Joint Tensor Factorization and Outlying Slab Suppression with Applications
This work addresses a practical challenge in tensor factorization for domains such as speech and social network analysis, offering an incremental improvement over prior methods by enhancing convergence and flexibility.
The paper tackles the problem of factoring low-rank tensors when some data slabs are outliers, proposing an alternating optimization framework with group-sparsity promotion to handle this issue. It demonstrates effectiveness through simulations and real data experiments in applications like blind speech separation and social network mining.
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.