Compact Random Feature Maps [article]

Raffay Hamid and Ying Xiao and Alex Gittens and Dennis DeCoste
2013 arXiv   pre-print
Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this challenge, we propose compact random feature maps (CRAFTMaps) to approximate polynomial kernels more concisely and accurately. We prove the error bounds of CRAFTMaps demonstrating
more » ... r superior kernel reconstruction performance compared to the previous approximation schemes. We show how structured random matrices can be used to efficiently generate CRAFTMaps, and present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class classifiers. We present experiments on multiple standard data-sets with performance competitive with state-of-the-art results.
arXiv:1312.4626v1 fatcat:iirwzpbnj5b5bncejzr76cxjaa