메뉴 건너뛰기




Volumn 74, Issue 9, 2011, Pages 1391-1401

Spectral clustering with more than K eigenvectors

Author keywords

Spectral clustering; Spectral gap

Indexed keywords

APPROXIMATE SOLUTION; CUTTING PROBLEMS; DIMENSIONAL SUBSPACE; EIGEN-VALUE; EIGENVALUES; EIGENVECTORS; GAP SIZE; LINEAR SPAN; NORMALIZED LAPLACIAN; NP COMPLETE; OPTIMAL PARTITIONS; PROBABILISTIC ALGORITHM; REAL-WORLD GRAPHS; SPECTRAL CLUSTERING; SPECTRAL GAP; SPECTRAL TECHNIQUES; STATE OF THE ART;

EID: 79953051126     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.12.008     Document Type: Article
Times cited : (34)

References (40)
  • 2
    • 33749317042 scopus 로고    scopus 로고
    • Learning spectral clustering, with application to speech separation
    • Bach F.R., Jordan M.I. Learning spectral clustering, with application to speech separation. Journal of Machine Learning Research 2006, 7:1963-2001.
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 1963-2001
    • Bach, F.R.1    Jordan, M.I.2
  • 3
    • 33750729556 scopus 로고    scopus 로고
    • Manifold regularization: a geometric framework for learning from labeled and unlabeled examples
    • Belkin M., Niyogi P., Sindhwani V. Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research 2006, 7:2399-2434.
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 2399-2434
    • Belkin, M.1    Niyogi, P.2    Sindhwani, V.3
  • 4
    • 79953059041 scopus 로고    scopus 로고
    • Learning segmentation by random walks, in: NIPS
    • M. Meilâ, J. Shi, Learning segmentation by random walks, in: NIPS, 2000, pp. 873-879.
    • (2000) , pp. 873-879
    • Meilâ, M.1    Shi, J.2
  • 5
    • 79953048288 scopus 로고    scopus 로고
    • On spectral clustering: analysis and an algorithm, in: NIPS
    • A.Y. Ng, M.I. Jordan, Y. Weiss, On spectral clustering: analysis and an algorithm, in: NIPS, 2001, pp. 849-856.
    • (2001) , pp. 849-856
    • Ng, A.Y.1    Jordan, M.I.2    Weiss, Y.3
  • 6
    • 14344257496 scopus 로고    scopus 로고
    • k-Means clustering via principal component analysis, in: ICML
    • C.H.Q. Ding, X. He, k-Means clustering via principal component analysis, in: ICML, 2004.
    • (2004)
    • Ding, C.H.Q.1    He, X.2
  • 7
    • 79953053470 scopus 로고    scopus 로고
    • Partially labeled classification with Markov random walks, in: NIPS
    • M. Szummer, T. Jaakkola, Partially labeled classification with Markov random walks, in: NIPS, 2001, pp. 945-952.
    • (2001) , pp. 945-952
    • Szummer, M.1    Jaakkola, T.2
  • 8
    • 1942484960 scopus 로고    scopus 로고
    • Transductive learning via spectral graph partitioning, in: ICML
    • T. Joachims, Transductive learning via spectral graph partitioning, in: ICML, 2003, pp. 290-297.
    • (2003) , pp. 290-297
    • Joachims, T.1
  • 9
    • 79953046353 scopus 로고    scopus 로고
    • Diffusion maps-a probabilistic interpretation for spectral embedding and clustering algorithms
    • B. Nadler, S. Lafon, R. Coifman, I.G. Kevrekidis. Diffusion maps-a probabilistic interpretation for spectral embedding and clustering algorithms, 2007.
    • (2007)
    • Nadler, B.1    Lafon, S.2    Coifman, R.3    Kevrekidis, I.G.4
  • 10
    • 79953043045 scopus 로고
    • A projection technique for partitioning the nodes of a graph
    • F. Rendl, H. Wolkowicz, A projection technique for partitioning the nodes of a graph, 1995.
    • (1995)
    • Rendl, F.1    Wolkowicz, H.2
  • 11
    • 84887005409 scopus 로고
    • On the performance of spectral graph partitioning methods, in: SODA
    • S. Guattery, G.L. Miller, On the performance of spectral graph partitioning methods, in: SODA, 1995, pp. 233-242.
    • (1995) , pp. 233-242
    • Guattery, S.1    Miller, G.L.2
  • 14
    • 0000827674 scopus 로고
    • A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
    • Fiedler M. A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czechoslovak Mathematical Journal 1975, 25.
    • (1975) Czechoslovak Mathematical Journal , vol.25
    • Fiedler, M.1
  • 15
    • 0029354779 scopus 로고
    • Recent directions in netlist partitioning: a survey
    • Alpert C.J., Kahng A.B. Recent directions in netlist partitioning: a survey. Integration: The VLSI Journal 1995, 19:1-81.
    • (1995) Integration: The VLSI Journal , vol.19 , pp. 1-81
    • Alpert, C.J.1    Kahng, A.B.2
  • 16
    • 79959469955 scopus 로고    scopus 로고
    • Fixing two weaknesses of the spectral method, in: NIPS
    • K. Lang, Fixing two weaknesses of the spectral method, in: NIPS, 2005.
    • (2005)
    • Lang, K.1
  • 17
    • 58449123872 scopus 로고    scopus 로고
    • An algorithm for improving graph partitions, in: SODA
    • R. Andersen, K.J. Lang, An algorithm for improving graph partitions, in: SODA, 2008, pp. 651-660.
    • (2008) , pp. 651-660
    • Andersen, R.1    Lang, K.J.2
  • 18
    • 79953058082 scopus 로고
    • Circuit placement by eigenvector decomposition, in: ICCAD
    • J.A. Frankle, R.M. Karp, Circuit placement by eigenvector decomposition, in: ICCAD, 1986.
    • (1986)
    • Frankle, J.A.1    Karp, R.M.2
  • 19
    • 79953032805 scopus 로고
    • Circuit placement methods using multiple eigenvectors and linear probe techniques. Ph.D. Thesis, EECS Department, University of California, Berkeley
    • J.A. Frankle, Circuit placement methods using multiple eigenvectors and linear probe techniques. Ph.D. Thesis, EECS Department, University of California, Berkeley, 1987.
    • (1987)
    • Frankle, J.A.1
  • 20
    • 35448945640 scopus 로고    scopus 로고
    • Spectral clustering with eigenvector selection
    • Xiang T., Gong S. Spectral clustering with eigenvector selection. Pattern Recognition 2008, 41(3):1012-1029.
    • (2008) Pattern Recognition , vol.41 , Issue.3 , pp. 1012-1029
    • Xiang, T.1    Gong, S.2
  • 21
    • 77952586130 scopus 로고    scopus 로고
    • Spectral clustering with eigenvector selection based on entropy ranking
    • Zhao F., Jiao L., Liu H., Gao X., Gong M. Spectral clustering with eigenvector selection based on entropy ranking. Neurocomputing 2010, 73(10-12):1704-1717.
    • (2010) Neurocomputing , vol.73 , Issue.10-12 , pp. 1704-1717
    • Zhao, F.1    Jiao, L.2    Liu, H.3    Gao, X.4    Gong, M.5
  • 22
    • 84887001092 scopus 로고    scopus 로고
    • A randomized algorithm for spectral clustering, in: ESANN
    • N. Rebagliati, A. Verri, A randomized algorithm for spectral clustering, in: ESANN, 2010, pp. 381-386.
    • (2010) , pp. 381-386
    • Rebagliati, N.1    Verri, A.2
  • 23
    • 79953042679 scopus 로고    scopus 로고
    • Self-tuning spectral clustering, in: NIPS
    • L. Zelnik-Manor, P. Perona, Self-tuning spectral clustering, in: NIPS, 2004.
    • (2004)
    • Zelnik-Manor, L.1    Perona, P.2
  • 24
    • 79953057829 scopus 로고    scopus 로고
    • Spectral graph theory, in: CBMS Regional Conference Series in Mathematics, AMS, February
    • F.R.K. Chung, Spectral graph theory, in: CBMS Regional Conference Series in Mathematics, vol. 92, AMS, February 1997.
    • (1997) , vol.92
    • Chung, F.R.K.1
  • 25
    • 0027697605 scopus 로고
    • An optimal graph theoretic approach to data clustering: theory and its application to image segmentation
    • Wu Z., Leahy R. An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 1993, 15(11):1101-1113.
    • (1993) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.15 , Issue.11 , pp. 1101-1113
    • Wu, Z.1    Leahy, R.2
  • 26
    • 34548583274 scopus 로고    scopus 로고
    • A tutorial on spectral clustering
    • von Luxburg U. A tutorial on spectral clustering. Statistics and Computing 2007, 17(4):395-416.
    • (2007) Statistics and Computing , vol.17 , Issue.4 , pp. 395-416
    • von Luxburg, U.1
  • 27
    • 33749236636 scopus 로고    scopus 로고
    • The uniqueness of a good optimum for k-means, in: ICML
    • M. Meilâ, The uniqueness of a good optimum for k-means, in: ICML, 2006, pp. 625-632.
    • (2006) , pp. 625-632
    • Meilâ, M.1
  • 28
    • 0000282987 scopus 로고
    • Maximum properties and inequalities for the eigenvalues of completely continuous operators
    • Fan K. Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proceedings of the National Academy of Science 1951, 37(November):760-766.
    • (1951) Proceedings of the National Academy of Science , vol.37 , Issue.NOVEMBER , pp. 760-766
    • Fan, K.1
  • 29
    • 79953033556 scopus 로고    scopus 로고
    • Regularized spectral learning, Technical report, Proceedings of the Artificial Intelligence and Statistics Workshop (AISTATS 05)
    • M. Meila, S. Shortreed, L. Xu, Regularized spectral learning, Technical report, Proceedings of the Artificial Intelligence and Statistics Workshop (AISTATS 05), 2005.
    • (2005)
    • Meila, M.1    Shortreed, S.2    Xu, L.3
  • 30
    • 79953038428 scopus 로고    scopus 로고
    • From graph to manifold Laplacian: the convergence rate
    • A. Singer, From graph to manifold Laplacian: the convergence rate, 2006.
    • (2006)
    • Singer, A.1
  • 31
    • 12244256379 scopus 로고    scopus 로고
    • Kernel k-means: spectral clustering and normalized cuts, in: KDD
    • I.S. Dhillon, Y. Guan, B. Kulis, Kernel k-means: spectral clustering and normalized cuts, in: KDD, 2004, pp. 551-556.
    • (2004) , pp. 551-556
    • Dhillon, I.S.1    Guan, Y.2    Kulis, B.3
  • 32
    • 79953030879 scopus 로고    scopus 로고
    • Spectral techniques for clustering, Ph.D. Thesis
    • N. Rebagliati, Spectral techniques for clustering, Ph.D. Thesis, 2010.
    • (2010)
    • Rebagliati, N.1
  • 34
    • 33244482593 scopus 로고    scopus 로고
    • On the largest principal angle between random subspaces
    • Absil P.-A., Edelman A., Koev P. On the largest principal angle between random subspaces. Linear Algebra Application 2006, 414(1):288-294.
    • (2006) Linear Algebra Application , vol.414 , Issue.1 , pp. 288-294
    • Absil, P.-A.1    Edelman, A.2    Koev, P.3
  • 35
    • 33646424751 scopus 로고    scopus 로고
    • The efficient evaluation of the hypergeometric function of a matrix argument
    • Koev P., Edelman A. The efficient evaluation of the hypergeometric function of a matrix argument. Mathematics of Computation 2006, 75:833-846.
    • (2006) Mathematics of Computation , vol.75 , pp. 833-846
    • Koev, P.1    Edelman, A.2
  • 36
    • 9444274777 scopus 로고    scopus 로고
    • Comparing clusterings by the variation of information, in: COLT
    • M. Meilâ, Comparing clusterings by the variation of information, in: COLT, 2003, pp. 173-187.
    • (2003) , pp. 173-187
    • Meilâ, M.1
  • 38
    • 4544356055 scopus 로고    scopus 로고
    • A combined evolutionary search and multilevel approach to graph partitioning, Journal of Global Optimization
    • A.J. Soper, C. Walshaw, M. Cross, A combined evolutionary search and multilevel approach to graph partitioning, Journal of Global Optimization, 2004.
    • (2004)
    • Soper, A.J.1    Walshaw, C.2    Cross, M.3
  • 40
    • 79953038063 scopus 로고
    • New spectral methods for ratio cut partitioning and clustering
    • L.W. Hagen, A.B. Kahng, New spectral methods for ratio cut partitioning and clustering, 1992.
    • (1992)
    • Hagen, L.W.1    Kahng, A.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.