Compact Random Feature Maps
This work addresses a specific bottleneck in kernel approximation for machine learning practitioners, offering an incremental improvement over existing methods.
The paper tackles the problem of rank deficiency in previous polynomial kernel approximation methods by proposing compact random feature maps (CRAFTMaps), which achieve more concise and accurate approximations with proven error bounds and competitive performance on standard datasets.
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 their 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.