OWA-based robust fuzzy clustering of time series with typicality degrees

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.