Norm, Point, and Distance Estimation Over Multiple Signals Using Max-Stable Distributions

Consider a set of signals fs : {1, . . . , N} [0, . . . , M] appearing as a stream of tuples (i, fs(i)) in arbitrary order of i and s. We would like to devise one pass approximate algorithms for estimating various functionals on the dominant signal fmax, defined as fmax = {(i, maxs fs(i)), i}. For example, the "worst case influence" which is the F1? norm of the dominant signal [7], general Fp?norms, and special types of distances between dominant signals. The only known previous work in this setting are the algorithms of Cormode and Muthukrishnan [7] and Pavan and Tirthapura [18] which can only estimate the F1?norm over fmax. No previous work addressed more general norms or distance estimation. In this work, we use a novel sketch, based on the properties of max?stable distributions, for these more general problems. The max?stable sketch is a significant improvement over previous alternatives in terms of simplicity of implementation, space requirements, and insertion cost, w...

• Type: Conference
• Year: 2007
• Where: ICDE
• Authors: Stilian Stoev, Marios Hadjieleftheriou, George Kollios, Murad S. Taqqu
• Keywords: Database, Dominant Signal, Dominant Signal Fmax, Dominant Signals, ICDE 2007