Random Projections for k-means Clustering

11/21/2010

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by   Christos Boutsidis, et al.

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This paper discusses the topic of dimensionality reduction for k-means clustering. We prove that any set of n points in d dimensions (rows in a matrix A ∈^n × d) can be projected into t = Ω(k / ^2) dimensions, for any ∈ (0,1/3), in O(n d ^-2 k/ (d) ) time, such that with constant probability the optimal k-partition of the point set is preserved within a factor of 2+. The projection is done by post-multiplying A with a d × t random matrix R having entries +1/√(t) or -1/√(t) with equal probability. A numerical implementation of our technique and experiments on a large face images dataset verify the speed and the accuracy of our theoretical results.