A novel way to formalize stable graph cores by using matching-graphs. (November 2022) - Fuchs, Mathias; Riesen, Kaspar
Highlights: We propose a new data structure called matching-graph, that incorporates the similarity core of two graphs. We present both, a distance based classifier and a graph embedding kernel based on the novel matching-graphs. We confirm a significant improvement of classification algorithms that directly, or indirectly, use matching-graphs. Graphical abstract: Abstract: The increasing amount of data available and the rate at which it is collected leads to rapid developments of systems for intelligent information processing and pattern recognition. Often the underlying data is inherently complex, making it difficult to represent it by linear, vectorial data structures. This is where graphs offer a versatile alternative for formal data representation. Actually, quite an amount of graph-based methods for pattern recognition has been proposed. A considerable part of these methods rely on graph matching. In the present paper, we propose a novel encoding of specific graph matching information. The basic idea is to formalize the stable cores of individual classes of graphs – discovered during intra-class matchings – by means of so called matching-graphs. We evaluate the benefit of these matching-graphs by researching two classification approaches that rely on this novel data structure. The first approach is a distance based classifier focusing on the matching-graphs during dissimilarity computation. For the second approach, we propose to use sets of matching-graphs to embed input graphs into a vector space. The basic idea is to produce hundreds of matching-graphs first, and then represent each graph g as a vector that shows the occurrence of, or the distance to, each matching-graph. In a thorough experimental evaluation on seven real world data sets we empirically confirm that our novel approaches are able to improve the classification accuracy of systems that rely on comparable information as well as state-of-the-art methods.