Probabilistic Tensor Canonical Polyadic Decomposition With Orthogonal Factors

Abstract

Tensor canonical polyadic decomposition (CPD), which recovers the latent factor matrices from multidimensional data, is an important tool in signal processing. In many applications, some of the factor matrices are known to have orthogonality structure, and this information can be exploited to improve the accuracy of latent factors recovery. However, existing methods for CPD with orthogonal factors all require the knowledge of tensor rank, which is difficult to acquire, and have no mechanism to handle outliers in measurements. To overcome these disadvantages, in this paper, a novel tensor CPD algorithm based on the probabilistic inference framework is devised. In particular, the problem of tensor CPD with orthogonal factors is interpreted using a probabilistic model, based on which an inference algorithm is proposed that alternatively estimates the factor matrices, recovers the tensor rank, and mitigates the outliers. Simulation results using synthetic data and real-world applications are presented to illustrate the excellent performance of the proposed algorithm in terms of accuracy and robustness.