A Finite Multi-Dimensional Generalized Gamma Mixture Model

Abstract

Over the last two decades, statistical mixture models have been widely exploited to tackle the issue of data modeling. Examples of statistical mixture models' applications in data modeling include object recognition, speech recognition, information retrieval, and intrusion detection. In this paper, an unsupervised learning algorithm, based on a finite multi-dimensional generalized Gamma mixture model (GGMM) is presented for the purpose of positive vectors clustering. Maximum likelihood (ML) is a well-known method conducted via expectation maximization algorithm (EM) and used for estimating the parameters of the proposed model. Newton Raphson's optimization algorithm was also utilized to solve the problem (obstacle) of the non-existence of closed form. Experiments are conducted using both synthetic data and a real data set of images representing shapes to test the performance of the proposed model. Moreover, we compared the performance of the generalized Gamma mixture model with Gamma and Gaussian mixture models.