Exact mean computation in dynamic time warping spaces

Averaging time series under dynamic time warping is an important tool for improving nearest-neighbor classifiers and formulating centroid-based clustering. The most promising approach poses time series averaging as the problem of minimizing a Fréchet function. Minimizing the Fréchet function is NP-h...

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Bibliographic Details
Published in:Data mining and knowledge discovery Vol. 33; no. 1; pp. 252 - 291
Main Authors: Brill, Markus, Fluschnik, Till, Froese, Vincent, Jain, Brijnesh, Niedermeier, Rolf, Schultz, David
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2019
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Chemistry and Earth Sciences
Clustering
Computer Science
Computing time
Data Mining and Knowledge Discovery
Heuristic
Information Storage and Retrieval
Physics
Polynomials
State of the art
Statistics for Engineering
Time series
Warping
Dynamic programming
Time series analysis
Fréchet function
Empirical evaluation of heuristics
Exact exponential-time algorithm
ISSN:1384-5810, 1573-756X
Online Access:Get full text
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Summary:Averaging time series under dynamic time warping is an important tool for improving nearest-neighbor classifiers and formulating centroid-based clustering. The most promising approach poses time series averaging as the problem of minimizing a Fréchet function. Minimizing the Fréchet function is NP-hard and so far solved by several heuristics and inexact strategies. Our contributions are as follows: we first discuss some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Then we propose an exponential-time dynamic program for computing a global minimum of the Fréchet function. The proposed algorithm is useful for benchmarking and evaluating known heuristics. In addition, we present an exact polynomial-time algorithm for the special case of binary time series. Based on the proposed exponential-time dynamic program, we empirically study properties like uniqueness and length of a mean, which are of interest for devising better heuristics. Experimental evaluations indicate substantial deficits of state-of-the-art heuristics in terms of their output quality.
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ISSN:1384-5810
1573-756X
DOI:10.1007/s10618-018-0604-8