Slice-Wise Irregular Tensor Decomposition and Its Application

Tensor decompositions are promising fundamental tools for multidimensional data (i.e., tensor) processing and analysis. However, with the advancement of acquisition techniques, slice-wise irregular tensors (i.e., tensors with frontal slices of various sizes) have been emerging, e.g., multiple organisms gene expression, movie ratings, and electronic health records, which bring new challenges to classical tensor decompositions. The pioneering PARAFAC2 decomposition was introduced to represent slice-wise irregular tensors, but it mainly exploits the low-rankness along the regular mode, ignoring other modes. In this paper, we propose a slice-wise irregular tensor decomposition (SITD) with the theoretical approximation error for emerging slice-wise irregular multidimensional data. In SITD, the slice-wise irregular tensor is firstly decomposed into the irregular face-wise product of the latent regular tensor and slice-wise irregular factor tensor, and then the latent regular tensor is decomposed into the product of a core tensor and factor matrices along different modes. As compared with the PARAFAC2 decomposition, SITD can fully and flexibly exploit the low-rankness along different modes of the slice-wise irregular tensor. Empowered with SITD, we develop a slice-wise irregular tensor imputation model and provide the generalization error bound for the resulting model. Then, we design the corresponding algorithm to solve the proposed nonconvex model and establish the theoretical convergence guarantee. Extensive experiments on the simulated data and real-world gene expression data show SITD is superior to competing approaches and benefits the downstream application.