A robust alternating least squares K-means clustering approach for times series using dynamic time warping dissimilarities

Abstract

Time series clustering is a usual task in many different areas. Algorithms such as K-means and model-based clustering procedures are used relating to multivariate assumptions on the datasets, as the consideration of Euclidean distances, or a probabilistic distribution of the observed variables. However, in many cases the observed time series are of unequal length and/or there is missing data or, simply, the time periods observed for the series are not comparable between them, which does not allow the direct application of these methods. In this framework, dynamic time warping is an advisable and well-known elastic dissimilarity procedure, in particular when the analysis is accomplished in terms of the shape of the time series. In relation to a dissimilarity matrix, K-means clustering can be performed using a particular procedure based on classical multidimensional scaling in full dimension, which can result in a clustering problem in high dimensionality for large sample sizes. In this paper, we propose a procedure robust to dimensionality reduction, based on an auxiliary configuration estimated from the squared dynamic time warping dissimilarities, using an alternating least squares procedure. The performance of the model is compared to that obtained using classical multidimensional scaling, as well as to that of model-based clustering using this related auxiliary linear projection. An extensive Monte Carlo procedure is employed to analyze the performance of the proposed method in which real and simulated datasets are considered. The results obtained indicate that the proposed K-means procedure, in general, slightly improves the one based on the classical configuration, both being robust in reduced dimensionality, making it advisable for large datasets. In contrast, model-based clustering in the classical projection is greatly affected by high dimensionality, offering worse results than K-means, even in reduced dimension.

Keywords

• k-means
• dynamic time warping
• model-based clustering
• time series
• multidimensional scaling
• alscal