Discriminative feature selection for uncertain graph classification

Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interest-ingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objects are certain, and the binary edges within each graph represent the "presence" of linkages among the nodes. In many real-world applications, however, the linkage structure of the graphs is inherently uncertain. Therefore, existing measurements of interestingness based upon certain graphs are unable to capture the structural uncertainty in these applications effectively. In this paper, we study the problem of discriminative subgraph feature selection from uncertain graphs. This problem is challenging and different from conventional subgraph mining problems because both the structure of the graph objects and the discrimination score of each subgraph feature are uncertain. To address these challenges, we propose a novel discriminative subgraph feature selection method, Dug, which can find discriminative subgraph features in uncertain graphs based upon different statistical measures including expectation, median, mode and ℓ-probability. We first compute the probability distribution of the discrimination scores for each subgraph feature based on dynamic programming. Then a branch-and-bound algorithm is proposed to search for discriminative subgraphs efficiently. Extensive experiments on various neuroimaging applications (i.e., Alzheimers Disease, ADHD and HIV) have been performed to analyze the gain in performance by taking into account structural uncertainties in identifying discriminative subgraph features for graph classification.