Very Sparse Stable Random Projections, Estimators and Tail Bounds for Stable Random Projections

The method of stable random projections [39, 41] is popular for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the lα distance between a pair of streams, for any 0 < α ≤ 2. [18] and [20] applied stable random projections for approximating the Hamming norm and the max-dominance norm, respectively, using very small α. Another application is to approximate all pairwise lα distances in a data matrix to speed up clustering, classification, or kernel computations. Given that stable random projections have been successful in various applications, this paper will focus on three different aspects in improving the current practice of stable random projections.