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# Authors: Nicolas Goix <nicolas.goix@telecom-paristech.fr>
# Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# License: BSD 3 clause
import warnings
from numbers import Real
import numpy as np
from ..base import OutlierMixin, _fit_context
from ..utils import check_array
from ..utils._param_validation import Interval, StrOptions
from ..utils.metaestimators import available_if
from ..utils.validation import check_is_fitted
from ._base import KNeighborsMixin, NeighborsBase
__all__ = ["LocalOutlierFactor"]
class LocalOutlierFactor(KNeighborsMixin, OutlierMixin, NeighborsBase):
"""Unsupervised Outlier Detection using the Local Outlier Factor (LOF).
The anomaly score of each sample is called the Local Outlier Factor.
It measures the local deviation of the 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.
.. versionadded:: 0.19
Parameters
----------
n_neighbors : int, 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'}, default='auto'
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, default=30
Leaf is 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 : str or callable, default='minkowski'
Metric to use for distance computation. Default is "minkowski", which
results in the standard Euclidean distance when p = 2. See the
documentation of `scipy.spatial.distance
<https://docs.scipy.org/doc/scipy/reference/spatial.distance.html>`_ and
the metrics listed in
:class:`~sklearn.metrics.pairwise.distance_metrics` for valid metric
values.
If metric is "precomputed", X is assumed to be a distance matrix and
must be square during fit. X may be a :term:`sparse graph`, in which
case only "nonzero" elements may be considered neighbors.
If metric is a callable function, it takes two arrays representing 1D
vectors as inputs and must return one value indicating the distance
between those vectors. This works for Scipy's metrics, but is less
efficient than passing the metric name as a string.
p : float, default=2
Parameter for the Minkowski metric from
:func:`sklearn.metrics.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, default=None
Additional keyword arguments for the metric function.
contamination : 'auto' or float, default='auto'
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 scores of the samples.
- if 'auto', the threshold is determined as in the
original paper,
- if a float, the contamination should be in the range (0, 0.5].
.. versionchanged:: 0.22
The default value of ``contamination`` changed from 0.1
to ``'auto'``.
novelty : bool, default=False
By default, LocalOutlierFactor is only meant to be used for outlier
detection (novelty=False). Set novelty to True if you want to use
LocalOutlierFactor for novelty detection. In this case be aware that
you should only use predict, decision_function and score_samples
on new unseen data and not on the training set; and note that the
results obtained this way may differ from the standard LOF results.
.. versionadded:: 0.20
n_jobs : int, default=None
The number of parallel jobs to run for neighbors search.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
Attributes
----------
negative_outlier_factor_ : ndarray of shape (n_samples,)
The opposite LOF of the training samples. The higher, the more normal.
Inliers tend to have a LOF score close to 1
(``negative_outlier_factor_`` 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_ : int
The actual number of neighbors used for :meth:`kneighbors` queries.
offset_ : float
Offset used to obtain binary labels from the raw scores.
Observations having a negative_outlier_factor smaller than `offset_`
are detected as abnormal.
The offset is set to -1.5 (inliers score around -1), except when a
contamination parameter different than "auto" is provided. In that
case, the offset is defined in such a way we obtain the expected
number of outliers in training.
.. versionadded:: 0.20
effective_metric_ : str
The effective metric used for the distance computation.
effective_metric_params_ : dict
The effective additional keyword arguments for the metric function.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_samples_fit_ : int
It is the number of samples in the fitted data.
See Also
--------
sklearn.svm.OneClassSVM: Unsupervised Outlier Detection using
Support Vector Machine.
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.
Examples
--------
>>> import numpy as np
>>> from sklearn.neighbors import LocalOutlierFactor
>>> X = [[-1.1], [0.2], [101.1], [0.3]]
>>> clf = LocalOutlierFactor(n_neighbors=2)
>>> clf.fit_predict(X)
array([ 1, 1, -1, 1])
>>> clf.negative_outlier_factor_
array([ -0.9821..., -1.0370..., -73.3697..., -0.9821...])
"""
_parameter_constraints: dict = {
**NeighborsBase._parameter_constraints,
"contamination": [
StrOptions({"auto"}),
Interval(Real, 0, 0.5, closed="right"),
],
"novelty": ["boolean"],
}
_parameter_constraints.pop("radius")
def __init__(
self,
n_neighbors=20,
*,
algorithm="auto",
leaf_size=30,
metric="minkowski",
p=2,
metric_params=None,
contamination="auto",
novelty=False,
n_jobs=None,
):
super().__init__(
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
self.novelty = novelty
def _check_novelty_fit_predict(self):
if self.novelty:
msg = (
"fit_predict is not available when novelty=True. Use "
"novelty=False if you want to predict on the training set."
)
raise AttributeError(msg)
return True
@available_if(_check_novelty_fit_predict)
def fit_predict(self, X, y=None):
"""Fit the model to the training set X and return the labels.
**Not available for novelty detection (when novelty is set to True).**
Label is 1 for an inlier and -1 for an outlier according to the LOF
score and the contamination parameter.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), default=None
The query sample or samples to compute the Local Outlier Factor
w.r.t. the training samples.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
is_inlier : ndarray of shape (n_samples,)
Returns -1 for anomalies/outliers and 1 for inliers.
"""
# As fit_predict would be different from fit.predict, fit_predict is
# only available for outlier detection (novelty=False)
return self.fit(X)._predict()
@_fit_context(
# LocalOutlierFactor.metric is not validated yet
prefer_skip_nested_validation=False
)
def fit(self, X, y=None):
"""Fit the local outlier factor detector from the training dataset.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features) or \
(n_samples, n_samples) if metric='precomputed'
Training data.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : LocalOutlierFactor
The fitted local outlier factor detector.
"""
self._fit(X)
n_samples = self.n_samples_fit_
if self.n_neighbors > n_samples:
warnings.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(
n_neighbors=self.n_neighbors_
)
if self._fit_X.dtype == np.float32:
self._distances_fit_X_ = self._distances_fit_X_.astype(
self._fit_X.dtype,
copy=False,
)
self._lrd = self._local_reachability_density(
self._distances_fit_X_, _neighbors_indices_fit_X_
)
# Compute lof score over training samples to define offset_:
lrd_ratios_array = (
self._lrd[_neighbors_indices_fit_X_] / self._lrd[:, np.newaxis]
)
self.negative_outlier_factor_ = -np.mean(lrd_ratios_array, axis=1)
if self.contamination == "auto":
# inliers score around -1 (the higher, the less abnormal).
self.offset_ = -1.5
else:
self.offset_ = np.percentile(
self.negative_outlier_factor_, 100.0 * self.contamination
)
return self
def _check_novelty_predict(self):
if not self.novelty:
msg = (
"predict is not available when novelty=False, use "
"fit_predict if you want to predict on training data. Use "
"novelty=True if you want to use LOF for novelty detection "
"and predict on new unseen data."
)
raise AttributeError(msg)
return True
@available_if(_check_novelty_predict)
def predict(self, X=None):
"""Predict the labels (1 inlier, -1 outlier) of X according to LOF.
**Only available for novelty detection (when novelty is set to True).**
This method allows to generalize prediction to *new observations* (not
in the training set). Note that the result of ``clf.fit(X)`` then
``clf.predict(X)`` with ``novelty=True`` may differ from the result
obtained by ``clf.fit_predict(X)`` with ``novelty=False``.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The query sample or samples to compute the Local Outlier Factor
w.r.t. the training samples.
Returns
-------
is_inlier : ndarray of shape (n_samples,)
Returns -1 for anomalies/outliers and +1 for inliers.
"""
return self._predict(X)
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).
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), default=None
The query sample or samples to compute the Local Outlier Factor
w.r.t. the training samples. If None, makes prediction on the
training data without considering them as their own neighbors.
Returns
-------
is_inlier : ndarray of shape (n_samples,)
Returns -1 for anomalies/outliers and +1 for inliers.
"""
check_is_fitted(self)
if X is not None:
shifted_opposite_lof_scores = self.decision_function(X)
is_inlier = np.ones(shifted_opposite_lof_scores.shape[0], dtype=int)
is_inlier[shifted_opposite_lof_scores < 0] = -1
else:
is_inlier = np.ones(self.n_samples_fit_, dtype=int)
is_inlier[self.negative_outlier_factor_ < self.offset_] = -1
return is_inlier
def _check_novelty_decision_function(self):
if not self.novelty:
msg = (
"decision_function is not available when novelty=False. "
"Use novelty=True if you want to use LOF for novelty "
"detection and compute decision_function for new unseen "
"data. Note that the opposite LOF of the training samples "
"is always available by considering the "
"negative_outlier_factor_ attribute."
)
raise AttributeError(msg)
return True
@available_if(_check_novelty_decision_function)
def decision_function(self, X):
"""Shifted opposite of the Local Outlier Factor of X.
Bigger is better, i.e. large values correspond to inliers.
**Only available for novelty detection (when novelty is set to True).**
The shift offset allows a zero threshold for being an outlier.
The argument X is supposed to contain *new data*: if X contains a
point from training, it considers the later in its own neighborhood.
Also, the samples in X are not considered in the neighborhood of any
point.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The query sample or samples to compute the Local Outlier Factor
w.r.t. the training samples.
Returns
-------
shifted_opposite_lof_scores : ndarray of shape (n_samples,)
The shifted opposite of the Local Outlier Factor of each input
samples. The lower, the more abnormal. Negative scores represent
outliers, positive scores represent inliers.
"""
return self.score_samples(X) - self.offset_
def _check_novelty_score_samples(self):
if not self.novelty:
msg = (
"score_samples is not available when novelty=False. The "
"scores of the training samples are always available "
"through the negative_outlier_factor_ attribute. Use "
"novelty=True if you want to use LOF for novelty detection "
"and compute score_samples for new unseen data."
)
raise AttributeError(msg)
return True
@available_if(_check_novelty_score_samples)
def score_samples(self, X):
"""Opposite of the Local Outlier Factor of X.
It is the opposite as bigger is better, i.e. large values correspond
to inliers.
**Only available for novelty detection (when novelty is set to True).**
The argument X is supposed to contain *new data*: if X contains a
point from training, it considers the later in its own neighborhood.
Also, the samples in X are not considered in the neighborhood of any
point. Because of this, the scores obtained via ``score_samples`` may
differ from the standard LOF scores.
The standard LOF scores for the training data is available via the
``negative_outlier_factor_`` attribute.
Parameters
----------
X : {array-like, sparse matrix} of 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 : ndarray of shape (n_samples,)
The opposite of the Local Outlier Factor of each input samples.
The lower, the more abnormal.
"""
check_is_fitted(self)
X = check_array(X, accept_sparse="csr")
distances_X, neighbors_indices_X = self.kneighbors(
X, n_neighbors=self.n_neighbors_
)
if X.dtype == np.float32:
distances_X = distances_X.astype(X.dtype, copy=False)
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 : ndarray of shape (n_queries, self.n_neighbors)
Distances to the neighbors (in the training samples `self._fit_X`)
of each query point to compute the LRD.
neighbors_indices : ndarray of shape (n_queries, self.n_neighbors)
Neighbors indices (of each query point) among training samples
self._fit_X.
Returns
-------
local_reachability_density : ndarray of shape (n_queries,)
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 1.0 / (np.mean(reach_dist_array, axis=1) + 1e-10)
def _more_tags(self):
return {
"preserves_dtype": [np.float64, np.float32],
}