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Similarity measurement is crucial for classification. Based on the manifold assumption, many graph-based algorithms were developed. Almost all methods follow the k-rule or ε-rule to construct a graph, and then focus on the algorithms based on the graph. However, the graph may not represent the local structure well, and it does not fully utilize the label information yet. The local structure can be presented by the local density and the distance between the samples and their neighbors. And the graph constructed by the guidance of label information will be better approximate of the relationship of the input data. In this paper, we propose an adaptive semi-supervised graph constructing method. The similarity is learned when constructing the graph. The advantages of the similarity learned by our method include: (1) The similarity is measured along the manifold by constructing a graph; (2) nearby points and points in the same cluster share high similarity; (3) samples from the same class have higher similarity than samples from different classes. Experimental results show that using the proposed similarity for classification task could get better recognition accuracy. [ABSTRACT FROM AUTHOR]

Function-Described Graphs (FDGs) have been introduced by the authors as a representation of an ensemble of Attributed Graphs (AGs) for structural pattern recognition alternative to first-order random graphs. Both optimal and approximate algorithms for error-tolerant graph matching, which use a distance measure between AGs and FDGs, have been reported elsewhere. In this paper, both the supervised and the unsupervised synthesis of FDGs from a set of graphs is addressed. First, two procedures are described to synthesize an FDG from a set of commonly labeled AGs or FDGs, respectively. Then, the unsupervised synthesis of FDGs is studied in the context of clustering a set of AGs and obtaining an FDG model for each cluster. Two algorithms based on incremental and hierarchical clustering, respectively, are proposed, which are parameterized by a graph matching method. Some experimental results both on synthetic data and a real 3D-object recognition application show that the proposed algorithms are effective for clustering a set of AGs and synthesizing the FDGs that describe the classes. Moreover, the synthesized FDGs are shown to be useful for pattern recognition thanks to the distance measure and matching algorithm previously reported. [ABSTRACT FROM AUTHOR]