A general trimming approach to robust Cluster Analysis

TL;DR

This paper presents a robust clustering method that handles contaminated data and varying cluster scatters by imposing eigenvalue ratio restrictions, ensuring well-defined solutions and consistency.

Contribution

It introduces a general trimming approach with eigenvalue ratio constraints, unifying and extending existing clustering methods for robustness and theoretical guarantees.

Findings

Method guarantees robustness against contamination.

Ensures consistency of sample solutions.

Flexible approach covering various clustering scenarios.

Abstract

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the method. As a characteristic feature, restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. This makes the problem to be well defined and guarantees the consistency of the sample solutions to the population ones. The method covers a wide range of clustering approaches depending on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem.