Finding Outliers in Gaussian Model-Based Clustering
This addresses the lack of robust outlier handling in clustering for data analysts, though it is incremental as it builds on existing trimming methods.
The paper tackles the problem of outlier detection in Gaussian mixture model-based clustering by proposing OCLUST, a trimming method that inherently estimates the number of outliers without pre-specification, using an approximate distribution for log-likelihoods to remove implausible points until they fit a reference distribution.
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 post hoc outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample squared 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.