Statistical Significance of Clustering using Soft Thresholding

TL;DR

This paper improves the statistical evaluation of clustering in high-dimensional data by introducing a soft thresholding method for eigenvalue estimation, reducing false positives and enhancing reliability.

Contribution

It presents a novel likelihood-based soft thresholding approach for eigenvalue estimation, significantly improving the SigClust method's accuracy in high-dimensional clustering analysis.

Findings

Enhanced SigClust performance demonstrated through simulations

Mathematical analysis validates the new eigenvalue estimation method

Applications to cancer genomic data show practical utility

Abstract

Clustering methods have led to a number of important discoveries in bioinformatics and beyond. A major challenge in their use is determining which clusters represent important underlying structure, as opposed to spurious sampling artifacts. This challenge is especially serious, and very few methods are available, when the data are very high in dimension. Statistical Significance of Clustering (SigClust) is a recently developed cluster evaluation tool for high dimensional low sample size data. An important component of the SigClust approach is the very definition of a single cluster as a subset of data sampled from a multivariate Gaussian distribution. The implementation of SigClust requires the estimation of the eigenvalues of the covariance matrix for the null multivariate Gaussian distribution. We show that the original eigenvalue estimation can lead to a test that suffers from severe inflation of type-I error, in the important case where there are a few very large eigenvalues. This paper addresses this critical challenge using a novel likelihood based soft thresholding approach to estimate these eigenvalues, which leads to a much improved SigClust. Major improvements in SigClust performance are shown by both mathematical analysis, based on the new notion of Theoretical Cluster Index, and extensive simulation studies. Applications to some cancer genomic data further demonstrate the usefulness of these improvements.