Non-Central Generalized Gamma Mixtures for the Classification of High-Dimensional Data

• Activity Number: 638
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Alejandro Murua* and Bertrand Saulnier
• Companies: University of Montreal and Université de Montréal
• Keywords: classification ; finite mixture ; high-dimensional data ; generalized gamma distribution ; central limit theorem ; gene expression

Abstract

The method of kernel mixture models (KMM) developed by Murua and Wicker (2014) introduced a data classification method based on distances of transformed data observations to centroids on each class. The fact that the squared distance of a multivariate normal variable is a gamma variable is the base to represent each data class by a mixture of gamma distributions. On the other hand, Leonard and Gauvin (2013) modeled the distance of untransformed high-dimension observations to centroids by normal distributions applying the asymptotic theory of the central limit theorem to the data dimension. In this work, we show that an alternative asymptotic distribution of the distances can be used. This distribution turns out to be a generalized extension of the gamma distribution. We refer to it as a non-central generalized gamma distribution, or NCG-gamma law, for short. We propose to replace the gamma mixture distribution used in the KMM model with a mixture formed by NCG-Gamma distributions when the dimension of the data is big. One advantage of this law with respect to the gamma one used in the original KMM is that it has a stronger theoretical basis. We apply this model to large data sets