k-Shape

Abstract

The proliferation and ubiquity of temporal data across many disciplines has generated substantial interest in the analysis and mining of time series. Clustering is one of the most popular data mining methods, not only due to its exploratory power, but also as a preprocessing step or subroutine for other techniques. In this paper, we describe k-Shape, a novel algorithm for time-series clustering. k-Shape relies on a scalable iterative refinement procedure, which creates homogeneous and well-separated clusters. As its distance measure, k-Shape uses a normalized version of the cross-correlation measure in order to consider the shapes of time series while comparing them. Based on the properties of that distance measure, we develop a method to compute cluster centroids, which are used in every iteration to update the assignment of time series to clusters. An extensive experimental evaluation against partitional, hierarchical, and spectral clustering methods, with the most competitive distance measures, showed the robustness of k-Shape. Overall, k-Shape emerges as a domain-independent, highly accurate, and efficient clustering approach for time series with broad applications.