Penalized Model-Based Functional Clustering: A Regularization Approach via Shrinkage Methods
Nicola Pronello, Rosaria Ignaccolo, Luigi Ippoliti, Sara Fontanella · Studies in classification, data analysis, and knowledge organization · 2023
Abstract 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 aL1penalization. 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.