Distance metric learning for graph structured data

Graphs are versatile tools for representing structured data. As a result, variety of machine learning methods have been studied graph data analysis. Although many such depend on the measurement differences between input graphs, defining an appropriate distance metric graphs remains controversial issue. Hence, we propose supervised method classification problem. Our method, named interpretable (IGML), learns discriminative metrics in subgraph-based feature space, which has strong representation capability. By introducing sparsity-inducing penalty weight each subgraph, IGML can identify small number important subgraphs that provide insight into given task. Because our formulation large optimization variables, efficient algorithm uses pruning techniques based safe screening and working set selection is also proposed. An property solution optimality guaranteed because problem formulated as convex strategies only discard unnecessary subgraphs. Furthermore, show applicable to other itemset sequence data, it incorporate vertex-label similarity by using transportation-based subgraph feature. We empirically evaluate computational efficiency performance several benchmark datasets some illustrative examples how identifies from dataset.