# Authors: Nicolas Goix <nicolas.goix@telecom-paristech.fr>
# Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# License: BSD 3 clause
import numpy as np
from warnings import warn
from scipy.stats import scoreatpercentile
from .base import NeighborsBase
from .base import KNeighborsMixin
from .base import UnsupervisedMixin
from ..utils.validation import check_is_fitted
from ..utils import check_array
__all__ = ["LocalOutlierFactor"]
class LocalOutlierFactor(NeighborsBase, KNeighborsMixin, UnsupervisedMixin):
"""Unsupervised Outlier Detection using Local Outlier Factor (LOF)
The anomaly score of each sample is called Local Outlier Factor.
It measures the local deviation of density of a given sample with
respect to its neighbors.
It is local in that the anomaly score depends on how isolated the object
is with respect to the surrounding neighborhood.
More precisely, locality is given by k-nearest neighbors, whose distance
is used to estimate the local density.
By comparing the local density of a sample to the local densities of
its neighbors, one can identify samples that have a substantially lower
density than their neighbors. These are considered outliers.
Parameters
----------
n_neighbors : int, optional (default=20)
Number of neighbors to use by default for :meth:`kneighbors` queries.
If n_neighbors is larger than the number of samples provided,
all samples will be used.
algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, optional
Algorithm used to compute the nearest neighbors:
- 'ball_tree' will use :class:`BallTree`
- 'kd_tree' will use :class:`KDTree`
- 'brute' will use a brute-force search.
- 'auto' will attempt to decide the most appropriate algorithm
based on the values passed to :meth:`fit` method.
Note: fitting on sparse input will override the setting of
this parameter, using brute force.
leaf_size : int, optional (default=30)
Leaf size passed to :class:`BallTree` or :class:`KDTree`. This can
affect the speed of the construction and query, as well as the memory
required to store the tree. The optimal value depends on the
nature of the problem.
metric : string or callable, default 'minkowski'
metric used for the distance computation. Any metric from scikit-learn
or scipy.spatial.distance can be used.
If 'precomputed', the training input X is expected to be a distance
matrix.
If metric is a callable function, it is called on each
pair of instances (rows) and the resulting value recorded. The callable
should take two arrays as input and return one value indicating the
distance between them. This works for Scipy's metrics, but is less
efficient than passing the metric name as a string.
Valid values for metric are:
- from scikit-learn: ['cityblock', 'cosine', 'euclidean', 'l1', 'l2',
'manhattan']
- from scipy.spatial.distance: ['braycurtis', 'canberra', 'chebyshev',
'correlation', 'dice', 'hamming', 'jaccard', 'kulsinski',
'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto',
'russellrao', 'seuclidean', 'sokalmichener', 'sokalsneath',
'sqeuclidean', 'yule']
See the documentation for scipy.spatial.distance for details on these
metrics:
http://docs.scipy.org/doc/scipy/reference/spatial.distance.html
p : integer, optional (default=2)
Parameter for the Minkowski metric from
:func:`sklearn.metrics.pairwise.pairwise_distances`. When p = 1, this
is equivalent to using manhattan_distance (l1), and euclidean_distance
(l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
metric_params : dict, optional (default=None)
Additional keyword arguments for the metric function.
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. When fitting this is used to define the
threshold on the decision function.
n_jobs : int, optional (default=1)
The number of parallel jobs to run for neighbors search.
If ``-1``, then the number of jobs is set to the number of CPU cores.
Affects only :meth:`kneighbors` and :meth:`kneighbors_graph` methods.
Attributes
----------
negative_outlier_factor_ : numpy array, shape (n_samples,)
The opposite LOF of the training samples. The lower, the more abnormal.
Inliers tend to have a LOF score close to 1, while outliers tend
to have a larger LOF score.
The local outlier factor (LOF) of a sample captures its
supposed 'degree of abnormality'.
It is the average of the ratio of the local reachability density of
a sample and those of its k-nearest neighbors.
n_neighbors_ : integer
The actual number of neighbors used for :meth:`kneighbors` queries.
References
----------
.. [1] Breunig, M. M., Kriegel, H. P., Ng, R. T., & Sander, J. (2000, May).
LOF: identifying density-based local outliers. In ACM sigmod record.
"""
def __init__(self, n_neighbors=20, algorithm='auto', leaf_size=30,
metric='minkowski', p=2, metric_params=None,
contamination=0.1, n_jobs=1):
self._init_params(n_neighbors=n_neighbors,
algorithm=algorithm,
leaf_size=leaf_size, metric=metric, p=p,
metric_params=metric_params, n_jobs=n_jobs)
self.contamination = contamination
[docs] def fit_predict(self, X, y=None):
""""Fits the model to the training set X and returns the labels
(1 inlier, -1 outlier) on the training set according to the LOF score
and the contamination parameter.
Parameters
----------
X : array-like, shape (n_samples, n_features), default=None
The query sample or samples to compute the Local Outlier Factor
w.r.t. to the training samples.
Returns
-------
is_inlier : array, shape (n_samples,)
Returns -1 for anomalies/outliers and 1 for inliers.
"""
return self.fit(X)._predict()
[docs] def fit(self, X, y=None):
"""Fit the model using X as training data.
Parameters
----------
X : {array-like, sparse matrix, BallTree, KDTree}
Training data. If array or matrix, shape [n_samples, n_features],
or [n_samples, n_samples] if metric='precomputed'.
Returns
-------
self : object
Returns self.
"""
if not (0. < self.contamination <= .5):
raise ValueError("contamination must be in (0, 0.5]")
super(LocalOutlierFactor, self).fit(X)
n_samples = self._fit_X.shape[0]
if self.n_neighbors > n_samples:
warn("n_neighbors (%s) is greater than the "
"total number of samples (%s). n_neighbors "
"will be set to (n_samples - 1) for estimation."
% (self.n_neighbors, n_samples))
self.n_neighbors_ = max(1, min(self.n_neighbors, n_samples - 1))
self._distances_fit_X_, _neighbors_indices_fit_X_ = (
self.kneighbors(None, n_neighbors=self.n_neighbors_))
self._lrd = self._local_reachability_density(
self._distances_fit_X_, _neighbors_indices_fit_X_)
# Compute lof score over training samples to define threshold_:
lrd_ratios_array = (self._lrd[_neighbors_indices_fit_X_] /
self._lrd[:, np.newaxis])
self.negative_outlier_factor_ = -np.mean(lrd_ratios_array, axis=1)
self.threshold_ = -scoreatpercentile(
-self.negative_outlier_factor_, 100. * (1. - self.contamination))
return self
def _predict(self, X=None):
"""Predict the labels (1 inlier, -1 outlier) of X according to LOF.
If X is None, returns the same as fit_predict(X_train).
This method allows to generalize prediction to new observations (not
in the training set). As LOF originally does not deal with new data,
this method is kept private.
Parameters
----------
X : array-like, shape (n_samples, n_features), default=None
The query sample or samples to compute the Local Outlier Factor
w.r.t. to the training samples. If None, makes prediction on the
training data without considering them as their own neighbors.
Returns
-------
is_inlier : array, shape (n_samples,)
Returns -1 for anomalies/outliers and +1 for inliers.
"""
check_is_fitted(self, ["threshold_", "negative_outlier_factor_",
"n_neighbors_", "_distances_fit_X_"])
if X is not None:
X = check_array(X, accept_sparse='csr')
is_inlier = np.ones(X.shape[0], dtype=int)
is_inlier[self._decision_function(X) <= self.threshold_] = -1
else:
is_inlier = np.ones(self._fit_X.shape[0], dtype=int)
is_inlier[self.negative_outlier_factor_ <= self.threshold_] = -1
return is_inlier
def _decision_function(self, X):
"""Opposite of the Local Outlier Factor of X (as bigger is better,
i.e. large values correspond to inliers).
The argument X is supposed to contain *new data*: if X contains a
point from training, it consider the later in its own neighborhood.
Also, the samples in X are not considered in the neighborhood of any
point.
The decision function on training data is available by considering the
opposite of the negative_outlier_factor_ attribute.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The query sample or samples to compute the Local Outlier Factor
w.r.t. the training samples.
Returns
-------
opposite_lof_scores : array, shape (n_samples,)
The opposite of the Local Outlier Factor of each input samples.
The lower, the more abnormal.
"""
check_is_fitted(self, ["threshold_", "negative_outlier_factor_",
"_distances_fit_X_"])
X = check_array(X, accept_sparse='csr')
distances_X, neighbors_indices_X = (
self.kneighbors(X, n_neighbors=self.n_neighbors_))
X_lrd = self._local_reachability_density(distances_X,
neighbors_indices_X)
lrd_ratios_array = (self._lrd[neighbors_indices_X] /
X_lrd[:, np.newaxis])
# as bigger is better:
return -np.mean(lrd_ratios_array, axis=1)
def _local_reachability_density(self, distances_X, neighbors_indices):
"""The local reachability density (LRD)
The LRD of a sample is the inverse of the average reachability
distance of its k-nearest neighbors.
Parameters
----------
distances_X : array, shape (n_query, self.n_neighbors)
Distances to the neighbors (in the training samples `self._fit_X`)
of each query point to compute the LRD.
neighbors_indices : array, shape (n_query, self.n_neighbors)
Neighbors indices (of each query point) among training samples
self._fit_X.
Returns
-------
local_reachability_density : array, shape (n_samples,)
The local reachability density of each sample.
"""
dist_k = self._distances_fit_X_[neighbors_indices,
self.n_neighbors_ - 1]
reach_dist_array = np.maximum(distances_X, dist_k)
# 1e-10 to avoid `nan' when nb of duplicates > n_neighbors_:
return 1. / (np.mean(reach_dist_array, axis=1) + 1e-10)
