Decomposition of Big Tensors With Low Multilinear Rank

TL;DR

This paper introduces scalable algorithms for tensor decomposition tailored for big data, including a fast CP decomposition method and a distributed Tucker approach, validated through extensive simulations.

Contribution

It proposes two novel scalable tensor decomposition algorithms: FFCP based on Tucker compression and a distributed randomized Tucker method for large, low-rank tensors.

Findings

Algorithms effectively handle huge dense tensors.

Empirical results demonstrate high efficiency and validity.

Approaches outperform existing methods in scalability.

Abstract

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most existing approaches are not designed to meet the major challenges posed by big data analytics. This paper attempts to improve the scalability of tensor decompositions and provides two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank. These two algorithms can deal with huge tensors, even if they are dense. Extensive simulations provide empirical evidence of the validity and efficiency of the proposed algorithms.