, y_train, X_test, y_test = generate_data(
... n_train=n_train, n_test=n_test,
... contamination=contamination, random_state=42)
>>> clf = LOCI()
>>> clf.fit(X_train)
LOCI(alpha=0.5, contamination=0.1, k=None)
"""
def __init__(self, contamination=0.1, alpha=0.5, k=3):
super(LOCI, self).__init__(contamination=contamination)
self.alpha = alpha
self.threshold_ = k
def _get_alpha_n(self, dist_matrix, indices, r):
"""Computes the alpha neighbourhood points.
Parameters
----------
dist_matrix : array-like, shape (n_samples, n_features)
The distance matrix w.r.t. to the training samples.
indices : int
Subsetting index
r : int
Neighbourhood radius
Returns
-------
alpha_n : array, shape (n_alpha, )
Returns the alpha neighbourhood points.
"""
if type(indices) is int:
alpha_n = np.count_nonzero(
dist_matrix[indices, :] < (r * self.alpha))
return alpha_n
else:
alpha_n = np.count_nonzero(
dist_matrix[indices, :] < (r * self.alpha), axis=1)
return alpha_n
def _calculate_decision_score(self, X):
"""Computes the outlier scores.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The input data points.
Returns
-------
outlier_scores : list
Returns the list of outlier scores for input dataset.
"""
outlier_scores = [0] * X.shape[0]
dist_matrix = squareform(pdist(X, metric="euclidean"))
max_dist = dist_matrix.max()
r_max = max_dist / self.alpha
for p_ix in range(X.shape[0]):
critical_values = _get_critical_values(dist_matrix, self.alpha,
p_ix, r_max)
for r in critical_values:
n_values = self._get_alpha_n(dist_matrix,
_get_sampling_N(dist_matrix,
p_ix, r), r)
cur_alpha_n = self._get_alpha_n(dist_matrix, p_ix, r)
n_hat = np.mean(n_values)
mdef = 1 - (cur_alpha_n / n_hat)
sigma_mdef = np.std(n_values) / n_hat
if n_hat >= 20:
outlier_scores[p_ix] = mdef / sigma_mdef
if mdef > (self.threshold_ * sigma_mdef):
break
return np.asarray(outlier_scores)
def fit(self, X, y=None):
"""Fit the model using X as training data.
Parameters
----------
X : array, shape (n_samples, n_features)
Training data.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
"""
X = check_array(X)
self._set_n_classes(y)
self.decision_scores_ = self._calculate_decision_score(X)
self.labels_ = (self.decision_scores_ > self.threshold_).astype(
'int').ravel()
# calculate for predict_proba()
self._mu = np.mean(self.decision_scores_)
self._sigma = np.std(self.decision_scores_)
return self
def decision_function(self, X):
check_is_fitted(self, ['decision_scores_', 'threshold_', 'labels_'])
X = check_array(X)
return self._calculate_decision_score(X)