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.
.. versionadded:: 0.19
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 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
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 : '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
.
.. versionchanged:: 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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` for more details.
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 :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.
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...
)
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.