An Overview of Outlier Detection Methods from PyOD – Part 1

PyOD is an outlier detection package developed with a comprehensive API to support multiple techniques. This post will showcase Part 1 of an overview of techniques that can be used to analyze anomalies in data.

A previous post from Matthew Mayo titled: Intuitive Visualization of Outlier Detection Methods gave an overview of the PyOD package developed by Yue Zhao.
This post will continue from there into a multiple part series to outline the different outlier detection methods available in the package. I will be using information from the PyOD documentation so as to not to cause confusion from overlapping techniques.


1. PCA (Principal Component Analysis)


pyod.models.pca.PCA(n_components=None, n_selected_components=None, contamination=0.1, copy=True, whiten=False, svd_solver='auto', tol=0.0, iterated_power='auto', random_state=None, weighted=True, standardization=True)


PCA is a linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space. In this procedure, covariance matrix of the data can be decomposed to orthogonal vectors, called eigenvectors, associated with eigenvalues. The eigenvectors with high eigenvalues capture most of the variance in the data.

Therefore, a low dimensional hyperplane constructed by k eigenvectors can capture most of the variance in the data. However, outliers are different from normal data points, which is more obvious on the hyperplane constructed by the eigenvectors with small eigenvalues. Therefore, outlier scores can be obtained as the sum of the projected distance of a sample on all eigenvectors.


2. MCD (Minimum Covariance Determinant), store_precision=True, assume_centered=False, support_fraction=None, random_state=None)


The Minimum Covariance Determinant covariance estimator is to be applied on Gaussian-distributed data, but could still be relevant on data drawn from a unimodal, symmetric distribution. It is not meant to be used with multi-modal data (the algorithm used to fit a MinCovDet object is likely to fail in such a case). One should consider projection pursuit methods to deal with multi-modal datasets.


3. OCSVM (Once-Class Support Vector Machine)


pyod.models.ocsvm.OCSVM(kernel='rbf', degree=3, gamma='auto', coef0=0.0, tol=0.001, nu=0.5, shrinking=True, cache_size=200, verbose=False, max_iter=-1, contamination=0.1)

This is a type of unsupervised learning outlier detection method. The OCSVM algorithm maps input data into a high dimensional feature space (via a kernel) and iteratively finds the maximal margin hyperplane which best separates the training data from the origin.


4. LOF (Local Outlier Factor)


pyod.models.lof.LOF(n_neighbors=20, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, contamination=0.1, n_jobs=1)

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.