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