Kotz Mixture Model with Semi-Supervised Projected Model-Based Clustering

Kotz mixture model (KMM) is a family of multivariate elliptically contoured distributions. In this paper, we propose the KMM using a semi-supervised projected modelbased clustering method (KMM-SeSProC). The parameters of KMM-SeSProC are estimated using the maximum-likelihood approach via the expectation-maximization (EM) algorithm and the Newton-Raphson method. Model selection in mixtures is considered essential for determining the optimal number of mixture components. Therefore, we propose a model selection criterion for KMM-SeSProC based on the minimum message length (MML) framework. For modeling data, KMM-SeSProC is applied to synthetic data and real datasets from various medical experiments. To validate the effectiveness of data clustering, the proposed model is compared with KMM, Laplace mixture model (LMM), and Gaussian mixture model (GMM). To evaluate the effectiveness of model selection, MML is used to identify the exact number of components in various datasets. The proposed model selection is compared with seven different model selection criteria. The experimental results show that the proposed KMM-SeSProC and the MML model selection criterion have demonstrated their effectiveness.