The problem of graph classification has attracted great interest in the last decade. Current research on graph classification assumes the existence of large amounts of labeled training graphs. However, in many applications, the labels of graph data are very expensive or difficult to obtain, while there are often copious amounts of unlabeled graph data available. In this paper, we study the problem of semi-supervised feature selection for graph classification and propose a novel solution, called gSSC, to efficiently search for optimal subgraph features with labeled and unlabeled graphs. Different from existing feature selection methods in vector spaces which assume the feature set is given, we perform semi-supervised feature selection for graph data in a progressive way together with the subgraph feature mining process. We derive a feature evaluation criterion, named gSemi, to estimate the usefulness of subgraph features based upon both labeled and unlabeled graphs. Then we propose a branch-and-bound algorithm to efficiently search for optimal subgraph features by judiciously pruning the subgraph search space. Empirical studies on several real-world tasks demonstrate that our semi-supervised feature selection approach can effectively boost graph classification performances with semi-supervised feature selection and is very efficient by pruning the subgraph search space using both labeled and unlabeled graphs.
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