2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS) (2014)

Philadelphia, PA, USA

Oct. 18, 2014 to Oct. 21, 2014

ISSN: 0272-5428

ISBN: 978-1-4799-6517-5

pp: 581-590

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2014.68

ABSTRACT

We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset is chosen arbitrarily from an unknown subspace of low dimension, and then perturbed by full-dimensional Gaussian noise. We design spectral NNS algorithms whose query time depends polynomially on the dimension and logarithmically on the size of the point set. These spectral algorithms use a repeated computation of the top PCA vector/subspace, and are effective even when the random-noise magnitude is much larger than the interpoint distances. Our motivation is that in practice, a number of spectral NNS algorithms outperform the random-projection methods that seem otherwise theoretically optimal on worst-case datasets. In this paper we aim to provide theoretical justification for this disparity. The full version of this extended abstract is available on arXiv.

INDEX TERMS

Principal component analysis, Noise, Algorithm design and analysis, Vectors, Partitioning algorithms, Data structures, Nearest neighbor searches

CITATION

A. Abdullah, A. Andoni, R. Kannan and R. Krauthgamer, "Spectral Approaches to Nearest Neighbor Search,"

*2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS)*, Philadelphia, PA, USA, 2014, pp. 581-590.

doi:10.1109/FOCS.2014.68

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