sklearn.neighbors.LocalOutlierFactor

class sklearn.neighbors.LocalOutlierFactor(n_neighbors=20, *, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, contamination='auto', novelty=False, n_jobs=None) [source]

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.

New in version 0.19.

Parameters

n_neighborsint, default=20

Number of neighbors to use by default for 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 BallTree
• ‘kd_tree’ will use KDTree
• ‘brute’ will use a brute-force search.
• ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_sizeint, default=30

Leaf size passed to BallTree or 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.

metricstr or callable, default=’minkowski’

metric used for the distance computation. Any metric from scikit-learn or scipy.spatial.distance can be used.

If metric is “precomputed”, X is assumed to be a distance matrix and must be square. X may be a sparse matrix, in which case only “nonzero” elements may be considered neighbors.

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’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’]

See the documentation for scipy.spatial.distance for details on these metrics: https://docs.scipy.org/doc/scipy/reference/spatial.distance.html

pint, default=2

Parameter for the Minkowski metric from 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_paramsdict, 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].

Changed in version 0.22: The default value of contamination changed from 0.1 to 'auto'.

noveltybool, 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 that you should only use predict, decision_function and score_samples on new unseen data and not on the training set.

New in version 0.20.

n_jobsint, default=None

The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary 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 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.

New in version 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_samples_fit_int

It is the number of samples in the fitted data.

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...])

Methods

fit(X[, y])	Fit the local outlier factor detector from the training dataset.
get_params([deep])	Get parameters for this estimator.
kneighbors([X, n_neighbors, return_distance])	Finds the K-neighbors of a point.
kneighbors_graph([X, n_neighbors, mode])	Computes the (weighted) graph of k-Neighbors for points in X
set_params(**params)	Set the parameters of this estimator.

property decision_function

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

Xarray-like 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_scoresndarray 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.

fit(X, y=None) [source]

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.

yIgnored

Not used, present for API consistency by convention.

Returns

selfLocalOutlierFactor

The fitted local outlier factor detector.

property fit_predict

Fits the model to the training set X and returns 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

Xarray-like of 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.

yIgnored

Not used, present for API consistency by convention.

Returns

is_inlierndarray of shape (n_samples,)

Returns -1 for anomalies/outliers and 1 for inliers.

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsdict

Parameter names mapped to their values.

kneighbors(X=None, n_neighbors=None, return_distance=True) [source]

Finds the K-neighbors of a point.

Returns indices of and distances to the neighbors of each point.

Parameters

Xarray-like, shape (n_queries, n_features), or (n_queries, n_indexed) if metric == ‘precomputed’, default=None

The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor.

n_neighborsint, default=None

Number of neighbors required for each sample. The default is the value passed to the constructor.

return_distancebool, default=True

Whether or not to return the distances.

Returns

neigh_distndarray of shape (n_queries, n_neighbors)

Array representing the lengths to points, only present if return_distance=True

neigh_indndarray of shape (n_queries, n_neighbors)

Indices of the nearest points in the population matrix.

Examples

In the following example, we construct a NearestNeighbors class from an array representing our data set and ask who’s the closest point to [1,1,1]

>>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh = NearestNeighbors(n_neighbors=1)
>>> neigh.fit(samples)
NearestNeighbors(n_neighbors=1)
>>> print(neigh.kneighbors([[1., 1., 1.]]))
(array([[0.5]]), array([[2]]))

As you can see, it returns [[0.5]], and [[2]], which means that the element is at distance 0.5 and is the third element of samples (indexes start at 0). You can also query for multiple points:

>>> X = [[0., 1., 0.], [1., 0., 1.]]
>>> neigh.kneighbors(X, return_distance=False)
array([[1],
       [2]]...)

kneighbors_graph(X=None, n_neighbors=None, mode='connectivity') [source]

Computes the (weighted) graph of k-Neighbors for points in X

Parameters

Xarray-like of shape (n_queries, n_features), or (n_queries, n_indexed) if metric == ‘precomputed’, default=None

The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. For metric='precomputed' the shape should be (n_queries, n_indexed). Otherwise the shape should be (n_queries, n_features).

n_neighborsint, default=None

Number of neighbors for each sample. The default is the value passed to the constructor.

mode{‘connectivity’, ‘distance’}, default=’connectivity’

Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, in ‘distance’ the edges are Euclidean distance between points.

Returns

Asparse-matrix of shape (n_queries, n_samples_fit)

n_samples_fit is the number of samples in the fitted data A[i, j] is assigned the weight of edge that connects i to j. The matrix is of CSR format.

See also

NearestNeighbors.radius_neighbors_graph

Examples

>>> X = [[0], [3], [1]]
>>> from sklearn.neighbors import NearestNeighbors
>>> neigh = NearestNeighbors(n_neighbors=2)
>>> neigh.fit(X)
NearestNeighbors(n_neighbors=2)
>>> A = neigh.kneighbors_graph(X)
>>> A.toarray()
array([[1., 0., 1.],
       [0., 1., 1.],
       [1., 0., 1.]])

property predict

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).

Parameters

Xarray-like of shape (n_samples, n_features)

The query sample or samples to compute the Local Outlier Factor w.r.t. to the training samples.

Returns

is_inlierndarray of shape (n_samples,)

Returns -1 for anomalies/outliers and +1 for inliers.

property score_samples

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. The score_samples on training data is available by considering the the negative_outlier_factor_ attribute.

Parameters

Xarray-like 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_scoresndarray of shape (n_samples,)

The opposite of the Local Outlier Factor of each input samples. The lower, the more abnormal.

set_params(**params) [source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**paramsdict

Estimator parameters.

Returns

selfestimator instance

Estimator instance.

Examples using sklearn.neighbors.LocalOutlierFactor