Fuzzy probabilistic-distance clustering of time and numerical series modeled by penalized spline

Clustering of numerical series (time series, longitudinal data, ...) has application in various domains. We propose a fuzzy method for clustering data series modeled by weighted penalized spline. Raw data are simultaneously analyzed through weighted penalized splines allowing for an efficient separation of the signal from the measurement noise. The probabilistic clustering framework makes it possible to jointly update the weighting system involved in the definition of the within cluster trends and the probabilistic allocation of the observed series to the clusters. We evaluate the performances of our procedure dealing with simulated and real data using different distance measures. We discuss the applicability of the proposed clustering method to analyze general classes of time series emphasizing its fuzzy nature.