Visual Similarity Perception of Directed Acyclic Graphs: A Study on Influencing Factors

While visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology), knowledge about humans' perception of graph similarity is currently quite limited. By graph similarity perception we mean how humans perceive commonalities and differences in graphs and herewith come to a similarity judgment. As a step toward filling this gap the study reported in this paper strives to identify factors which influence the similarity perception of DAGs. In particular, we conducted a card-sorting study employing a qualitative and quantitative analysis approach to identify 1) groups of DAGs that are perceived as similar by the participants and 2) the reasons behind their choice of groups. Our results suggest that similarity is mainly influenced by the number of levels, the number of nodes on a level, and the overall shape of the graph.Comment: Graph Drawing 2017 - arXiv Version; Keywords: Graphs, Perception, Similarity, Comparison, Visualizatio

RASCAL: calculation of graph similarity using maximum common edge subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection

Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance or similarity metric is, however, not trivial and can be highly dependent on the application at hand. In this work, we propose a novel metric learning method to evaluate distance between graphs that leverages the power of convolutional neural networks, while exploiting concepts from spectral graph theory to allow these operations on irregular graphs. We demonstrate the potential of our method in the field of connectomics, where neuronal pathways or functional connections between brain regions are commonly modelled as graphs. In this problem, the definition of an appropriate graph similarity function is critical to unveil patterns of disruptions associated with certain brain disorders. Experimental results on the ABIDE dataset show that our method can learn a graph similarity metric tailored for a clinical application, improving the performance of a simple k-nn classifier by 11.9% compared to a traditional distance metric.Comment: International Conference on Medical Image Computing and Computer-Assisted Interventions (MICCAI) 201