Many-to-Many Graph Matching: A Continuous Relaxation Approach

  • Mikhail Zaslavskiy
  • Francis Bach
  • Jean-Philippe Vert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6323)


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.


Chinese Character Graph Match Discrete Optimization Problem Continuous Relaxation Vertex Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mikhail Zaslavskiy
    • 1
    • 2
    • 3
    • 5
  • Francis Bach
    • 4
  • Jean-Philippe Vert
    • 1
    • 2
    • 3
  1. 1.Center for Computational Biology, Mines ParisTech, FontainebleauFrance
  2. 2.Institut Curie 
  3. 3.INSERM, U900ParisFrance
  4. 4.INRIA-WILLOW project, Ecole Normale SupérieureParisFrance
  5. 5.Center for Mathematical Morphology, Mines ParisTech, FontainebleauFrance

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