Integrating Time Alignment and Self-Organizing Maps

Clustering time series has become in recent years a topic of great interest in a wide range of fields. The several approaches differ mainly in their notion of similarity (for a review see Focardi, 2001). Most researches use the Euclidean distance or some variation of it because of its easy implementation, even if it is very sensitive to temporal axis alignment. Furthermore, there are many applications where it is demonstrated that the Euclidean distances between raw data fail to capture the notion of similarity. The principal reason why Euclidean distance may fail to produce an intuitively correct measure of similarity between two sequences is that it is very sensitive to small distortions in the time axis as, for example, in the case of two sequences having approximately the same overall shape but not aligned in time axis. A method that allows this elastic shifting of the X-axis is desired in order to detect similar shapes with different phases. For this purpose, the Dynamical Time Warping (DTW) distance has been recently introduced (Berndt, Clifford, 1994), technique that was already known in the speech processing community (Sakoe, Chiba, 1978; Rabiner, Juang, 1993). Nevertheless the DTW algorithm can produce incorrect results in presence of salient features or noise in the data and the algorithm’s time complexity causes a problem in a way that “...performance on very large databases may be a limitation”. Morlini et al. (2005) proposes a modification of this algorithm that considers a smoothed version of the data and demonstrate that their approach allows to obtain points which are less noisy and dependent on the overall shape of the series. The clustering algorithms proposed in this approach are hierarchical clustering and K-means algorithms. The current paper proposes a new approach based on the implementation of the DTW distance in a Self Organizing Map algorithm (Kohonen, 2001) with the aim of classifying a set of curves. To show the results of this approach, we illustrate an application of our method on simulated data; while in the extended paper version we will propose an application on topographic real data.