Nonnegative Structured Kruskal Tensor Regression

Abstract

Many contemporary data analysis problems use tensors (multidimensional arrays) as covariates. For example, regression or classification tasks may need to be performed on a set of image covariates sampled from diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), or hyperspectral imaging (HSI). By en-forcing a low-rank constraint on the parameter tensor, tensor regression models effectively leverage the temporal and spatial structure of tensor covariates. In this paper, we study Kruskal tensor regression with sparsity and smoothness inducing regularization and non-negativity constraints. We solve the corresponding penalized nonnegative Kruskal tensor regression (KTR) problem using an efficient block-wise alternating minimization method. The efficiency of the proposed approach is illustrated via simulations.