메뉴 건너뛰기




Volumn 37, Issue 12, 2015, Pages 2505-2517

Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians

Author keywords

diffusion distances; dimensionality reduction; Joint diagonalization; Laplace Beltrami operator; manifold alignment; manifold learning; multimodal clustering; multimodal data

Indexed keywords

CLUSTERING ALGORITHMS; DIFFUSION; GEOMETRY; LAPLACE TRANSFORMS;

EID: 84939541806     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2015.2408348     Document Type: Article
Times cited : (66)

References (52)
  • 2
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Comput., vol. 15, pp. 1373-1396, 2002.
    • (2002) Neural Comput. , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 4
    • 19644394100 scopus 로고    scopus 로고
    • Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
    • R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, and S. W. Zucker, "Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps," PNAS, vol. 102, no. 21, pp. 7426-7431, 2005.
    • (2005) PNAS , vol.102 , Issue.21 , pp. 7426-7431
    • Coifman, R.R.1    Lafon, S.2    Lee, A.B.3    Maggioni, M.4    Nadler, B.5    Warner, F.6    Zucker, S.W.7
  • 5
    • 78149301227 scopus 로고    scopus 로고
    • A min-max cut algorithm for graph partitioning and data clustering
    • C. Ding, X. He, H. Zha, M. Gu, and H. Simon, "A min-max cut algorithm for graph partitioning and data clustering," in Proc. Conf. Data Mining, 2001.
    • (2001) Proc. Conf. Data Mining
    • Ding, C.1    He, X.2    Zha, H.3    Gu, M.4    Simon, H.5
  • 7
    • 0034244751 scopus 로고    scopus 로고
    • Normalized cuts and image segmentation
    • Aug.
    • J. Shi and J. Malik, "Normalized cuts and image segmentation," IEEE Trans. Pattern Anal. Mach. Intel., vol. 22, no. 8, pp. 888-905, Aug. 2000.
    • (2000) IEEE Trans. Pattern Anal. Mach. Intel. , vol.22 , Issue.8 , pp. 888-905
    • Shi, J.1    Malik, J.2
  • 8
    • 33845430065 scopus 로고    scopus 로고
    • Laplace-Beltrami eigenfunctions towards an algorithm that "understands" geometry
    • B. Levy, "Laplace-Beltrami eigenfunctions towards an algorithm that "understands" geometry," in Proc. Shape Model. Int., 2006.
    • (2006) Proc. Shape Model. Int.
    • Levy, B.1
  • 9
    • 46749109554 scopus 로고    scopus 로고
    • Spectral mesh deformation
    • G. Rong, Y. Cao, and X. Guo, "Spectral mesh deformation," Vis. Comput., vol. 24, no. 7, pp. 787-796, 2008.
    • (2008) Vis. Comput. , vol.24 , Issue.7 , pp. 787-796
    • Rong, G.1    Cao, Y.2    Guo, X.3
  • 13
    • 77955654853 scopus 로고    scopus 로고
    • Large scale image annotation: Learning to rank with joint word-image embeddings
    • J. Weston, S. Bengio, and N. Usunier, "Large scale image annotation: Learning to rank with joint word-image embeddings," Mach. Learn., vol. 81, no. 1, pp. 21-35, 2010.
    • (2010) Mach. Learn , vol.81 , Issue.1 , pp. 21-35
    • Weston, J.1    Bengio, S.2    Usunier, N.3
  • 15
    • 79952712776 scopus 로고    scopus 로고
    • Learning multi-modal similarity
    • B. McFee and G. R. G. Lanckriet, "Learning multi-modal similarity," J. Mach. Learn. Res., vol. 12, pp. 491-523, 2011.
    • (2011) J. Mach. Learn. Res. , vol.12 , pp. 491-523
    • McFee, B.1    Lanckriet, G.R.G.2
  • 19
    • 0040350289 scopus 로고
    • Numerical methods for simultaneous diagonalization
    • A. Bunse-Gerstner, R. Byers, and V. Mehrmann, "Numerical methods for simultaneous diagonalization," SIAM J. Matrix Anal. Appl., vol. 14, no. 4, pp. 927-949, 1993.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , Issue.4 , pp. 927-949
    • Bunse-Gerstner, A.1    Byers, R.2    Mehrmann, V.3
  • 20
    • 0027812550 scopus 로고
    • Blind beamforming for non-Gaussian signals
    • J.-F. Cardoso and A. Souloumiac, "Blind beamforming for non-Gaussian signals," Radar Signal Process., vol. 140, no. 6, pp. 362-370, 1993.
    • (1993) Radar Signal Process , vol.140 , Issue.6 , pp. 362-370
    • Cardoso, J.-F.1    Souloumiac, A.2
  • 21
    • 0030544243 scopus 로고    scopus 로고
    • Jacobi angles for simultaneous diagonalization
    • J. F. Cardoso and A. Souloumiac, "Jacobi angles for simultaneous diagonalization," SIAM J. Matrix Anal. Appl, vol. 17, pp. 161-164, 1996.
    • (1996) SIAM J. Matrix Anal. Appl , vol.17 , pp. 161-164
    • Cardoso, J.F.1    Souloumiac, A.2
  • 22
    • 0036648367 scopus 로고    scopus 로고
    • Non-orthogonal joint diagonalization in the leastsquares sense with application in blind source separation
    • A. Yeredor, "Non-orthogonal joint diagonalization in the leastsquares sense with application in blind source separation," Trans. Signal Proc., vol. 50, no. 7, pp. 1545-1553, 2002.
    • (2002) Trans. Signal Proc. , vol.50 , Issue.7 , pp. 1545-1553
    • Yeredor, A.1
  • 26
    • 51449094566 scopus 로고    scopus 로고
    • Unsupervised anchor shot detection using multi-modal spectral clustering
    • C. Ma and C.-H. Lee, "Unsupervised anchor shot detection using multi-modal spectral clustering," in Proc. ICASSP, 2008.
    • (2008) Proc. ICASSP
    • Ma, C.1    Lee, C.-H.2
  • 31
    • 56449084264 scopus 로고    scopus 로고
    • Manifold alignment using procrustes analysis
    • ser. ICML '08. New York, NY, USA: ACM
    • C. Wang and S. Mahadevan, "Manifold alignment using procrustes analysis," in Proc. 25th Int. Conf. Mach. Learning, ser. ICML '08. New York, NY, USA: ACM, 2008, pp. 1120-1127.
    • (2008) Proc. 25th Int. Conf. Mach. Learning , pp. 1120-1127
    • Wang, C.1    Mahadevan, S.2
  • 32
    • 34548583274 scopus 로고    scopus 로고
    • A tutorial on spectral clustering
    • Dec.
    • U. von Luxburg, "A tutorial on spectral clustering," Statistics Comput., vol. 17, no. 4, pp. 395-416, Dec. 2007.
    • (2007) Statistics Comput. , vol.17 , Issue.4 , pp. 395-416
    • Von Luxburg, U.1
  • 33
    • 57349159581 scopus 로고    scopus 로고
    • Convergence of the cotangent formula: An overview
    • ser. Oberwolfach Seminars, A. I. Bobenko, J. M. Sullivan, P. Schröder, and G. M. Ziegler, Eds. Birkhäuser Basel
    • M. Wardetzky, "Convergence of the cotangent formula: An overview," in Discrete Differential Geometry, ser. Oberwolfach Seminars, A. I. Bobenko, J. M. Sullivan, P. Schröder, and G. M. Ziegler, Eds. Birkhäuser Basel, 2008, vol. 38, pp. 275-286.
    • (2008) Discrete Differential Geometry , vol.38 , pp. 275-286
    • Wardetzky, M.1
  • 34
    • 84868361941 scopus 로고
    • Über ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen
    • C. Jacobi, " Über ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen," J. für reine und Angew. Math., vol. 30, pp. 51-95, 1846.
    • (1846) J. Für Reine und Angew. Math , vol.30 , pp. 51-95
    • Jacobi, C.1
  • 36
    • 0003835709 scopus 로고    scopus 로고
    • Geometric optimization methods for blind source separation of signals
    • K. Rahbar and J. P. Reilly, "Geometric optimization methods for blind source separation of signals," in Proc. ICA, 2000.
    • (2000) Proc. ICA
    • Rahbar, K.1    Reilly, J.P.2
  • 37
    • 84879905842 scopus 로고    scopus 로고
    • A feasible method for optimization with orthogonality constraints
    • Z. Wen and W. Yin, "A feasible method for optimization with orthogonality constraints," Math. Prog., vol. 142, no. 1-2, pp. 397-434, 2013.
    • (2013) Math. Prog. , vol.142 , Issue.1-2 , pp. 397-434
    • Wen, Z.1    Yin, W.2
  • 41
    • 84882852323 scopus 로고    scopus 로고
    • Matrix commutators: Their asymptotic metric properties and relation to approximate joint diagonalization
    • K. Glashoff and M. M. Bronstein, "Matrix commutators: Their asymptotic metric properties and relation to approximate joint diagonalization," Linear Algebra Appl., vol. 439, no. 8, pp. 2503-2513, 2013.
    • (2013) Linear Algebra Appl. , vol.439 , Issue.8 , pp. 2503-2513
    • Glashoff, K.1    Bronstein, M.M.2
  • 43
    • 0000988974 scopus 로고
    • A generalized solution of the orthogonal procrustes problem
    • P. Schönemann, "A generalized solution of the orthogonal procrustes problem," Psychometrika, vol. 31, no. 1, pp. 1-10, 1966.
    • (1966) Psychometrika , vol.31 , Issue.1 , pp. 1-10
    • Schönemann, P.1
  • 44
    • 0022064511 scopus 로고
    • A best possible heuristic for the k-center problem
    • D. S. Hochbaum and D. B. Shmoys, "A best possible heuristic for the k-center problem," Math. Oper. Res., pp. 180-184, 1985.
    • (1985) Math. Oper. Res. , pp. 180-184
    • Hochbaum, D.S.1    Shmoys, D.B.2
  • 45
    • 74049158146 scopus 로고    scopus 로고
    • Nus-wide: A real-world web image database from National University of Singapore
    • T.-S. Chua, J. Tang, R. Hong, H. Li, Z. Luo, and Y.-T. Zheng, "Nus-wide: A real-world web image database from National University of Singapore," in Proc. CIVR, 2009.
    • (2009) Proc. CIVR
    • Chua, T.-S.1    Tang, J.2    Hong, R.3    Li, H.4    Luo, Z.5    Zheng, Y.-T.6
  • 46
    • 22444454855 scopus 로고    scopus 로고
    • Cascading classifiers
    • E. Alpaydin and C. Kaynak, "Cascading classifiers," Kybernetika, vol. 34, no. 4, pp. 369-374, 1998.
    • (1998) Kybernetika , vol.34 , Issue.4 , pp. 369-374
    • Alpaydin, E.1    Kaynak, C.2
  • 47
    • 84886433522 scopus 로고    scopus 로고
    • Multi-view clustering via joint nonnegative matrix factorization
    • J. Liu, C. Wang, J. Gao, and J. Han, "Multi-view clustering via joint nonnegative matrix factorization," in Proc. SDM, 2013.
    • (2013) Proc. SDM
    • Liu, J.1    Wang, C.2    Gao, J.3    Han, J.4
  • 48
    • 80052204125 scopus 로고    scopus 로고
    • Learning from multiple partially observed views-an application to multilingual text categorization
    • M. R. Amini, N. Usunier, and C. Goutte, "Learning from multiple partially observed views-an application to multilingual text categorization," in Proc. Neural Inf. Process. Syst., 2009.
    • (2009) Proc. Neural Inf. Process. Syst.
    • Amini, M.R.1    Usunier, N.2    Goutte, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.