Time-series similarity problems and well-separated geometric sets

Authors:
Béla Bollobás;Gautam Das;Dimitrios Gunopulos;Heikki Mannila
Affiliations:
University of Memphis, Department of Mathematical Sciences, Memphis, TN and Trinity College, Cambridge CB2 1TQ, UK;Microsoft Research, One Microsoft Way, Redmond, WA;Department of Computer Science and Engineering, University of California, Riverside, Riverside, CA;Helsinki Institute of Information Technology, Basic Research Unit, PO Box 26, FIN-00014, University of Helsinki, Finland
Venue:
Nordic Journal of Computing
Year:
2001

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Abstract

Given a pair of nonidentical complex objects, defining (and determining) how similar they are to each other is a nontrivial problem. In data mining applications, one frequently needs to determine the similarity between two time series. We analyze a model of time-series similarity that allows outliers, different scaling functions, and variable sampling rates. We present several deterministic and randomized algorithms for computing this notion of similarity. The algorithms are based on nontrivial tools and methods from computational geometry. In particular, we use properties of families of well-separated geometric sets. The randomized algorithm has provably good performance and also works extremely efficiently in practice.