# From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering

## TL;DR

This paper compares sparse finite mixture models and Dirichlet process mixtures for clustering, demonstrating the flexibility of sparse finite mixtures for various data types and highlighting the importance of hyper prior choices over model type.

## Contribution

It extends sparse finite mixture concepts to non-Gaussian data and compares their performance with Dirichlet process mixtures under different hyper prior settings.

## Key findings

- Sparse finite mixtures can be applied to diverse data types.
- Hyper prior choice significantly influences clustering results.
- Model type has less impact than hyper prior on cluster inference.

## Abstract

In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with $K$ components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than $K$ with high probability. The number of cluster is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.