Many-to-many graph matching: a continuous relaxation approach

  • Authors:

  • Mikhail Zaslavskiy;Francis Bach;Jean-Philippe Vert

  • Affiliations:

  • Bioinformatics Group, Cellectis S.A. and Center for Computational Biology, Mines ParisTech, Fontainebleau, France and Institut Curie and INSERM, Paris, France and Center for Mathematical Morpholog ...;INRIA, Ecole Normale Supérieure, Paris, France;Center for Computational Biology, Mines ParisTech, Fontainebleau, France and Institut Curie and INSERM, Paris, France

  • Venue:
  • ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
  • Year:
  • 2010

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Abstract

Graphs provide an efficient tool for object representation in various machine learning applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs which optimally aligns their structure. In the classical formulation of graph matching, only one-to-one correspondences between vertices are considered. However, in many applications, graphs cannot be matched perfectly and it is more interesting to consider many-to-many correspondences where clusters of vertices in one graph are matched to clusters of vertices in the other graph. In this paper, we formulate the many-to-many graph matching problem as a discrete optimization problem and propose two approximate algorithms based on alternative continuous relaxations of the combinatorial problem. We compare new methods with other existing methods on several benchmark datasets.