Dimension Reduction in Kernel Spaces from Locality-Sensitive Hashing

We provide novel methods for efficient dimensionality reduction in kernel spaces. That is, we provide efficient and explicit randomized maps from “data spaces” into “kernel spaces” of low dimension, which approximately preserve the original kernel values. The constructions are based on observing that such maps can be obtained from Locality-Sensitive Hash (LSH) functions, a primitive developed for fast approximate nearest neighbor search. Thus, we relate the question of dimensionality reduction in kernel spaces to the already existing theory of LSH functions. Efficient dimensionality reduction in kernel spaces enables a substantial speedup of kernelbased algorithms, as experimentally shown in Rahimi-Recht (NIPS’07). Our framework generalizes one of their constructions.