The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings

Code

• github.com/joneswack/dp-rfs
  pytorch★ 22
• github.com/dnbaker/frp
  none★ 0

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.

Tasks

Reproductions