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Volumn 51, Issue 3, 2009, Pages 545-566

Spectral properties of the alignment matrices in manifold learning

Author keywords

Eigenvalue problem; Manifold learning; Nonlinear dimension reduction; Null space; Perturbation analysis

Indexed keywords

EIGENVALUE PROBLEM; MANIFOLD LEARNING; NONLINEAR DIMENSION REDUCTION; NULL SPACE; PERTURBATION ANALYSIS;

EID: 68649111457     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/060676829     Document Type: Article
Times cited : (31)

References (18)
  • 1
    • 84880203756 scopus 로고    scopus 로고
    • M. BELKIN AND P. NIYOGI, Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering, Adv. Neural Inform. Process. Systems 14, MIT Press, Cambridge, MA, 2002.
    • M. BELKIN AND P. NIYOGI, Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering, Adv. Neural Inform. Process. Systems 14, MIT Press, Cambridge, MA, 2002.
  • 2
    • 84898990205 scopus 로고    scopus 로고
    • M. BRAND, Charting a Manifold, Adv. Neural Inform. Process. Systems 15, MIT Press, Cambridge, MA, 2003.
    • M. BRAND, Charting a Manifold, Adv. Neural Inform. Process. Systems 15, MIT Press, Cambridge, MA, 2003.
  • 5
    • 0037948870 scopus 로고    scopus 로고
    • Hessian eigenmaps: New tools for nonlinear dimensionality reduction
    • D. DONOHO AND C. GRIMES, Hessian eigenmaps: New tools for nonlinear dimensionality reduction, Proc. Natl. Acad. Sci., 100 (2003), pp. 5591-5596.
    • (2003) Proc. Natl. Acad. Sci , vol.100 , pp. 5591-5596
    • DONOHO, D.1    GRIMES, C.2
  • 6
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed, Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • GOLUB, G.H.1    VAN LOAN, C.F.2
  • 7
    • 0026821495 scopus 로고
    • Conditions for unique graph realizations
    • B. HENDRICKSON, Conditions for unique graph realizations, SIAM J. Comput., 21 (1992), pp. 65-84.
    • (1992) SIAM J. Comput , vol.21 , pp. 65-84
    • HENDRICKSON, B.1
  • 8
    • 78649400333 scopus 로고    scopus 로고
    • E. LEVINA AND P. BICKEL, Maximum Likelihood Estimation of Intrinsic Dimension, Adv. Neural Inform. Process. Systems 17, MIT Press, Cambridge, MA, 2005.
    • E. LEVINA AND P. BICKEL, Maximum Likelihood Estimation of Intrinsic Dimension, Adv. Neural Inform. Process. Systems 17, MIT Press, Cambridge, MA, 2005.
  • 10
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • S. ROWEIS AND L. SAUL, Nonlinear dimensionality reduction by locally linear embedding, Science, 290 (2000), pp. 2323-2326.
    • (2000) Science , vol.290 , pp. 2323-2326
    • ROWEIS, S.1    SAUL, L.2
  • 12
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimension reduction
    • J. TENENBAUM, V. DE SILVA, AND J. LANGFORD, A global geometric framework for nonlinear dimension reduction, Science, 290 (2000), pp. 2319-2323.
    • (2000) Science , vol.290 , pp. 2319-2323
    • TENENBAUM, J.1    DE SILVA, V.2    LANGFORD, J.3
  • 13
    • 84864069440 scopus 로고    scopus 로고
    • J. WANG AND Z. ZHANG, MLLE: Modified Locally Linear Embedding Using Multiple Weights, Adv. Neural Inform. Process. Systems 19, MIT Press, Cambridge, MA, 2007.
    • J. WANG AND Z. ZHANG, MLLE: Modified Locally Linear Embedding Using Multiple Weights, Adv. Neural Inform. Process. Systems 19, MIT Press, Cambridge, MA, 2007.
  • 17
    • 14544307975 scopus 로고    scopus 로고
    • Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
    • Z. ZHANG AND H. ZHA, Principal manifolds and nonlinear dimensionality reduction via tangent space alignment, SIAM J. Sci. Comput., 26 (2004), pp. 313-338.
    • (2004) SIAM J. Sci. Comput , vol.26 , pp. 313-338
    • ZHANG, Z.1    ZHA, H.2
  • 18
    • 68649118453 scopus 로고    scopus 로고
    • Z. ZHANG AND H. ZHA, A Domain Decomposition Method for Fast Manifold Learning, Adv. Neural Inform. Process. Systems 18, MIT Press, Cambridge, MA, 2006.
    • Z. ZHANG AND H. ZHA, A Domain Decomposition Method for Fast Manifold Learning, Adv. Neural Inform. Process. Systems 18, MIT Press, Cambridge, MA, 2006.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.