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Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds
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  • Cong Ye ,
  • Konstantinos Slavakis ,
  • Johan Nakuci ,
  • Sarah F. Muldoon ,
  • John Medaglia
Konstantinos Slavakis
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Johan Nakuci
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Sarah F. Muldoon
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John Medaglia
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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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