Graph dissimilarities provide a powerful and ubiquitous approach for applying machine learning algorithms to edge-attributed graphs. However, conventional optimal transport-based dissimilarities cannot handle edge-attributes. In this paper, we propose an optimal transport-based dissimilarity between graphs with edge-attributes. The proposed method, multi-dimensional fused Gromov-Wasserstein discrepancy (MFGW), naturally incorporates the mismatch of edge-attributes into the optimal transport theory. Unlike conventional optimal transport-based dissimilarities, MFGW can directly handle edge-attributes in addition to structural information of graphs. Furthermore, we propose an iterative algorithm, which can be computed on GPUs, to solve non-convex quadratic programming problems involved in MFGW.  Experimentally, we demonstrate that MFGW outperforms the conventional optimal transport-based dissimilarity in several machine learning applications including supervised classification, subgraph matching, and graph barycenter calculation.

During software requirements analysis, developers and stakeholders have many alternatives of requirements to be achieved and should make decisions to select an alternative out of them. There are two significant points to be considered for supporting these decision making processes in requirements analysis; 1) dependencies among alternatives and 2) evaluation based on multi-criteria and their trade-off. This paper proposes the technique to address the above two issues by using an extended version of goal-oriented analysis. In goal-oriented analysis, elicited goals and their dependencies are represented with an AND-OR acyclic directed graph. We use this technique to model the dependencies of the alternatives. Furthermore we associate attribute values and their propagation rules with nodes and edges in a goal graph in order to evaluate the alternatives with them. The attributes and their calculation rules greatly depend on the characteristics of a development project. Thus, in our approach, we select and use the attributes and their rules that can be appropriate for the project. TOPSIS method is adopted to show alternatives and their resulting attribute values.

In this paper, we define an attributed random graph, which can be considered as a generalization of conventional ones, to include multiple attributes as well as numeric attribute instead of a single nominal attribute in random vertices and edges. Then we derive the probability equations for an attributed graph to be an outcome graph of the attributed random graph, and the equations for the entropy calculation of the attributed random graph. Finally, we propose the application areas to computer vision and machine learning using these concepts.