A Fast Implementation for the Canonical Polyadic Decomposition

TL;DR

This paper introduces a fast, memory-efficient implementation of the canonical polyadic decomposition (CPD) using a damped Gauss-Newton algorithm, improving computational speed and reducing resource usage for tensor decomposition tasks.

Contribution

It presents a novel, accelerated damped Gauss-Newton method for CPD that outperforms existing implementations in speed and memory efficiency.

Findings

Reduced computational complexity compared to state-of-the-art methods

Lower memory usage in tensor decomposition tasks

Faster convergence with the proposed implementation

Abstract

A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging problem which has been approached in several manners. Alternating least squares algorithms were used for a long time, but they convergence properties are limited. Nonlinear least squares (NLS) algorithms - more precisely, damped Gauss-Newton (dGN) algorithms - are much better in this sense, but they require inverting large Hessians, and for this reason there is just a few implementations using this approach. In this paper, we propose a fast dGN implementation to compute the CPD. In this paper, we make the case to always compress the tensor, and propose a fast damped Gauss-Newton implementation to compute the canonical polyadic decomposition.