A Coupled Random Projection Approach to Large-Scale Canonical Polyadic Decomposition
This work addresses a computational bottleneck in tensor decomposition for large-scale data, offering an incremental improvement in accuracy for applications in fields like signal processing or machine learning.
The authors tackled the problem of computing canonical polyadic decomposition for large-scale tensors by proposing a coupled random projection approach, which improved accuracy over existing methods by exploiting more data samples through joint decomposition.
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.