Gaussian Mixture Clustering Using Relative Tests of Fit
This addresses the need for more reliable clustering in fields like bioinformatics, though it is incremental as it builds on prior SigClust work.
The paper tackles the problem of low power in significance-based clustering methods for Gaussian Mixture Models by introducing a new relative fit test that compares a mixture to a single Gaussian without assuming model correctness, resulting in provable error control and exact finite sample type I error in one version.
We consider clustering based on significance tests for Gaussian Mixture Models (GMMs). Our starting point is the SigClust method developed by Liu et al. (2008), which introduces a test based on the k-means objective (with k = 2) to decide whether the data should be split into two clusters. When applied recursively, this test yields a method for hierarchical clustering that is equipped with a significance guarantee. We study the limiting distribution and power of this approach in some examples and show that there are large regions of the parameter space where the power is low. We then introduce a new test based on the idea of relative fit. Unlike prior work, we test for whether a mixture of Gaussians provides a better fit relative to a single Gaussian, without assuming that either model is correct. The proposed test has a simple critical value and provides provable error control. One version of our test provides exact, finite sample control of the type I error. We show how our tests can be used for hierarchical clustering as well as in a sequential manner for model selection. We conclude with an extensive simulation study and a cluster analysis of a gene expression dataset.