Fast binary embeddings with Gaussian circulant matrices: improved bounds
Information Theory
2017-12-27 v2 Data Structures and Algorithms
math.IT
Abstract
We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian circulant embeddings, we largely fix a gap in the proof of the best known fast binary embedding method. Our bounds also show that well-spreadness assumptions on the data vectors, which were needed in earlier work on variance bounds, are unnecessary. In addition, we propose a new binary embedding with a faster running time on sparse data.
Cite
@article{arxiv.1608.06498,
title = {Fast binary embeddings with Gaussian circulant matrices: improved bounds},
author = {Sjoerd Dirksen and Alexander Stollenwerk},
journal= {arXiv preprint arXiv:1608.06498},
year = {2017}
}