Time Series Retrieval Using DTW-Preserving Shapelets

Abstract

Dynamic Time Warping (DTW) is a very popular similarity measure used for time series classification, retrieval or clustering. DTW is, however, a costly measure, and its application on numerous and/or very long time series is difficult in practice. This paper proposes a new approach for time series retrieval: time series are embedded into another space where the search procedure is less computationally demanding, while still accurate. This approach is based on transforming time series into highdimensional vectors using DTW-preserving shapelets. That transform is such that the relative distance between the vectors in the Euclidean transformed space well reflects the corresponding DTW measurements in the original space. We also propose strategies for selecting a subset of shapelets in the transformed space, resulting in a trade-off between the complexity of the transformation and the accuracy of the retrieval. Experimental results using the well known UCR time series demonstrate the importance of this trade-off.

CDPS: Constrained DTW-Preserving Shapelets

“…Subsequently, Mueen et al [14] introduce logical shapelets, which combines shapelets with complex rules of discrimination to increase the reliability of the shapelets and their ability to discriminate between the time-series. Sperandio [22] presents a detailed review of early shapelet approaches.…”

“…In this way the algorithm is guided to converge on a result that is meaningful to the user without explicitly, nor exhaustively labelling samples. Generally, time series are characterised by trend, shapes, and distortions either to time or shape [22] and therefore exhibit phase shifts and warping. As such, the Euclidean distance is unsuitable and several similarity measures specific to time-series have been proposed [17], for example compression-based measures [7], Levenshtein Distance [10], Longest Common Subsequnce [25] and Dynamic Time Warping (DTW) [19,20].…”

“…Moreover, Paparrizos et al show that DTW is a good basis for calculating embeddings, an approach that employs a similarity to construct a new representation. Time series also exhibit complex structure which are often highly correlated [22]. This makes their analysis difficult to achieve and time consuming, indeed several attempts to accelerate DTW's computation have been proposed [1,22].…”

“…Time series also exhibit complex structure which are often highly correlated [22]. This makes their analysis difficult to achieve and time consuming, indeed several attempts to accelerate DTW's computation have been proposed [1,22]. Shapelets [30] offer a simpler approach to increase the accuracy of time-series analysis.…”