skhubness.neighbors.LocalOutlierFactor¶

class skhubness.neighbors.LocalOutlierFactor(n_neighbors=20, algorithm: str = 'auto', algorithm_params: Optional[dict] = None, hubness: Optional[str] = None, hubness_params: Optional[dict] = None, 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.

Parameters

n_neighborsint, optional (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’, ‘hnsw’, ‘lsh’, ‘falconn_lsh’, ‘nng’, ‘rptree’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

‘hnsw’ will use HNSW
‘lsh’ will use PuffinnLSH
‘falconn_lsh’ will use FalconnLSH
‘nng’ will use NNG
‘rptree’ will use RandomProjectionTree
‘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 exact algorithm based on the values passed to fit() method. This will not select an approximate nearest neighbor algorithm.

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

algorithm_paramsdict, optional

Override default parameters of the NN algorithm. For example, with algorithm=’lsh’ and algorithm_params={n_candidates: 100} one hundred approximate neighbors are retrieved with LSH. If parameter hubness is set, the candidate neighbors are further reordered with hubness reduction. Finally, n_neighbors objects are used from the (optionally reordered) candidates.

hubness{‘mutual_proximity’, ‘local_scaling’, ‘dis_sim_local’, None}, optional

Hubness reduction algorithm

‘mutual_proximity’ or ‘mp’ will use MutualProximity
‘local_scaling’ or ‘ls’ will use LocalScaling
‘dis_sim_local’ or ‘dsl’ will use DisSimLocal

If None, no hubness reduction will be performed (=vanilla kNN).

hubness_params: dict, optional

Override default parameters of the selected hubness reduction algorithm. For example, with hubness=’mp’ and hubness_params={‘method’: ‘normal’} a mutual proximity variant is used, which models distance distributions with independent Gaussians.

leaf_size: int, optional (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.

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’, ‘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

p: integer, optional (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_params: dict, optional (default=None)

Additional keyword arguments for the metric function.

contamination: ‘auto’ or float, optional (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'.

novelty: boolean, 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.

n_jobs: int or None, optional (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. Affects only kneighbors() and kneighbors_graph() methods.

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.

Attributes

negative_outlier_factor_: numpy array, 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_: integer

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.

__init__(n_neighbors=20, algorithm: str = 'auto', algorithm_params: Optional[dict] = None, hubness: Optional[str] = None, hubness_params: Optional[dict] = None, leaf_size=30, metric='minkowski', p=2, metric_params=None, contamination='auto', novelty=False, n_jobs=None)[source]¶: Initialize self. See help(type(self)) for accurate signature.

Methods

`__init__`([n_neighbors, algorithm, …])	Initialize self.
`fit`(X[, y])	Fit the model using X as training data.
`get_params`([deep])	Get parameters for this estimator.
`kcandidates`([X, n_neighbors, return_distance])	Finds the K-neighbors of a point.
`kneighbors`([X, n_neighbors, return_distance])	TODO
`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.

Attributes

`decision_function`	Shifted opposite of the Local Outlier Factor of X.
`fit_predict`	“Fits the model to the training set X and returns the labels.
`predict`	Predict the labels (1 inlier, -1 outlier) of X according to LOF.
`score_samples`	Opposite of the Local Outlier Factor of X.

property decision_function¶

Shifted opposite of the Local Outlier Factor of X.

Bigger is better, i.e. large values correspond to inliers.

The shift offset allows a zero threshold for being an outlier. 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.

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

shifted_opposite_lof_scores: array, 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) → skhubness.neighbors.lof.LocalOutlierFactor[source]¶

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’.
y: Ignored: not used, present for API consistency by convention.

Returns

self: object

property fit_predict¶

“Fits the model to the training set X and returns the labels.

Label is 1 for an inlier and -1 for an outlier 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.
y: Ignored: not used, present for API consistency by convention.

Returns

is_inlier: array, shape (n_samples,): Returns -1 for anomalies/outliers and 1 for inliers.

get_params(deep=True)¶

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

paramsmapping of string to any: Parameter names mapped to their values.

kcandidates(X=None, n_neighbors=None, return_distance=True) → numpy.ndarray[source]¶

Finds the K-neighbors of a point. Returns indices of and distances to the neighbors of each point.

Parameters

Xarray-like, shape (n_query, n_features), or (n_query, n_indexed) if metric == ‘precomputed’: 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: Number of neighbors to get (default is the value passed to the constructor).
return_distanceboolean, optional. Defaults to True.: If False, distances will not be returned

Returns

distarray: Array representing the lengths to points, only present if return_distance=True
indarray: Indices of the nearest points in the population matrix.

Examples

In the following example, we construct a NeighborsClassifier 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 skhubness.neighbors import NearestNeighbors
>>> neigh = NearestNeighbors(n_neighbors=1)
>>> neigh.fit(samples) 
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> 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(X=None, n_neighbors=None, return_distance=True)[source]¶: TODO

kneighbors_graph(X=None, n_neighbors=None, mode='connectivity')¶

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

Parameters

Xarray-like, shape (n_queries, n_features), or (n_queries, n_indexed) if metric == ‘precomputed’: 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: Number of neighbors for each sample. (default is value passed to the constructor).
mode{‘connectivity’, ‘distance’}, optional: 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 graph in CSR format, 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.