Finding Outliers in Gaussian Model-Based Clustering

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and \textit{post hoc} outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample Mahalanobis distance is beta-distributed is used to derive an approximate distribution for the log-likelihoods of subset finite Gaussian mixture models. An algorithm is then proposed that removes the least plausible points according to the subset log-likelihoods, which are deemed outliers, until the subset log-likelihoods adhere to the reference distribution. This results in a trimming method, called OCLUST, that inherently estimates the number of outliers.