A weighted k-medoids algorithm for clustering time series' projections

Time-series clustering is one of the most common techniques used to discover similar structures in a dataset with dynamic objects. The main issue in time series clustering lies in the computation of a proper distance. A lot of approaches, based on statistical model parameters or on time series features, have been proposed in the literature. Some clustering approaches do not consider as units the single time series but their projections. In this case, it is very important to define a peculiar distance, taking into account the characteristics of the observations. In this framework, we propose a kMEDOID-type algorithm based on an optimal weighting scheme for multiple distances. The weights, obtained by minimizing the weighted squared distance between each i-th object from its k-th medoid, reflect the importance of the information contained in each distance. The performance of the proposed fast algorithm will be evaluated by comparing the results with those obtained using well-known clustering approaches. Furthermore, an application to real datasets is provided.