Adaptively Transforming Graph Matching

Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching problem, they have high complexity in space or time. In this paper, we introduce an adaptively transforming graph matching (ATGM) method from the perspective of functional representation. More precisely, under a transformation formulation, we aim to match two graphs by minimizing the discrepancy between the original graph and the transformed graph. With a linear representation map of the transformation, the pairwise edge attributes of graphs are explicitly represented by unary node attributes, which enables us to reduce the space and time complexity significantly. Due to an efficient Frank-Wolfe method-based optimization strategy, we can handle graphs with hundreds and thousands of nodes within an acceptable amount of time. Meanwhile, because transformation map can preserve graph structures, a domain adaptation-based strategy is proposed to remove the outliers. The experimental results demonstrate that our proposed method outperforms the state-of-the-art graph matching algorithms

Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio

A Descriptive Tolerance Nearness Measure for Performing Graph Comparison

Accepted versionThis article proposes the tolerance nearness measure (TNM) as a computationally reduced alternative to the graph edit distance (GED) for performing graph comparisons. The TNM is defined within the context of near set theory, where the central idea is that determining similarity between sets of disjoint objects is at once intuitive and practically applicable. The TNM between two graphs is produced using the Bron-Kerbosh maximal clique enumeration algorithm. The result is that the TNM approach is less computationally complex than the bipartite-based GED algorithm. The contribution of this paper is the application of TNM to the problem of quantifying the similarity of disjoint graphs and that the maximal clique enumeration-based TNM produces comparable results to the GED when applied to the problem of content-based image processing, which becomes important as the number of nodes in a graph increases."This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 418413."https://content.iospress.com/articles/fundamenta-informaticae/fi174