In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the graphs act as a constraint on the alignment. In this paper, we formalize the above problem as the weighted alignment between two directed acyclic graphs. We prove that this problem is NP-complete, show several upper bounds for approximating the solution, and finally introduce polynomial time algorithms for sub-classes of directed acyclic graphs.
In @cite_6 , graph matching is applied to conceptual system matching for translation. The work is very similar to ontology alignment, however, the authors formalize their problem in terms of any conceptual system rather than restricting the work specifically to an ontological formalization of a domain. They formalize conceptual systems as graphs, and introduce algorithms for matching both unweighted and weighted versions of these graphs.
@cite_6
103919619 2606149788 2964213755 2097746044
Ontology matching is an important task to achieve interoperation between semantic web applications using different ontologies. Structural similarity plays a central role in ontology matching. However, the existing approaches rely heavily on lexical similarity, and they mix up lexical similarity with structural similarity. In this paper, we present a graph matching approach for ontologies, called GMO. It uses bipartite graphs to represent ontologies, and measures the structural similarity between graphs by a new measurement. Furthermore, GMO can take a set of matched pairs, which are typically previously found by other approaches, as external input in matching process. Our implementation and experimental results are given to demonstrate the effectiveness of the graph matching approach. Despite significant progress of deep learning in recent years, state-of-the-art semantic matching methods still rely on legacy features such as SIFT or HoG. We argue that the strong invariance properties that are key to the success of recent deep architectures on the classification task make them unfit for dense correspondence tasks, unless a large amount of supervision is used. In this work, we propose a deep network, termed AnchorNet, that produces image representations that are well-suited for semantic matching. It relies on a set of filters whose response is geometrically consistent across different object instances, even in the presence of strong intra-class, scale, or viewpoint variations. Trained only with weak image-level labels, the final representation successfully captures information about the object structure and improves results of state-of-the-art semantic matching methods such as the deformable spatial pyramid or the proposal flow methods. We show positive results on the cross-instance matching task where different instances of the same object category are matched as well as on a new cross-category semantic matching task aligning pairs of instances each from a different object class. Despite significant progress of deep learning in recent years, state-of-the-art semantic matching methods still rely on legacy features such as SIFT or HoG. We argue that the strong invariance properties that are key to the success of recent deep architectures on the classification task make them unfit for dense correspondence tasks, unless a large amount of supervision is used. In this work, we propose a deep network, termed AnchorNet, that produces image representations that are well-suited for semantic matching. It relies on a set of filters whose response is geometrically consistent across different object instances, even in the presence of strong intra-class, scale, or viewpoint variations. Trained only with weak image-level labels, the final representation successfully captures information about the object structure and improves results of state-of-the-art semantic matching methods such as the Deformable Spatial Pyramid or the Proposal Flow methods. We show positive results on the cross-instance matching task where different instances of the same object category are matched as well as on a new cross-category semantic matching task aligning pairs of instances each from a different object class. In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.