Structural Pattern Recognition: A Random Graph Approach
This paper presents the notion of random graphs and their associated probability distributions. It addresses both the structural and probabilistic aspects of structural pattern recognition. A structural pattern can be explicitly represented in the form of attributed graphs and an ensemble of such representations can be considered as outcomes of a mapping, called random graph mapping. To account for the variation of structural patterns in the ensemble, a lower order probability distribution is used to approximate the high order joint probability. To synthesize an ensemble of attributed graphs into a probability distribution (or a set of distributions) of a random graph, we introduce a distance measure together with a hierarchical clustering algorithm. The distance measure is defined as the minimum change of a specially defined Shannon’s entropy before and after the merging of the distributions. With this new formulation, both supervised and unsupervised classification of structural patterns can be achieved.
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