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arXiv · 1703.00864

The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings

Krzysztof Choromanski·Mark Rowland·Adrian Weller
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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.

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Krzysztof Choromanski, Mark Rowland, Adrian Weller. 2017-03-02. The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings. https://arxiv.org/abs/1703.00864

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