Title: Classifying Time-Varying Complex Networks on the Tensor Manifold,
Abstract: At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, and/or regime-shift detection. Recently, to explore such
functional properties, a convenient representation has been to model such
dynamical systems as a weighted graph consisting of a finite, but very large
number of interacting agents. This said, there exists very limited relevant
statistical theory that is able cope with real-life data, i.e., how does
perform simple analysis and/or statistics over a family of networks as opposed
to a specific network or network-to-network variation. Here, we are interested
in the analysis of network families whereby each network represents a point on
an underlying statistical manifold. From this, we explore the Riemannian
structure of the statistical (tensor) manifold in order to define notions of
geodesics or shortest distance amongst such points as well as a statistical
framework for time-varying complex networks for which we can utilize in higher
order classification tasks.