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A time series consists of a series of values or events obtained over repeatedmeasurements in time. Analysis of time series represents and important tool inmany application areas, such as stock market analysis, process and qualitycontrol, observation of natural phenomena, medical treatments, etc. A vitalcomponent in many types of time-series analysis is the choice of an appropriatedistance/similarity measure. Numerous measures have been proposed to date, withthe most successful ones based on dynamic programming. Being of quadratic timecomplexity, however, global constraints are often employed to limit the searchspace in the matrix during the dynamic programming procedure, in order to speedup computation. Furthermore, it has been reported that such constrainedmeasures can also achieve better accuracy. In this paper, we investigate tworepresentative time-series distance/similarity measures based on dynamicprogramming, Dynamic Time Warping (DTW) and Longest Common Subsequence (LCS),and the effects of global constraints on them. Through extensive experiments ona large number of time-series data sets, we demonstrate how global constrainscan significantly reduce the computation time of DTW and LCS. We also showthat, if the constraint parameter is tight enough (less than 10-15% oftime-series length), the constrained measure becomes significantly differentfrom its unconstrained counterpart, in the sense of producing qualitativelydifferent 1-nearest neighbor graphs. This observation explains the potentialfor accuracy gains when using constrained measures, highlighting the need forcareful tuning of constraint parameters in order to achieve a good trade-offbetween speed and accuracy.

The Influence of Global Constraints on Similarity Measures for Time-Series Databases