A0218
Title: Mixture models for heavy-tailed tensor-variate data
Authors: Salvatore Daniele Tomarchio - University of Catania (Italy) [presenting]
Antonio Punzo - University of Catania (Italy)
Luca Bagnato - Catholic University of the Sacred Heart (Italy)
Abstract: Real data is assuming increasingly complicated structures, requiring more flexible statistical approaches. Tensor-variate (or multi-way) structures are a typical example of such kind of data. Unfortunately, atypical observations often occur in real data, making the traditional normality assumption inadequate. To cope with this problem, we introduce two tensor-variate distributions, both heavy-tailed generalizations of the tensor-variate normal distribution. Then, using finite mixture models, we use these distributions for model-based clustering. We apply the eigen-decomposition of the components' scale matrices to reach parsimony, resulting in two families of parsimonious tensor-variate mixtures. We illustrate variants of the well-known EM algorithm for parameter estimation. Since the order of the tensors affects the number of parsimonious models, we implement strategies intending to shorten the initialization and fitting processes. Simulated analyses are used to study these processes. Last but not least, we applied our parsimonious models to real datasets.
