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Volumn 112, Issue , 2013, Pages 92-108

Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation

Author keywords

Dimensionality reduction; Divergence; Manifold learning; Stochastic neighbor embedding

Indexed keywords

DIMENSIONALITY REDUCTION; DIVERGENCE; HIGH-DIMENSIONAL DATA SPACE; JENSEN-SHANNON DIVERGENCE; KULLBACK LEIBLER DIVERGENCE; MANIFOLD LEARNING; STATE-OF-THE-ART METHODS; STOCHASTIC NEIGHBOR EMBEDDING;

EID: 84877607226     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.12.036     Document Type: Article
Times cited : (92)

References (47)
  • 1
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson K. On lines and planes of closest fit to systems of points in space. Philos. Mag. 1901, 2:559-572.
    • (1901) Philos. Mag. , vol.2 , pp. 559-572
    • Pearson, K.1
  • 2
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • Hotelling H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 1933, 24:417-441.
    • (1933) J. Educ. Psychol. , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 4
    • 0002361037 scopus 로고
    • Discussion of a set of points in terms of their mutual distances
    • Young G., Householder A. Discussion of a set of points in terms of their mutual distances. Psychometrika 1938, 3:19-22.
    • (1938) Psychometrika , vol.3 , pp. 19-22
    • Young, G.1    Householder, A.2
  • 5
    • 84950351930 scopus 로고
    • Multidimensional scaling, I. theory and method
    • Torgerson W. Multidimensional scaling, I. theory and method. Psychometrika 1952, 17:401-419.
    • (1952) Psychometrika , vol.17 , pp. 401-419
    • Torgerson, W.1
  • 7
    • 84887006810 scopus 로고
    • A nonlinear mapping algorithm for data structure analysis
    • Sammon J. A nonlinear mapping algorithm for data structure analysis. IEEE Trans. Comput. 1969, CC-18(5):401-409.
    • (1969) IEEE Trans. Comput. , vol.18 CC , Issue.5 , pp. 401-409
    • Sammon, J.1
  • 9
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum J., de Silva V., Langford J. A global geometric framework for nonlinear dimensionality reduction. Science 2000, 290(5500):2319-2323.
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.1    de Silva, V.2    Langford, J.3
  • 12
    • 1542680971 scopus 로고    scopus 로고
    • Curvilinear distance analysis versus isomap
    • Lee J., Verleysen M. Curvilinear distance analysis versus isomap. Neurocomputing 2004, 57:49-76.
    • (2004) Neurocomputing , vol.57 , pp. 49-76
    • Lee, J.1    Verleysen, M.2
  • 14
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis S., Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science 2000, 290(5500):2323-2326.
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.1    Saul, L.2
  • 17
    • 61849137245 scopus 로고    scopus 로고
    • Quality assessment of dimensionality reduction. rank-based criteria
    • Lee J., Verleysen M. Quality assessment of dimensionality reduction. rank-based criteria. Neurocomputing 2009, 72(7-9):1431-1443.
    • (2009) Neurocomputing , vol.72 , Issue.7-9 , pp. 1431-1443
    • Lee, J.1    Verleysen, M.2
  • 19
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • also available as technical report 44 at the Max Planck Institute for Biological Cybernetics, Tübingen, Germany, December 1996
    • Schölkopf B., Smola A., Müller K.-R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 1998, 10:1299-1319. also available as technical report 44 at the Max Planck Institute for Biological Cybernetics, Tübingen, Germany, December 1996.
    • (1998) Neural Comput. , vol.10 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.2    Müller, K.-R.3
  • 20
    • 11144299132 scopus 로고    scopus 로고
    • A kernel view of the dimensionality reduction of manifolds
    • 21th International Conference on Machine Learning (ICML-04), also available as technical report TR-102 at Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2003.
    • J. Ham, D. Lee, S. Mika, B. Schölkopf, A kernel view of the dimensionality reduction of manifolds, in: 21th International Conference on Machine Learning (ICML-04), 2004, pp. 369-376, also available as technical report TR-102 at Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2003.
    • (2004) , pp. 369-376
    • Ham, J.1    Lee, D.2    Mika, S.3    Schölkopf, B.4
  • 22
    • 9444224602 scopus 로고    scopus 로고
    • Spectral clustering and kernel PCA are learning eigenfunctions, Technical Report. 1239
    • Département d'Informatique et Recherche Opérationnelle, Université de Montréal, Montréal (Jul.)
    • Y. Bengio, P. Vincent, J.-F. Paiement, O. Delalleau, M. Ouimet, N. Le Roux, Spectral clustering and kernel PCA are learning eigenfunctions, Technical Report. 1239, Département d'Informatique et Recherche Opérationnelle, Université de Montréal, Montréal (Jul. 2003).
    • (2003)
    • Bengio, Y.1    Vincent, P.2    Paiement, J.-F.3    Delalleau, O.4    Ouimet, M.5    Le Roux, N.6
  • 24
    • 77949507946 scopus 로고    scopus 로고
    • Information retrieval perspective to nonlinear dimensionality reduction for data visualization
    • Venna J., Peltonen J., Nybo K., Aidos H., Kaski S. Information retrieval perspective to nonlinear dimensionality reduction for data visualization. J. Mach. Learn. Res. 2010, 11:451-490.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 451-490
    • Venna, J.1    Peltonen, J.2    Nybo, K.3    Aidos, H.4    Kaski, S.5
  • 25
    • 79958246734 scopus 로고    scopus 로고
    • Shift-invariant similarities circumvent distance concentration in stochastic neighbor embedding and variants
    • (ICCS 2011), Singapore
    • J. Lee, M. Verleysen, Shift-invariant similarities circumvent distance concentration in stochastic neighbor embedding and variants, in: Proceedings of the International Conference on Computational Science (ICCS 2011), Singapore, 2011, pp. 538-547.
    • (2011) Proceedings of the International Conference on Computational Science , pp. 538-547
    • Lee, J.1    Verleysen, M.2
  • 28
    • 0346061723 scopus 로고    scopus 로고
    • High-Dimensional Data Analysis: The Curse and Blessings of Dimensionality, aide-mémoire for a lecture for the American Mathematical Society
    • D. Donoho, High-Dimensional Data Analysis: The Curse and Blessings of Dimensionality, aide-mémoire for a lecture for the American Mathematical Society "Mathematical Challenges of the 21st Century", 2000.
    • (2000) Mathematical Challenges of the 21st Century
    • Donoho, D.1
  • 29
    • 33646201094 scopus 로고    scopus 로고
    • High-throughput multi-dimensional scaling (HiT-MDS) for cDNA-array expression data
    • W. Duch (Ed.), Artificial Neural Networks: Biological Inspirations (Part I), Lecture Notes in Computer Science, Springer
    • M. Strickert, S. Teichmann, N. Sreenivasulu, U. Seiffert, High-throughput multi-dimensional scaling (HiT-MDS) for cDNA-array expression data, in: W. Duch (Ed.), Proceedings of the ICANN 2005, Artificial Neural Networks: Biological Inspirations (Part I), Lecture Notes in Computer Science, vol. 3696, Springer, 2005, pp. 625-634.
    • (2005) Proceedings of the ICANN 2005 , vol.3696 , pp. 625-634
    • Strickert, M.1    Teichmann, S.2    Sreenivasulu, N.3    Seiffert, U.4
  • 30
    • 34250359479 scopus 로고    scopus 로고
    • Correlation-maximizing surrogate gene space for visual mining of gene expression patterns in developing barley endosperm tissue
    • Strickert M., Sreenivasulu N., Usadel B., Seiffert U. Correlation-maximizing surrogate gene space for visual mining of gene expression patterns in developing barley endosperm tissue. BMC Bioinformatics 2007, 8:165.
    • (2007) BMC Bioinformatics , vol.8 , pp. 165
    • Strickert, M.1    Sreenivasulu, N.2    Usadel, B.3    Seiffert, U.4
  • 31
    • 84860235712 scopus 로고    scopus 로고
    • Stochastic neighbor embedding (SNE) for dimension reduction and visualization using arbitrary divergences
    • Bunte K., Haase S., Biehl M., Villmann T. Stochastic neighbor embedding (SNE) for dimension reduction and visualization using arbitrary divergences. Neurocomputing 2012, 90:23-45.
    • (2012) Neurocomputing , vol.90 , pp. 23-45
    • Bunte, K.1    Haase, S.2    Biehl, M.3    Villmann, T.4
  • 32
    • 77956416620 scopus 로고    scopus 로고
    • Families of alpha- beta- and gamma-divergences. flexible and robust measures of similarities
    • Cichocki A., Amari S.-i. Families of alpha- beta- and gamma-divergences. flexible and robust measures of similarities. Entropy 2010, 12:1532-1568.
    • (2010) Entropy , vol.12 , pp. 1532-1568
    • Cichocki, A.1    Amari, S.-I.2
  • 33
    • 0020126872 scopus 로고
    • On the convexity of some divergence measures based on entropy functions
    • Burbea J., Rao C. On the convexity of some divergence measures based on entropy functions. IEEE Trans. Inf. Theory 1982, 28(3):489-495.
    • (1982) IEEE Trans. Inf. Theory , vol.28 , Issue.3 , pp. 489-495
    • Burbea, J.1    Rao, C.2
  • 34
    • 0025952277 scopus 로고
    • Divergence measures based on the Shannon entropy
    • Lin J. Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 1991, 37(1):145-151.
    • (1991) IEEE Trans. Inf. Theory , vol.37 , Issue.1 , pp. 145-151
    • Lin, J.1
  • 35
    • 79958275324 scopus 로고    scopus 로고
    • On the role and impact of the metaparameters in t-distributed stochastic neighbor embedding
    • Y. Lechevallier, G. Saporta (Eds.), Paris (France)
    • J. Lee, M. Verleysen, On the role and impact of the metaparameters in t-distributed stochastic neighbor embedding, in: Y. Lechevallier, G. Saporta (Eds.), Proceedings of the 19th COMPSTAT, Paris (France), 2010, pp. 337-348.
    • (2010) Proceedings of the 19th COMPSTAT , pp. 337-348
    • Lee, J.1    Verleysen, M.2
  • 36
    • 0003523991 scopus 로고
    • Algorithms for drawing graphs: an annotated bibliography
    • Brown University (Jun.)
    • G. Di Battista, P. Eades, R. Tamassia, I. Tollis, Algorithms for drawing graphs: an annotated bibliography, Technical Report. Brown University (Jun. 1994).
    • (1994) Technical Report
    • Di Battista, G.1    Eades, P.2    Tamassia, R.3    Tollis, I.4
  • 38
    • 33746617306 scopus 로고    scopus 로고
    • Local multidimensional scaling
    • Venna J., Kaski S. Local multidimensional scaling. Neural Networks 2006, 19:889-899.
    • (2006) Neural Networks , vol.19 , pp. 889-899
    • Venna, J.1    Kaski, S.2
  • 39
    • 0030736375 scopus 로고    scopus 로고
    • Curvilinear component analysis. a self-organizing neural network for nonlinear mapping of data sets
    • Demartines P., Hérault J. Curvilinear component analysis. a self-organizing neural network for nonlinear mapping of data sets. IEEE Trans. Neural Networks 1997, 8(1):148-154.
    • (1997) IEEE Trans. Neural Networks , vol.8 , Issue.1 , pp. 148-154
    • Demartines, P.1    Hérault, J.2
  • 40
    • 0003840341 scopus 로고    scopus 로고
    • Columbia object image library (COIL-20)
    • Technical Report. CUCS-005-96, Columbia University
    • S.A. Nene, S.K. Nayar, H. Murase, Columbia object image library (COIL-20), Technical Report. CUCS-005-96, Columbia University, 1996.
    • (1996)
    • Nene, S.A.1    Nayar, S.K.2    Murase, H.3
  • 41
    • 0032203257 scopus 로고    scopus 로고
    • Gradient-based learning applied to document recognition
    • LeCun Y., Bottou L., Bengio Y., Haffner P. Gradient-based learning applied to document recognition. Proc. IEEE 1998, 86(11):2278-2324.
    • (1998) Proc. IEEE , vol.86 , Issue.11 , pp. 2278-2324
    • LeCun, Y.1    Bottou, L.2    Bengio, Y.3    Haffner, P.4
  • 42
    • 77957908161 scopus 로고    scopus 로고
    • Scale-independent quality criteria for dimensionality reduction
    • Lee J., Verleysen M. Scale-independent quality criteria for dimensionality reduction. Pattern Recognition Lett. 2010, 31(14):2248-2257.
    • (2010) Pattern Recognition Lett. , vol.31 , Issue.14 , pp. 2248-2257
    • Lee, J.1    Verleysen, M.2
  • 43
    • 84958976659 scopus 로고    scopus 로고
    • Neighborhood preservation in nonlinear projection methods. an experimental study
    • Springer, Berlin, G. Dorffner, H. Bischof, K. Hornik (Eds.)
    • Venna J., Kaski S. Neighborhood preservation in nonlinear projection methods. an experimental study. Proceedings of ICANN 2001 2001, 485-491. Springer, Berlin. G. Dorffner, H. Bischof, K. Hornik (Eds.).
    • (2001) Proceedings of ICANN 2001 , pp. 485-491
    • Venna, J.1    Kaski, S.2
  • 44
    • 0000071395 scopus 로고
    • Some distance properties of latent root and vector methods used in multivariate analysis
    • Gower J. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 1966, 53:325-338.
    • (1966) Biometrika , vol.53 , pp. 325-338
    • Gower, J.1
  • 45
    • 34250926052 scopus 로고
    • The analysis of proximities. multidimensional scaling with an unknown distance function (parts 1 and 2)
    • 219-249
    • Shepard R. The analysis of proximities. multidimensional scaling with an unknown distance function (parts 1 and 2). Psychometrika 1962, 27:125-140. 219-249.
    • (1962) Psychometrika , vol.27 , pp. 125-140
    • Shepard, R.1
  • 46
    • 0041654220 scopus 로고
    • Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
    • Kruskal J. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 1964, 29:1-28.
    • (1964) Psychometrika , vol.29 , pp. 1-28
    • Kruskal, J.1
  • 47
    • 79960337319 scopus 로고    scopus 로고
    • Generalized alpha-beta divergences and their application to robust nonnegative matrix factorization
    • Cichocki A., Cruces S., Amari S.-i. Generalized alpha-beta divergences and their application to robust nonnegative matrix factorization. Entropy 2011, 13:134-170.
    • (2011) Entropy , vol.13 , pp. 134-170
    • Cichocki, A.1    Cruces, S.2    Amari, S.-I.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.