A Coupled Random Projection Approach to Large-Scale Canonical Polyadic Decomposition

TL;DR

This paper introduces a coupled random projection method for efficiently computing the canonical polyadic decomposition of large-scale tensors, improving accuracy over traditional single-projection techniques.

Contribution

It extends the RAP technique to multiple coupled projections, enabling joint decomposition and more accurate factorization of large tensors.

Findings

CoRAP improves decomposition accuracy over RAP.

The method effectively handles large-scale tensor data.

Experimental results demonstrate enhanced performance.

Abstract

We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale decompositions, from one single projection to multiple but coupled random projections (CoRAP). The proposed CoRAP technique yields a set of tensors that together admits a coupled CPD (C-CPD) and a C-CPD algorithm is then used to jointly decompose these tensors. The results of C-CPD are finally fused to obtain factor matrices of the original large-scale data tensor. As more data samples are jointly exploited via C-CPD, the proposed CoRAP based CPD is more accurate than RAP based CPD. Experiments are provided to illustrate the performance of the proposed approach.