Daniel Remondini

Eleonora Andreotti, Armando Bazzani, Daniel Remondini et al.

In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on graphs with (m,k)-star subgraphs is feasible, keeping the same eigenvalues with reduced multiplicity. Moreover, some useful eigenvectors properties are derived up to a product with a suitable matrix. Finally, we relate these results with Fiedler spectral partitioning of the graph. The physical relevance of the results is shortly discussed.

Carlo Mengucci, Daniel Remondini, Gastone Castellani et al.

WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by the Wishart distribution WISDoM can be applied to tasks of supervised learning, like classification, in particular when such matrices are generated by data of different dimensionality (e.g. time series with same number of variables but different time sampling). We show the application of the method in two different scenarios. The first is the ranking of features associated to electro encephalogram (EEG) data with a time series design, providing a theoretically sound approach for this type of studies. The second is the classification of autistic subjects of the ABIDE study, using brain connectivity measurements.