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Graph structures have been proved important in high level-vision since they can be used to represent structural and relational arrangements of objects in a scene. One of the problems that arises in the analysis of structural abstractions of object is graph clustering. In this paper, we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering. We explore three different approaches to characterize the heat kernel trace as a function of time. These are the heat kernel trace moments, heat content invariants and symmetric polynomials with Laplacian eigenvalues as inputs. Experiments on the COIL 100 and Caltech 256 databases reveal that the proposed invariants are effective and outperform the tradition methods.
Date of Conference: 8-11 Dec. 2008