Model-Based Clustering

Abstract

Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

Marketing analytics: Methods, practice, implementation, and links to other fields

“…This gives advantages in terms of flexibility, but limits some of the output from the procedures in terms of parameter significance and model selection criteria. Mixture model based clustering (Banfield and Raftery, 1993;Fraley and Raftery, 2002;McNicholas, 2016) approaches that make distributional assumptions have been increasingly utilized for marketing segmentation purposes, particularly over the last few decades. In mixture model based clustering, the observed data are considered to come from a "mixture" of different distributions.…”

Reduction of multivariate mixtures and its applications

“…We also do not provide a comparison with model-based clustering (see e.g. [32,37]). Using Algorithm 1 to subdivide scattered points into groups requires further analysis and we plan to address it elsewhere.…”

A matrix variate skew‐t distribution

“…McNicholas (2016a) traces the association between clustering and mixture models back to Tiedeman (1955), and the earliest use of a finite mixture model for clustering can be found in Wolfe (1965), who uses a Gaussian mixture model. Other early work in this area can be found in Baum, Petrie, Soules & Weiss (1970) and Scott & Symons (1971), and a recent review of model-based clustering is given by McNicholas (2016b).…”