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

arXiv: https://arxiv.org/abs/2105.04084 · HTML: https://mlsanity.com/paper/2105.04084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 3 of 3)

- [Randomized Matrix Decompositions using R](https://mlsanity.com/paper/1608.02148/) (2016)
- [Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction](https://mlsanity.com/paper/1901.01652/) (2019)
- [Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation](https://mlsanity.com/paper/1612.09466/) (2016)

## Abstract (arXiv)

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.