  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).
