Fuzzy Clustering Of Ordinal Time Series Based On Two Novel Distances

Abstract

[Abstract]: Clustering of time series is a central machine learning task with applications in many fields. While most procedures focus on real-valued time series, very few works consider series with alternative ranges. In this paper, the problem of clustering ordinal time series is addressed. To this aim, two novel distances between ordinal series are introduced and used as input for the fuzzy C-medoids algorithm. Both metrics are based on estimated cumulative probabilities, thus automatically taking advantage of the underlying ordering existing in the series range. The corresponding clustering algorithms are able to group series generated from similar underlying stochastic processes, achieve accurate results with series coming from a wide variety of models and are computationally efficient. Moreover, the consideration of the fuzzy approach allows the techniques to properly handle time series showing an uncertain behaviour. An extensive simulation study shows that the proposed methods outperform several alternative procedures.