We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the Johnson-Lindenstrauss transform and the angular kernel, we show that we can select matrices yielding guaranteed improved performance in accuracy and/or speed compared to earlier methods. We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.
@article{arxiv.1703.00864,
title = {The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings},
author = {Krzysztof Choromanski and Mark Rowland and Adrian Weller},
journal= {arXiv preprint arXiv:1703.00864},
year = {2018}
}