Hongteng Xu
Graph representation is significant for many real-world applications, e.g., network analysis, molecule clustering, and classification, etc. In this talk, I will introduce a new nonlinear factorization model, representing graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudo-metric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It achieves a novel and flexible factorization mechanism under the GW discrepancy, which estimates observed graphs as GW barycenters constructed by a set of atoms with different weights. The atoms and the weights associated with the observed graphs are learned by minimizing the GW discrepancy between the observed graphs and the barycenters of the atoms. I will show that this GW factorization model represents graphs with different sizes as vectorized permutation-invariant features. The learning algorithms of this model, its extensions, and potential applications will be discussed in-depth.
