메뉴 건너뛰기




Volumn 45, Issue 4, 2011, Pages 737-759

Persistent Cohomology and Circular Coordinates

Author keywords

Computational topology; Dimensionality reduction; Persistent cohomology; Persistent homology

Indexed keywords


EID: 79954629188     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-011-9344-x     Document Type: Article
Times cited : (130)

References (19)
  • 1
    • 84880203756 scopus 로고    scopus 로고
    • Laplacian eigenmaps and spectral techniques for embedding and clustering
    • T. Diettrich, S. Becker, and Z. Ghahramani (Eds.), Cambridge: MIT Press
    • Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Diettrich, T., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14, pp. 585-591. MIT Press, Cambridge (2002).
    • (2002) Advances in Neural Information Processing Systems 14 , pp. 585-591
    • Belkin, M.1    Niyogi, P.2
  • 5
    • 4143089050 scopus 로고    scopus 로고
    • Hessian eigenmaps: new locally linear embedding techniques for high-dimensional data
    • Department of Statistics, Stanford University
    • Donoho, D. L., Grimes, C.: Hessian eigenmaps: new locally linear embedding techniques for high-dimensional data. Technical Report TR 2003-08, Department of Statistics, Stanford University (2003).
    • (2003) Technical Report TR 2003-08
    • Donoho, D.L.1    Grimes, C.2
  • 6
    • 70349220130 scopus 로고    scopus 로고
    • Persistent homology-a survey
    • Contemporary Mathematics, J. E. Goodman, J. Pach, and R. Pollack (Eds.), Providence: American Mathematical Society
    • Edelsbrunner, H., Harer, J.: Persistent homology-a survey. In: Goodman, J. E., Pach, J., Pollack, R. (eds.) Surveys on Discrete and Computational Geometry: Twenty Years Later. Contemporary Mathematics, vol. 453, pp. 257-282. American Mathematical Society, Providence (2008).
    • (2008) Surveys on Discrete and Computational Geometry: Twenty Years Later , vol.453 , pp. 257-282
    • Edelsbrunner, H.1    Harer, J.2
  • 8
    • 41849100389 scopus 로고    scopus 로고
    • Barcodes: the persistent topology of data
    • Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61-75 (2008).
    • (2008) Bull. Am. Math. Soc. , vol.45 , Issue.1 , pp. 61-75
    • Ghrist, R.1
  • 10
    • 0004193355 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002).
    • (2002) Algebraic Topology
    • Hatcher, A.1
  • 11
    • 21744433228 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction of data manifolds with essential loops
    • Lee, J. A., Verleysen, M.: Nonlinear dimensionality reduction of data manifolds with essential loops. Neurocomputing 67, 29-53 (2005).
    • (2005) Neurocomputing , vol.67 , pp. 29-53
    • Lee, J.A.1    Verleysen, M.2
  • 14
    • 0039943513 scopus 로고
    • LSQR: an algorithm for sparse linear equations and sparse least squares
    • Paige, C. C., Saunders, M. A.: LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. 8(1), 43-71 (1982).
    • (1982) ACM Trans. Math. Softw. , vol.8 , Issue.1 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2
  • 16
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323-2326 (2000).
    • (2000) Science , vol.290 , pp. 2323-2326
    • Roweis, S.1    Saul, L.2
  • 18
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum, J. B., de Silva, V., Langford, J. C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319-2323 (2000).
    • (2000) Science , vol.290 , pp. 2319-2323
    • Tenenbaum, J.B.1    de Silva, V.2    Langford, J.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.