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 functionals on the dominant signal f_max, defined as f_max = {(i, max_s f_s (i)), ∀i}. For example, the "worst case influence" which is the F₁-norm of the dominant signal (Cormode and Muthukrishnan, 2003), general F_p-norms, and special types of distances between dominant signals. The only known previous work in this setting are the algorithms of Cormode and Muthukrishnan and Pavan and Tirtha-pura (2005) which can only estimate the F₁-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. The 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.