Sign Stable Random Projections for Large-Scale Learning

In this paper, we study the use of “sign α-stable random projections” (where 0 < α ≤ 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 α. Thus, this approach provides an effective strategy for approximating nonlinear learning algorithms essentially at the cost of linear learning. When α = 2, it is known that the corresponding nonlinear kernel is the arc-cosine kernel. When α = 1, the procedure approximates the arc-cos-χ kernel (under certain condition). When α → 0+, it corresponds to the resemblance kernel, which provides the exciting connection between two popular randomized algorithms: (i) stable random projections (ii) b-bit minwise hashing. No theoretical results are known so far for other α values except for α = 2, 1, or 0+.