Large sample statistics in the domain of graphs

Abstract

One challenge in bridging the gap between structural and statistical pattern recognition consists in studying combinatorial structures like graphs using probabilistic methods. This contribution presents the structural counterparts of the first and second fundamental theorem in probability, (1) the law of large numbers and (2) the central limit theorem. In addition, we derive characterizations and uniqueness conditions for the mean of graphs. As a special case, we investigate the weighted mean of two graphs. The proposed results establish a sound statistical foundation for unsupervised structural pattern recognition methods. © 2010 Springer-Verlag Berlin Heidelberg.