Deep Wasserstein Graph Discriminant Learning for Graph Classification

Graph topological structures are crucial to distinguish different-class graphs. In this work, we propose a deep Wasserstein graph discriminant learning (WGDL) framework to learn discriminative embeddings of graphs in Wassersteinmetric (W-metric) matching space. In order to bypass the calculation of W-metric class centers in discriminant analysis, as well as better support batch process learning, we introduce a reference set of graphs (aka graph dictionary) to express those representative graph samples (aka dictionary keys). On the bridge of graph dictionary, every input graph can be projected into the latent dictionary space through our proposed Wasserstein graph transformation (WGT). In WGT, we formulate inter-graph distance in W-metric space by virtue of the optimal transport (OT) principle, which effectively expresses the correlations of cross-graph structures. To make WGDL better representation ability, we dynamically update graph dictionary during training by maximizing the Wasserstein Discriminant loss, i.e. the ratio of inter-class versus intra-class Wasserstein distance. To evaluate our WGDL method, comprehensive experiments are conducted on six graph classification datasets. Experimental results demonstrate the effectiveness of our WGDL, and state-of-the-art performance.