Finite mixture models and model-based clustering

Finite Mixture Models and Model-Based Clustering

Finite mixture models have a long history in statistics, having been used to model pupulation heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends in the area, as well as open problems are also discussed.

Mixture models and clustering

Consider the dataset of height and weight in Figure 1. It is clear that there are two subpopulations in this data set, and in this case they are easy to interpret: one represents males and the other females. Within each class or cluster, the data is fairly well represented by a 2D Gaussian (as can be seen from the fitted ellipses), but to model the data as a whole, we need to use a mixture of G...

Positive Data Clustering Using Finite Inverted Dirichlet Mixture Models

Positive Data Clustering Using Finite Inverted Dirichlet Mixture Models Taoufik BDIRI In this thesis we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, whi...

Geodesic Finite Mixture Models

The use of Riemannian manifolds and their statistics has recently gained popularity in a wide range of applications involving non-linear data modeling. For instance, they have been used to model shape changes in the brain [1] and human motion [3]. In this work we tackle the problem of approximating the Probability Density Function (PDF) of a potentially large dataset that lies on a known Rieman...

On Model Selection and Concavity for Finite Mixture Models