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Title: A robust proposal for functional clustering via trimming and constraints Authors:  Luis Angel Garcia-Escudero - Universidad de Valladolid (Spain) [presenting]
Agustin Mayo-Iscar - Universidad de Valladolid (Spain)
Joaquin Ortega - Centro de Investigacion en Matematicas (Mexico)
Diego Rivera Garcia - Centro de Investigacion en Matematicas (Mexico)
Abstract: Many approaches can be found in the literature aimed at performing functional or curve clustering. However, the presence of (even a small fraction of) outlying curves may be extremely harmful for most of them, because they are not specifically designed to cope with contaminating curves. Taking this problem into account, a robust model-based clustering methodology is proposed. The proposed methodology relies on the ``small-ball pseudo-density'' approach for functional data that results in different model-based techniques. An impartial (i.e. data-driven) trimming is used to improve the associated robustness performance of these model-based approaches. Appropriate constraints on the involved scatter parameters are critical to get robustness and useful to avoid the detection of (non-interesting) spurious clusters. A computationally feasible algorithm is presented together with graphical tools aimed at making sensible choices for the corresponding tuning parameters. The procedure is illustrated in both simulated and real data sets.