Exponential Family Mixed Membership Models for Soft~Clustering of Multivariate Data

TL;DR

This paper introduces a method for fitting mixed membership models to exponential family data, enabling soft clustering of overlapping clusters, demonstrated on ultra running count data, and compared to standard mixture models.

Contribution

It presents a novel approach for fitting mixed membership models specifically for exponential family data, extending soft clustering capabilities.

Findings

The method effectively captures overlapping cluster structures.

It outperforms standard mixture models on count data.

Application to ultra running data demonstrates practical utility.

Abstract

For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.