Algorithms of maximum likelihood data clustering with applications

TL;DR

This paper introduces a parameter-free, maximum likelihood-based clustering method that automatically determines the number of clusters and offers transparent results, demonstrated on financial and gene expression data.

Contribution

The paper presents a novel unsupervised clustering algorithm based on maximum likelihood that does not require predefined cluster numbers or parameters.

Findings

The method is parameter-free and automatically determines the number of clusters.

It produces consistent cluster structures across different maximization algorithms.

Compared to standard methods, it shows less variability in results.

Abstract

We address the problem of data clustering by introducing an unsupervised, parameter free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information, we construct an expression for the likelihood of any possible cluster structure. The likelihood in turn depends only on the Pearson's coefficient of the data. We discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations. Compared to standard clustering methods, our approach has the advantages that i) it is parameter free, ii) the number of clusters need not be fixed in advance and iii) the interpretation of the results is transparent. In order to test our approach and compare it with standard clustering algorithms, we analyze two very different data sets: Time series of financial market returns and gene expression data. We find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability.