Hierarchical Agglomerative Clustering of Time-Warped Series

Abstract

We have developed a procedure for hierarchical agglomerative clustering of time series data. To measure the dissimilarity between these data, we use classically the Euclidean distance or we apply the costs of the series nonlinear alignment (time warping). In the latter approach, we use the classical costs or the modified ones. The modification consists in matching short signal segments instead of single signal samples. The procedure is applied to a few datasets from the internet archive of time series. In this archive, the series of the same classes possess visual similarity but their time evolution is often different (the characteristic waves have different location within the individual signals). Therefore the use of the Euclidean distance as the dissimilarity measure gives poor results. After time warping, the nonlinearly aligned signals match each other better, and therefore the total cost of the alignment appears to be a much more effective measure. It results in higher values of the Purity index used to evaluate the results of clustering. In most cases, the proposed modification of the alignment costs definition leads to still higher values of the index.