Gromov-Wasserstein Factorization Models for Graph Clustering

We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a set of atoms with different weights. By minimizing the GW discrepancy between each observed graph and its GW barycenter-based estimation, we learn the atoms and their weights associated with the observed graphs. The model achieves a novel and flexible factorization mechanism under GW discrepancy, in which both the observed graphs and the learnable atoms can be un-aligned and with different sizes. We design an effective approximate algorithm for learning this Gromov-Wasserstein factorization (GWF) model, unrolling loopy computations as stacked modules and computing gradients with backpropaga-tion. The stacked modules can be with two different architectures, which correspond to the proximal point algorithm (PP A) and Bregman alternating direction method of multipliers (BADMM), respectively. Experiments show that our model obtains encouraging results on clustering graphs. Introduction As an important methodology for machine learning, factorization models explore intrinsic structures of high-dimensional observations explicitly, which have been widely used in many learning tasks, e.g., data clustering (Ng, Jordan, and Weiss 2002), dimensionality reduction (Cand es et al. 2011), recommendation systems (Wang and Blei 2011), etc. In particular, factorization models decompose high-dimensional observations into a set of atoms under specific criteria and achieve their latent representations accordingly.