Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Abstract

<div>This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-of-the-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div><div><br></div>