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

Frühwirth-Schnatter, Sylvia and Malsiner-Walli, Gertraud (2019) From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering. Advances in Data Analysis and Classification, 13 (1). pp. 33-64. ISSN 1862-5355

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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. (Stat Comput 26:303-324, 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 clusters 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.

Item Type: Article
Additional Information: Open access funding provided by Austrian Science Fund (FWF).
Keywords: Mixture distributions, Latent class Analysis, Skew distributions, Marginal likelihoods, Count data, Dirichlet prior
Classification Codes: Mathematics Subject Classification: 62C10, 62F15, 62P99
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Version of the Document: Published
Depositing User: Gertraud Novotny
Date Deposited: 14 Nov 2018 07:58
Last Modified: 14 Jul 2019 13:25
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