Improving Statistical Characterization of Data Tensors with the Generalized Canonical Polyadic Tensor Decomposition

This work explores the potential of the generalized canonical polyadic (GCP) tensor decomposition to be used as a diagnostic tool to determine the underlying statistical nature of a dataset. The GCP reformulates the standard canonical polyadic (CP) decomposition problem as a maximum likelihood estimate and models the natural parameter of the statistical distribution assumed to be associated with a data tensor as opposed to modeling the data itself through the use of a variety of statistically motivated loss functions. This property is of particular interest when a dataset is strongly non-Gaussian, such as is the case with binary or count data. In the work presented, we compare competing CP models of datasets with differing statistical natures to determine if the GCP can be used as an exploratory tool for the statistical characterization of a data tensor of interest. The quality of competing models is assessed via multiple metrics that include fit score, cosine similarity of the tensors, and the Core Consistency Diagnostic (CORCONDIA) score. Results are presented for a variety of artificially generated data tensors.