Bunke H., Günter S., Jiang X. (2001) Towards Bridging the Gap between Statistical and Structural Pattern Recognition: Two New Concepts in Graph Matching. In: Singh S., Murshed N., Kropatsch W. (eds) Advances in Pattern Recognition — ICAPR 2001. ICAPR 2001. Lecture Notes in Computer Science, vol 2013. Springer, Berlin, Heidelberg
Two novel concepts in structural pattern recognition are discussed in this paper. The first, median of a set of graphs, can be used to characterize a set of graphs by just a single prototype. Such a characterization is needed in various tasks, for example, in clustering. The second novel concept is weighted mean of a pair of graphs. It can be used to synthesize a graph that has a specified degree of similarity, or distance, to each of a pair of given graphs. Such an operation is needed in many machine learning tasks. It is argued that with these new concepts various well-established techniques from statistical pattern recognition become applicable in the structural domain, particularly to graph representations. Concrete examples include k-means clustering, vector quantization, and Kohonen maps.
Graph matching error-tolerant matching edit distance median graph weighted mean