Obtaining the consensus of multiple correspondences between graphs through online learning

In structural pattern recognition, it is usual to compare a pair of objects through the generation of a correspondence between the elements of each of their local parts. To do so, one of the most natural ways to represent these objects is through attributed graphs. Several existing graph extraction methods could be implemented and thus, numerous graphs, which may not only differ in their nodes and edge structure but also in their attribute domains, could be created from the same object. Afterwards, a matching process is implemented to generate the correspondence between two attributed graphs, and depending on the selected graph matching method, a unique correspondence is generated from a given pair of attributed graphs. The combination of these factors leads to the possibility of a large quantity of correspondences between the two original objects. This paper presents a method that tackles this problem by considering multiple correspondences to conform a single one called a consensus correspondence, eliminating both the incongruences introduced by the graph extraction and the graph matching processes. Additionally, through the application of an online learning algorithm, it is possible to deduce some weights that influence on the generation of the consensus correspondence. This means that the algorithm automatically learns the quality of both the attribute domain and the correspondence for every initial correspondence proposal to be considered in the consensus, and defines a set of weights based on this quality. It is shown that the method automatically tends to assign larger values to high quality initial proposals, and therefore is capable to deduce better consensus correspondences.