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

Consider a set of signals f(s) : {1,...,N} --> [0,...,M] appearing as a stream of tuples (i, f(s)(i)) in arbitrary order of i and s. We would like to devise one pass approximate algorithms for estimating various Junctionals on the dominant signal f(max), defined as f(max) = {(i, max(s) f(s) (i)), for all(i)}. For example, the "worst case influence" which is the F-1-norm of the dominant signal [7], general F-p-norms, and special types of distances between dominant signals. Re 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 F-1-norm over f(max). 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. ne max-stable sketch is a significant improvement over previous alternatives in terms of simplicity of implementation, space requirements, and insertion cost, while providing similar approximation guarantees. To assert our statements, we also conduct an experimental evaluation using real datasets.