Penalized model-based functional clustering: a regularization approach via shrinkage methods

With the advance of modern technology, and with data being recorded continuously, functional data analysis has gained a lot of popularity in recent years. Working in a mixture model-based framework, we develop a flexible functional clustering technique achieving dimensionality reduction schemes through a L1 penalization. The proposed procedure results in an integrated modelling approach where shrinkage techniques are applied to enable sparse solutions in both the means and the covariance matrices of the mixture components, while preserving the underlying clustering structure. This leads to an entirely data-driven methodology suitable for simultaneous dimensionality reduction and clustering. Preliminary experimental results, both from simulation and real data, show that the proposed methodology is worth considering within the framework of functional clustering.