Graph-Valued Regression: Prediction of unlabelled networks in a Non-Euclidean Graph-Space
Saturday 23rd January 2021
Calissano, A.; Feragen, A; Vantini, S.
Understanding how unlabeled graphs depend on input values or vectors is of extreme interest in a range of applications. In this paper, we propose a regression model taking values in Graph Space, representing unlabeled graphs which can be weighted or unweighted, one or multi-layer, and have same or different numbers of nodes, as a function of real valued regressor. As Graph Space is not a manifold, well-known manifold regression models are not applicable. We provide flexible parameterized regression models for Graph Space, along with precise and computationally efficient estimation procedures given by the introduced Align All and Compute regression algorithm. We show the potential of the proposed model for two real datasets: a time dependent cryptocurrency correlation matrices and a set of bus mobility usage network in Copenhagen (DK) during the Covid-19 pandemic.