Large-scale Canonical Polyadic Decomposition via Regular Tensor Sampling

Charilaos I. Kanatsoulis, Nicholas D. Sidiropoulos

Abstract: Tensor decomposition models have proven to be effective analysis tools in various applications, including signal processing, machine learning, and communications, to name a few. Canonical polyadic decomposition (CPD) is a very popular model, which decomposes a higher order tensor signal into a sum of rank 1 terms. However, when the tensor size gets big, computing the CPD becomes a lot more challenging. Previous works proposed using random (generalized) tensor sampling or compression to alleviate this challenge. In this work, we propose using a regular tensor sampling framework instead. We show that by appropriately selecting the sampling mechanism, we can simultaneously control memory and computational complexity, while guaranteeing identifiability at the same time. Numerical experiments with synthetic and real data showcase the effectiveness of our approach.