A1159
Title: Simultaneous clustering and dimensionality reduction of functional data
Authors: Roberto Rocci - Sapienza University of Rome (Italy) [presenting]
Stefano Antonio Gattone - University G. d'Annunzio of Chieti-Pescara (Italy)
Abstract: A new technique for simultaneous clustering and dimensionality reduction of functional data is proposed. The observations are projected into a low-dimensional subspace and clustered by means of functional K-means. The subspace and the partition are estimated simultaneously by minimizing the within deviance in the reduced space. This allows us to find new dimensions with a very low within deviance, which should correspond to a high level of discriminant power. However, in some cases, the total deviance explained by the new dimensions is so low as to make the subspace and, therefore, the partition identified in it insignificant. In order to overcome this drawback, a penalty equal to the negative total deviance in the reduced space is added to the loss. In this way, subspaces with low deviance are avoided. It is shown how several existing methods are particular cases of the proposal simply by varying the weight of the penalty. A further penalty is added in order to take into account the functional nature of the data by smoothing the centroids, and an alternating least squares algorithm is introduced to compute model parameter estimates. An application to real and simulated data shows the effectiveness of the proposal.
