On Median Graphs: Properties, Algorithms, and Applications

ÐIn object prototype learning and similar tasks, median computation is an important technique for capturing the essential information of a given set of patterns. In this paper, we extend the median concept to the domain of graphs. In terms of graph distance, we introduce the novel concepts of set median and generalized median of a set of graphs. We study properties of both types of median graphs. For the more complex task of computing generalized median graphs, a genetic search algorithm is developed. Experiments conducted on randomly generated graphs demonstrate the advantage of generalized median graphs compared to set median graphs and the ability of our genetic algorithm to find approximate generalized median graphs in reasonable time. Application examples with both synthetic and nonsynthetic data are shown to illustrate the practical usefulness of the concept of median graphs. Index TermsÐMedian graph, graph distance, graph matching, genetic algorithm,