A global averaging method for dynamic time warping, with applications to clustering

Mining sequential data is an old topic that has been revived in the last decade, due to the increasing availability of sequential datasets. Most works in this field are centred on the definition and use of a distance (or, at least, a similarity measure) between sequences of elements. A measure called Dynamic Time Warping (DTW) seems to be currently the most relevant for a large panel of applications. This article is about the use of DTW in data mining algorithms, and focuses on the computation of an average of a set of sequences. Averaging is an essential tool for the analysis of data. For example, the K-means clustering algorithm repeatedly computes such an average, and needs to provide a description of the clusters it forms. Averaging is here a crucial step, which must be sound in order to make algorithms work accurately. When dealing with sequences, especially when sequences are compared with DTW, averaging is not a trivial task. Starting with existing techniques developed around DTW, the article suggests an analysis framework to classify averaging techniques. It then proceeds to study the two major questions lifted by the framework. First, we develop a global technique for averaging a set of sequences. This technique is original in that it avoids using iterative pairwise averaging. It is thus insensitive to ordering effects. Second, we describe a new strategy to reduce the length of the resulting average sequence. This has a favourable impact on performance, but also on the relevance of the results. Both aspects are evaluated on standard datasets, and the evaluation shows that they compare favourably with existing methods. The article ends by describing the use of averaging in clustering. The last section also introduces a new application domain, namely the analysis of satellite image time series, where data mining techniques provide an original approach.