Generalized Nonnegative Structured Kruskal Tensor Regression

Tensor decompositions have emerged as powerful analytical tools across diverse fields including signal/image processing [1, 2, 3, 4, 5, 6], chemometrics [7], geophysics [8, 9], and neuroscience [10, 11, 12, 13]. Their effectiveness stems from their ability to approximate high-dimensional tensors with low-rank decompositions, offering efficient dimensionality reduction while preserving essential structural information. For example, tensor decomposition techniques [14, 15, 16] are applied in hyperspectral image (HSI) analysis to extract low-rank structures for dimensionality reduction [9], and used in electroencephalogram (EEG) analysis to capture latent patterns across multiple dimensions [10]. Over the past decade, tensor regression (TR) models have received attention, with numerous approaches proposed in the literature, including Tucker tensor regression [17], low-rank orthogonally decomposable tensor regression [18], Bayesian Kruskal tensor regression (KTR) [19], Bayesian low rank tensor ring completion [20], graph-regularized tensor regression [21], and tensor regression network [22].