Geometric characterization and clustering of graphs using heat kernel embeddings

Image and Vision Computing

Volumn 28, Issue 6, 2010, Pages 1003-1021

  Xiao, Bai ^a   Hancock, Edwin R ^b   Wilson, Richard C ^b  

^a BEIHANG UNIVERSITY   (China)

^b UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Differential geometry; Graph clustering; Graph embedding; Graph spectra; Kernel methods

Indexed keywords

COMPUTER CRIME; GEODESY; GEOMETRY; INVARIANCE; LAPLACE TRANSFORMS; VECTOR SPACES;

DIFFERENTIAL GEOMETRY; GRAPH CLUSTERING; GRAPH EMBEDDINGS; GRAPH SPECTRA; KERNEL METHODS;

HEATING;

EID: 77649342083     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.imavis.2009.05.011     Document Type: Article

References (28)

1. Sachs H., Cvetkovic D.M., and Doob M. Spectra of Graphs (1980), Academic Press
2. Chung F.R.K. Spectral Graph Theory (1997), American Mathematical Society
3. A. Shokoufandeh, S. Dickinson, K. Siddiqi, S. Zucker, Indexing using a spectral encoding of topological structure, in: International Conference on Computer Vision and Pattern Recognition, 1999.
4. Luo B., Wilson R.C., and Hancock E.R. Spectral embedding of graphs. Pattern Recognition 36 (2003) 2213-2230
5. Wilson R.C., Luo B., and Hancock E.R. Pattern vectors from algebraic graph theory. IEEE Transactions on Pattern Analysis and Machine Intelligence 27 (2003) 2220-2237
6. Linial N., London E., and Rabinovich Y. The geometry of graphs and some of its algorithmic application. Combinatorica 15 (1995) 215-245
7. Tenenbaum J.B., Silva V.D., and Langford J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000) 586-591
8. Roweis S., and Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science 290 5500 (2000) 2323-2326
9. Belkin M., and Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15 (2000) 1373-1396
10. Atkins J.E., Bowman E.G., and Hendrickson B. A spectral algorithm for seriation and the consecutive ones problems. SIAM Journal on Computing 28 (1998) 297-310
11. J. Shi, J. Malik, Normalized cuts and image segmentation, in: International Conference on Computer Vision and Pattern Recognition, 1997.
12. Umeyama S. An eigendecomposition approach to weighted graph matching problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 10 5 (1988) 695-703
13. Luo B., and Hancock E.R. Structural graph matching using the em algorithm and singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 23 (2001) 1120-1136
14. Yau S.T., and Schoen R.M. Differential Geometry (1988), Science Publication
15. J. Lafferty, G. Lebanon, Diffusion kernels on statistical manifolds, CMUCS- 04-101, 2004.
16. Gilkey P.B. Invariant Theory, the Heat Equation, and the Atiyah-single Index Theorem (1984), Publish or Perish, Inc.
17. Grigor'yan A. Heat kernel on manifold, graphs and fractals. European Congress of Mathematics I (2001) 393-406
18. M.T. Barlow, Diffusions on fractals, Lectures on Probability Theory and Statistics, Lecture Notes Math., vol. 1690, 1998, pp. 1-121.
19. A.J. Smola, R. Kondor, Kernels and regularisation of graphs, 2004.
20. Bai Xiao, Edwin R. Hancock, Trace formula analysis of graphs, in: SSPR/SPR, 2006, pp. 306-313.
21. Verdiere C.d. Spectra of graphs. Math of France 4 (1998)
22. A. Grigor'yan, Heat kernels on manifolds, graphs and fractals, preprint, 2003.
23. Cox T., and Cox M. Multidimensional Scaling (1994), Chapman and Hall
24. Flusser J., and Suk T. Pattern recognition by affine moment invariants. Pattern Recognition 26 (1993) 167-174
25. Nene S.A., and Nayar S.K. HiroshiMurase, Columbia Object Image Library (coil 100) (1996), Columbia University
26. C.G. Harris, M.J. Stephens, A combined corner and edge detector, in: Fourth Alvey Vision Conference, 1994.
27. Rand W.M. Objective criteria for the evaluation of clustering. Journal of the American Statistical Association 66 (1971) 846-850
28. Lindman H., and Caelli T. Constant curvature Riemannian scaling. Journal of Mathematical Psychology 17 (1978) 89-109