Advances on Time Series Analysis using Elastic Measures of Similarity
Oregui Bravo, Izaskun
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A sequence is a collection of data instances arranged in an structured manner. When thisarrangement is held in the time domain, sequences are instead referred to as time series. As such,each observation in a time series represents an observation drawn from an underlying process,produced at a specific time instant. However, other type of data indexing structures, such as spaceorthreshold-based arrangements are possible. Data points that compose a time series are oftencorrelated to each other. To account for this correlation in data mining tasks, time series are usuallystudied as a whole data object rather than as a collection of independent observations. In thiscontext, techniques for time series analysis aim at analyzing this type of data structures by applyingspecific approaches developed to harness intrinsic properties of the time series for a wide range ofproblems such as, classification, clustering and other tasks alike.The development of monitoring and storage devices has made time series analysisproliferate in numerous application fields including medicine, economics, manufacturing andtelecommunications, among others. Over the years, the community has gathered efforts towards thedevelopment of new data-based techniques for time series analysis suited to address the problemsand needs of such application fields. In the related literature, such techniques can be divided in threemain groups: feature-, model- and distance- based methods. The first group (feature-based)transforms time series into a collection of features, which are then used by conventional learningalgorithms to provide solutions to the task under consideration. In contrast, methods belonging to thesecond group (model-based) assume that each time series is drawn from a generative model, whichis then harnessed to elicit information from data. Finally, distance-based techniques operate directlyon raw time series. To this end, these latter methods resort to specially defined measures of distanceor similarity for comparing time series, without requiring any further processing. Among them,elastic similarity measures (e.g., dynamic time warping and edit distance) compute the closenessbetween two sequences by finding the best alignment between them, disregarding differences intime gaps and thus focusing exclusively on shape differences.This Thesis presents several contributions to the field of distance-based techniques for timeseries analysis, namely: i) a novel multi-dimensional elastic similarity learning method for timeseries classification; ii) an adaptation of elastic measures to streaming time series scenarios; and iii)the use of distance-based time series analysis to make machine learning methods for imageclassification robust against adversarial attacks. Throughout the Thesis, each contribution is framedwithin its related state of the art, explained in detail and empirically evaluated. The obtained resultslead to new insights on the application of distance-based time series methods for the consideredscenarios, and motivates research directions that highlight the vibrant momentum of this researcharea.