Sign Stable Random Projections for Large-Scale Learning

TL;DR

This paper investigates sign alpha-stable random projections as a scalable method for approximating nonlinear kernels in large-scale machine learning, providing empirical evidence of their effectiveness across various datasets.

Contribution

It offers an extensive empirical evaluation of sign alpha-stable random projections for different alpha values, comparing them with existing methods like CWS.

Findings

Effective approximation of nonlinear kernels at scale

Comparable or superior performance to existing methods

Versatility across classification datasets

Abstract

We study the use of "sign $\alpha$-stable random projections" (where $0<\alpha\leq 2$) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and near-neighbor search). After the processing by sign stable random projections, the inner products of the processed data approximate various types of nonlinear kernels depending on the value of $\alpha$. Thus, this approach provides an effective strategy for approximating nonlinear learning algorithms essentially at the cost of linear learning. When $\alpha =2$, it is known that the corresponding nonlinear kernel is the arc-cosine kernel. When $\alpha=1$, the procedure approximates the arc-cos-$\chi^2$ kernel (under certain condition). When $\alpha\rightarrow0+$, it corresponds to the resemblance kernel. From practitioners' perspective, the method of sign $\alpha$-stable random projections is ready to be tested for large-scale learning applications, where $\alpha$ can be simply viewed as a tuning parameter. What is missing in the literature is an extensive empirical study to show the effectiveness of sign stable random projections, especially for $\alpha\neq 2$ or 1. The paper supplies such a study on a wide variety of classification datasets. In particular, we compare shoulder-by-shoulder sign stable random projections with the recently proposed "0-bit consistent weighted sampling (CWS)" (Li 2015).