In many cases, data are not expressed as individual values on a timeline, but are a collection of values obtained at certain moments in time - they are time series. In these cases, traditional clustering models for one-time data are unable to properly account for the time-variability of the data. In this paper, by considering the partitioning around medoids approach in a fuzzy framework, we propose fuzzy clustering models for multivariate time series. In order to neutralize the negative effects of outlier time series in the clustering process, we proposed robust fuzzy c-medoids clustering models for time series based on the combination of Huber's M-estimators and Yager's OWA operators. The proposed models are able to smooth the influence of anomalous time series by means of the so-called typicality parameter, capable to tune the influence of the outliers. The performance of the proposed models has been shown by means of a simulation and real-data sets study: (i) two-dimensional dataset of time series, (ii) the average daily time series of temperatures, and (iii) the pregnancy dataset of time series. The comparison made with the robust clustering models known from the literature indicates the competitiveness of the introduced model to others.

Two novel distances between categorical time series are introduced. Both of them measure discrepancy between extracted features describing the underlying serial dependence patterns. One distance is based on well-known association measures, namely Cramer’s v and Cohen’s κ. The other one relies on the so-called binarization of a categorical process, which indicates the presence of each category by means of a canonical vector. Binarization is used to construct a set of innovative association measures, which allow to identify different types of serial dependence. The metrics are used to perform crisp and fuzzy clustering of nominal series. The proposed approaches are able to group together series generated from similar stochastic processes, achieve accurate results with series coming from a broad range of models, and are computationally efficient. Extensive simulation studies show that both hard and soft clustering algorithms outperform several alternative procedures presented in the literature. Two applications involving biological sequences from different species highlight the usefulness of the introduced techniques.