Guarantees for the Kronecker Fast Johnson-Lindenstrauss Transform Using a Coherence and Sampling Argument
Abstract
In the recent paper [Jin, Kolda & Ward, arXiv:1909.04801], it is proved that the Kronecker fast Johnson-Lindenstrauss transform (KFJLT) is, in fact, a Johnson-Lindenstrauss transform, which had previously only been conjectured. In this paper, we provide an alternative proof of this, for when the KFJLT is applied to Kronecker vectors, using a coherence and sampling argument. Our proof yields a different bound on the embedding dimension, which can be combined with the bound in the paper by Jin et al. to get a better bound overall. As a stepping stone to proving our result, we also show that the KFJLT is a subspace embedding for matrices with columns that have Kronecker product structure. Lastly, we compare the KFJLT to four other sketch techniques in numerical experiments on both synthetic and real-world data.
Cite
@article{arxiv.1911.08424,
title = {Guarantees for the Kronecker Fast Johnson-Lindenstrauss Transform Using a Coherence and Sampling Argument},
author = {Osman Asif Malik and Stephen Becker},
journal= {arXiv preprint arXiv:1911.08424},
year = {2020}
}
Comments
Accepted to Linear Algebra and its Applications