Quantitative evaluation on heat kernel permutation invariants

Bai Xiao, Richard C Wilson, Edwin R Hancock

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationStructural, Syntactic, and Statistical Pattern Recognition. Proceedings of the Joint IAPR International Workshop, SSPR & SPR 2008.
Place of PublicationBerlin / Heidelberg
PublisherSpringer
Pages217-226
Number of pages10
Volume5342/2008
ISBN (Print)0302-9743
DOIs
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag

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Keywords

  • Technical presentations
  • Pattern recognition
  • Surface plasmon resonance
  • Syntactics
  • Laplace transforms

Cite this

Xiao, B., Wilson, R. C., & Hancock, E. R. (2008). Quantitative evaluation on heat kernel permutation invariants. In Structural, Syntactic, and Statistical Pattern Recognition. Proceedings of the Joint IAPR International Workshop, SSPR & SPR 2008. (Vol. 5342/2008, pp. 217-226). (Lecture Notes in Computer Science). Berlin / Heidelberg: Springer. https://doi.org/10.1007/978-3-540-89689-0_26