Analysis of Commute Time Embedding Based on Spectral Graph

스펙트럴 그래프 기반 Commute Time 임베딩 특성 분석

  • Received : 2013.09.04
  • Accepted : 2013.11.29
  • Published : 2014.01.31


In this paper an embedding algorithm based on commute time is implemented by organizing patches according to the graph-based metric, and its performance is analyzed by comparing with the results of principal component analysis embedding. It is usual that the dimensionality reduction be done within some acceptable approximation error. However this paper shows the proposed manifold embedding method generates the intrinsic geometry corresponding to the signal despite severe approximation error, so that it can be applied to the areas such as pattern classification or machine learning.


Commute time;Embedding;Manifold learning;Spectral graph;Graph Laplacian


  1. S.T. Roweis and L.K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, Vol. 290, pp. 2323-2326, 2000.
  2. H. Hahn, "Proposing a Connection Method for Measuring Differentiation of Tangent Vectors at Shape Manifold," Journal of Korea Multimedia Society, Vol. 16, No. 2, pp. 160-168, 2013.
  3. J.B. Tenenbaum, V. deSilva, and J.C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, Vol. 290, pp. 2319-2323, 2000.
  4. T.F. Cox and M.A.A. Cox, Multidimensional Scaling, Chapman and Hall/CRC, 2001, USA.
  5. D.L. Donoho and C. Grimes, "Hessian Eigenmaps: New Locally Linear Embedding Techniques for High Dimensional Data," Proc. the National Academy of Sciences, pp. 5591-5596, 2003.
  6. M. Belkin and P. Niyogi, "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering," Advances in Neural Information Processing Systems, Vol. 14, pp. 585-591, 2001.
  7. M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," Neural Computation, Vol. 15, No. 6, pp. 1373-1396, 2003.
  8. R.R. Coifman and S. Lafon, "Diffusion Maps," Applied and Computational Harmonic Analysis, Vol. 21, pp. 5-30, 2006.
  9. F. Chung, Spectral Graph Theory, American Mathematical Society, 1997, USA.
  10. H. Qiu and E.R. Hancock, "Clustering and Embedding using Commute Times," IEEE Trans. PAMI , Vol. 29, No. 11, pp. 1873-1890, 2007.
  11. K.S. Ni and T.Q. Nguyen, "A Model for Image Patch-Based Algorithms," ICIP2008, pp. 2588-2591, 2008.
  12. M. Zontak and M. Irani, "Internal Statistics of a Single Natural Image," CVPR2011, pp. 977-984, 2011.
  13. K.M. Taylor, The Geometry of Signal and Image Patch-Sets, Ph D Thesis of University of Colorado, 2011.

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