Robust MultiRelational Learning With Absolute Projection Rescal RESCAL is a popular approach for multirelational learning based on tensor decomposition. At the same time, RESCAL follows a L2norm formulation that can be very sensitive against outlying data corruptions. In this work, we propose ARESCAL: a corruptionresistant reformulation of RESCAL based on absolute projections. Specifically, we (i) show that rank1 ARESCAL can be cast as a combinatorial problem over antipodal binary variables and solve it exactly by exhaustive search; (ii) develop an efficient iterative algorithm for approximating the solution to rank1 ARESCAL; and (iii) extend our solver for general rank by means of subspace deflation. Our experimental studies on multiple benchmark datasets show that ARESCAL performs quite similarly to standard RESCAL when the processed data are nominal, while it is significantly more robust in the case of data corruption.

Robust Schattenp Norm Based Approach for Tensor Completion The matrix nuclear norm has been widely applied to approximate the matrix rank for lowrank tensor completion because of its convexity. However, this relaxation may make the solution seriously deviate from the original solution for realworld data recovery. In this paper, using a nonconvex approximation of rank, i.e., the Schattenp norm, we propose a novel model for tensor completion. Itxe2x80x99s hard to solve this model directly because the objective function of the model is nonconvex. To solve the model, we develop a variant of this model via the classical quadric penalty method, and propose an algorithm, i.e., SpBCD, based on the block coordinate descent method. Although the objective function of the variant is nonconvex, we show that the sequence generated by SpBCD is convergent to a critical point. Our numerical experiments on realworld data show that SpBCD delivers stateofart performance in recovering missing data.