Optimal encoding of graph homomorphism energy using fuzzy information aggregation operators

Abstract The attributed relational graph matching (ARG) strategy is a well-known approach to object/pattern recognition. In the past for the parallel solution of ARG matching problem, an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial-and-error for the parameters in the function. In this paper, the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes. To learn the parameters in the fuzzy information aggregation operators, the “learning from samples” strategy is used. The learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure. The learning procedure implicitly evaluates ambiguity, robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes. The learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic ARG matching problem can be optimally encoded in the energy function for the model. Experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures.