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http://dx.doi.org/10.5573/ieie.2015.52.2.162

Proposing the Methods for Accelerating Computational Time of Large-Scale Commute Time Embedding  

Hahn, Hee-Il (Department of Information and Communications Engineering, Hankuk University of Foreign Studies)
Publication Information
Journal of the Institute of Electronics and Information Engineers / v.52, no.2, 2015 , pp. 162-170 More about this Journal
Abstract
Commute time embedding involves computing the spectral decomposition of the graph Laplacian. It requires the computational burden proportional to $o(n^3)$, not suitable for large scale dataset. Many methods have been proposed to accelerate the computational time, which usually employ the Nystr${\ddot{o}}$m methods to approximate the spectral decomposition of the reduced graph Laplacian. They suffer from the lost of information by dint of sampling process. This paper proposes to reduce the errors by approximating the spectral decomposition of the graph Laplacian using that of the affinity matrix. However, this can not be applied as the data size increases, because it also requires spectral decomposition. Another method called approximate commute time embedding is implemented, which does not require spectral decomposition. The performance of the proposed algorithms is analyzed by computing the commute time on the patch graph.
Keywords
Manifold learning; Commute time embedding; Nystr${\ddot{o}}$m method; Approximate commute time embedding;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 D. Achlioptas, "Database-friendly random projections: Johnson-Lindenstrauss with binary coins,"Journal of Computer and System Sciences 66, pp. 671-687, 2003.   DOI   ScienceOn
2 M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Computation15(6), pp.1373-1396, 2003.   DOI   ScienceOn
3 A. Choromanska, T. Jebara, H. Kim, M. Mohan, and C. Monteleoni, "Fast Spectral clustering via the Nystrom method," ALT2013, LNAI 8139, pp. 367-381, 2013.
4 F. Chung, Spectral graph theory, American Mathematical Society, 1997.
5 P. Drineas and M.W. Mahoney, "On the Nystrom method for approximating a Gram matrix for improved kernel-based learning," Journal of Machine Learning Research 6, pp. 2153-2175, 2005.
6 H.I. Hahn, "Analysis of commute time embedding based on spectral graph," Journal of Korea Multimedia Society, Vol. 17, No. 1, pp. 34-42, 2013.   과학기술학회마을   DOI   ScienceOn
7 H.I. Hahn, "A Study on classification of waveforms using manifold embedding based on commute time," Journal of the Institute of Electronics and Information Engineers, Vol. 51, No. 2, pp. 148-155, 2014.   DOI
8 H. Qiu and E.R. Hancock, "Clustering and embedding using commute times," IEEE Trans. PAMI, Vol. 29, No. 11, Nov., 2007.
9 S. T. Roweis and L.K. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science Vol.290, 2000.
10 D. A. Spieman and N. Srivastava, "Graph sparsification by effective resistances," In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, STOC'04, pp. 81-90, 2004.
11 D.A. Spieman and S. Teng, "Nearly linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear system," arXiv:cs/0607105v5 [cs.NA], 2012.
12 J.B. Tenenbaum, V. deSilva, and J.C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science, Vol. 290, pp.2319-2323, 2000.   DOI   ScienceOn
13 C.K.I. Williams and M. Seeger, "Using the Nystrom method to speed up kernel machines," In Annual Advances in Neural Information Processing Systems 13: Proceeding of the 2000 Conference, pp. 682-688, 2001.