Randomized algorithms for Kroncecker tensor decomposition and applications

TL;DR

This paper introduces fast randomized algorithms for Kronecker Tensor Decomposition that significantly accelerate the process compared to existing methods, with demonstrated effectiveness on synthetic and real-world datasets for various applications.

Contribution

The paper presents novel randomized algorithms for KTD that reduce computational complexity and outperform deterministic algorithms in speed and efficiency.

Findings

Achieved several orders of magnitude acceleration in tensor decomposition.

Validated algorithms on synthetic and real datasets for multiple applications.

Demonstrated effectiveness in tensor completion, compression, and image processing.

Abstract

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our principal idea is to use the randomization framework to reduce computational complexity significantly. We provide extensive simulations to verify the effectiveness and performance of the proposed randomized algorithms with several orders of magnitude acceleration compared to the deterministic one. Our simulations use synthetics and real-world datasets with applications to tensor completion, video/image compression, image denoising, and image super-resolution