The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings

Abstract

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.

Cite

Text

Choromanski et al. "The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings." Neural Information Processing Systems, 2017.

Markdown

[Choromanski et al. "The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/choromanski2017neurips-unreasonable/)

BibTeX

@inproceedings{choromanski2017neurips-unreasonable,
  title     = {{The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings}},
  author    = {Choromanski, Krzysztof M and Rowland, Mark and Weller, Adrian},
  booktitle = {Neural Information Processing Systems},
  year      = {2017},
  pages     = {219-228},
  url       = {https://mlanthology.org/neurips/2017/choromanski2017neurips-unreasonable/}
}