Joint Tensor Factorization and Outlying Slab Suppression with Applications

TL;DR

This paper introduces a novel tensor factorization method robust to outlying slabs, using group sparsity and alternating optimization, with applications in speech separation, fluorescence analysis, and social network data mining.

Contribution

It formulates a new low-rank tensor factorization approach that handles outliers effectively and converges reliably, incorporating regularization and prior information.

Findings

Effective outlier suppression in tensor data.

Comparable complexity to standard tensor factorization algorithms.

Successful applications in speech, fluorescence, and social network analysis.

Abstract

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number of slabs and fitting, a procedure which may not converge. We formulate this problem from a group-sparsity promoting point of view, and propose an alternating optimization framework to handle the corresponding $\ell_p$ ($0<p\leq 1$) minimization-based low-rank tensor factorization problem. The proposed algorithm features a similar per-iteration complexity as the plain trilinear alternating least squares (TALS) algorithm. Convergence of the proposed algorithm is also easy to analyze under the framework of alternating optimization and its variants. In addition, regularization and constraints can be easily incorporated to make use of \emph{a priori} information on the latent loading factors. Simulations and real data experiments on blind speech separation, fluorescence data analysis, and social network mining are used to showcase the effectiveness of the proposed algorithm.