PDE regularized principal component analysis on bidimensional manifolds, with applications to neuroimaging data

Laura Sangalli

Politecnico di Milano, Mox - Dipartimento di Matematica

Monday 14th November 2016

11:30:00

Aula Consiglio VII Piano Dipartimento di Matematica, Politecnico di Milano

Motivated by the analysis of high-dimensional neuroimaging signals over the cerebral cortex, we introduce a principal component analysis technique that can be used for exploring the variability and performing dimensional reduction of signals observed over two-dimensional manifolds. The proposed method is based on a PDE regularization approach, involving the Laplace-Beltrami operator associated to the manifold domain. The model introduced can be applied to data observed over any two-dimensional manifold topology, and can naturally handle missing data and signals evaluated in different grids of points. The proposed method is applied to the analysis of resting state functional magnetic resonance imaging data from the Human Connectome Project. contact: laura.sangalli@polimi.it