Graph matching: filtering databases of graphs using machine learning techniques

Graphs are a powerful concept useful for various tasks in science and engineering. In applications such as pattern recognition and information retrieval, object similarity is an important issue. If graphs are used for object representation, then the problem of determining the similarity of objects turns into the problem of graph matching. Some of the most common graph matching paradigms include graph and subgraph isomorphism detection, maximum common subgraph extraction and error-tolerant graph matching. A number of solutions for all of these tasks have been proposed in the literature, but they all suffer from the high computational complexity inherent to graph matching. An additional problem arises in applications where an input graph is to be matched not only to another single graph, but to an entire database of graphs under a given matching paradigm. If the database is large, sequential comparison of the input graph with each graph from the database using conventional approaches becomes infeasible. In this thesis the comparison of input graphs with databases of graphs is studied. Different retrieval paradigms, namely graph isomorphism, subgraph isomorphism, and error-tolerant matching are considered. The approach pursued is based on comparing feature vectors which have been extracted from the graphs. The idea is to use features that can be quickly computed from a graph on the one hand, but are, on the other hand, effective in discriminating between the various graphs in the database. Given a potentially large number of such features, the most powerful ones for discriminating the graphs in the database are determined by means of decision tree induction algorithms as known from machine learning. Under the proposed procedure, given an input, i.e. a query graph, a (preferably small) subset of possible candidates will be retrieved from the database. Only the graphs contained in this subset are then subject to full-fledged, expensive graph matching. Significant savings in computation time can be expected as the time complexity of graph feature extraction and decision tree traversal is small compared to full graph matching. In this work database filters for three different matching paradigms (graph isomorphism, subgraph isomorphism and error-tolerant matching) have been developed. They have been successfully tested on synthetically generated graphs with various characteristics as well as on publicly available real-world graph databases.