Parallel Randomized Tucker Decomposition Algorithms

TL;DR

This paper introduces parallel randomized algorithms for Tucker tensor decomposition that significantly speed up computation while maintaining accuracy, enabling efficient processing of large multiway datasets.

Contribution

The paper presents novel parallel randomized Tucker decomposition algorithms using structured sketches, reducing computation and communication costs with theoretical error guarantees.

Findings

Achieved up to 16X speedup over deterministic methods

Reduced computational and communication costs

Maintained approximation accuracy with randomized algorithms

Abstract

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.