Robust Multi-Relational Learning With Absolute Projection Rescal

Abstract

RESCAL is a popular approach for multi-relational learning based on tensor decomposition. At the same time, RESCAL follows a L2-norm formulation that can be very sensitive against outlying data corruptions. In this work, we propose A-RESCAL: a corruption-resistant reformulation of RESCAL based on absolute projections. Specifically, we (i) show that rank-1 A-RESCAL 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 rank-1 A-RESCAL; and (iii) extend our solver for general rank by means of subspace deflation. Our experimental studies on multiple benchmark datasets show that A-RESCAL performs quite similarly to standard RESCAL when the processed data are nominal, while it is significantly more robust in the case of data corruption.