Quantitative Evaluation on Heat Kernel Permutation Invariants

  • Bai Xiao
  • Richard C. Wilson
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5342)


The Laplacian spectrum has proved useful for pattern analysis tasks, and one of its important properties is its close relationship with the heat equation. In this paper, we first show 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. We then use synthetic and real world datasets to give a quantitative evaluation of these feature invariants deduced from heat kernel analysis. We compare their performance with traditional spectrum invariants.


Zeta Function Heat Kernel Random Graph Symmetric Polynomial Edit Operation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bai Xiao
    • 1
  • Richard C. Wilson
    • 2
  • Edwin R. Hancock
    • 2
  1. 1.Department of Computer ScienceUniversity of BathBathUK
  2. 2.Department of Computer ScienceUniversity of YorkYorkUK

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