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Very sparse stable random projections, estimators and tail bounds for stable random projections (2006)
| Citations: | 5 - 2 self |
BibTeX
@TECHREPORT{Li06verysparse,
author = {Ping Li},
title = {Very sparse stable random projections, estimators and tail bounds for stable random projections},
institution = {},
year = {2006}
}
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Abstract
[36] proposed stable random projections, now a popular tool 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. [16] and [18] 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 become successful in various applications, this paper will focus on three different aspects in improving the current practice of stable random projections. Firstly, we propose very sparse stable random projections to significantly reduce the processing and storage cost, by replacing the α-stable distribution with a mixture of a symmetric α-Pareto distribution (with probability β, 0 < β ≤ 1) and a point mass at the origin (with a probability 1 − β). This leads to a significant 1 β-fold speedup for small β. We analyze the rate of convergence as a function of β, α, and the data regularity conditions. For example, when α = 1 and the data have bounded second moments, then
Keyphrases
stable random projection sparse stable random projection tail bound current practice second moment data mining symmetric pareto distribution stable distribution point mass data matrix storage cost different aspect single data stream pairwise distance elegant methodology data streaming max-dominance norm popular tool various application fold speedup data regularity condition hamming norm machine learning
