Model-Based Learning Using a Mixture of Mixtures of Gaussian and Uniform Distributions

Abstract

We introduce a mixture model whereby each mixture component is itself a mixture of a multivariate Gaussian distribution and a multivariate uniform distribution. Although this model could be used for model-based clustering (model-based unsupervised learning) or model-based classification (model-based semi-supervised learning), we focus on the more general model-based classification framework. In this setting, we fit our mixture models to data where some of the observations have known group memberships and the goal is to predict the memberships of observations with unknown labels. We also present a density estimation example. A generalized expectation-maximization algorithm is used to estimate the parameters and thereby give classifications in this mixture of mixtures model. To simplify the model and the associated parameter estimation, we suggest holding some parameters fixed-this leads to the introduction of more parsimonious models. A simulation study is performed to illustrate how the model allows for bursts of probability and locally higher tails. Two further simulation studies illustrate how the model performs on data simulated from multivariate Gaussian distributions and on data from multivariate t-distributions. This novel approach is also applied to real data and the performance of our approach under the various restrictions is discussed.

Image Segmentation Using a Trimmed Likelihood Estimator in the Asymmetric Mixture Model Based on Generalized Gamma and Gaussian Distributions

“…This also includes De Angelis et al [16] who offered a robust time interval measurement method based on a Gaussian-uniform mixture model. Browne et al [17] incorporated a multivariate Gaussian and uniform distributions as the component density, which allowed for superior mixture possessing. These methods demonstrate a competitive performance in fitting different shapes of observed data.…”

MMKK++ algorithm for clustering heterogeneous images into an unknown number of clusters

“…We used GMM (Gaussian Mixture Model) [46][51] [4] to define the visual code words from the descriptor vectors, which is a parametric probability density function represented as a weighted sum of (in our case 256) Gaussian component densities, as can be seen in Equation 1.…”

Model-Based Clustering

“…Hennig (2004) suggests adding an improper uniform distribution as an additional mixture component. Browne, McNicholas, and Sparling (2012) also make use of uniform distributions but they do so by making each component a mixture of a Gaussian and a uniform distribution. Rather than specifically accommodating bad points, this approach allows for what they call "bursts" of probability as well as locally heavier tails-this might have the effect of dealing with bad points for some data sets.…”