ONLINE CLASSIFICATION OF DYNAMIC MULTILAYER-NETWORK TIME SERIES IN
RIEMANNIAN MANIFOLDS
Abstract
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.
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