-
1
-
-
0026898892
-
Quantifying the neighborhood preservation of self-organizing maps
-
Bauer H.-U., and Pawelzik K. Quantifying the neighborhood preservation of self-organizing maps. IEEE Transactions on Neural Networks 3 (1992) 570-579
-
(1992)
IEEE Transactions on Neural Networks
, vol.3
, pp. 570-579
-
-
Bauer, H.-U.1
Pawelzik, K.2
-
2
-
-
84880203756
-
Laplacian eigenmaps and spectral techniques for embedding and clustering
-
Dietterich T., Becker S., and Ghahramani Z. (Eds), MIT Press, Cambridge, MA
-
Belkin M., and Niyogi P. Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Dietterich T., Becker S., and Ghahramani Z. (Eds). Advances in Neural Information Processing Systems (NIPS 2001) vol. 14 (2002), MIT Press, Cambridge, MA
-
(2002)
Advances in Neural Information Processing Systems (NIPS 2001)
, vol.14
-
-
Belkin, M.1
Niyogi, P.2
-
3
-
-
0042378381
-
Laplacian eigenmaps for dimensionality reduction and data representation
-
Belkin M., and Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15 6 (2003) 1373-1396
-
(2003)
Neural Computation
, vol.15
, Issue.6
, pp. 1373-1396
-
-
Belkin, M.1
Niyogi, P.2
-
4
-
-
9444224602
-
Spectral clustering and kernel PCA are learning eigenfunctions
-
Technical Report 1239, Département d'Informatique et Recherche Opérationnelle, Université de Montréal, Montréal, July
-
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, July 2003.
-
(2003)
-
-
Bengio, Y.1
Vincent, P.2
Paiement, J.-F.3
Delalleau, O.4
Ouimet, M.5
Le Roux, N.6
-
5
-
-
61849119166
-
-
M. Brand, K. Huang, A unifying theorem for spectral embedding and clustering, in: C. Bishop, B. Frey (Eds.), Proceedings of International Workshop on Artificial Intelligence and Statistics (AISTATS'03), Key West, FL, 2003, also presented at NIPS 2002 Workshop on Spectral Methods, Available as Technical Report TR2002-042.
-
M. Brand, K. Huang, A unifying theorem for spectral embedding and clustering, in: C. Bishop, B. Frey (Eds.), Proceedings of International Workshop on Artificial Intelligence and Statistics (AISTATS'03), Key West, FL, 2003, also presented at NIPS 2002 Workshop on Spectral Methods, Available as Technical Report TR2002-042.
-
-
-
-
6
-
-
37249089617
-
-
Ph.D. Thesis, University of Pennsylvania, July
-
L. Chen, Local multidimensional scaling for nonlinear dimensionality reduction, graph layout, and proximity analysis, Ph.D. Thesis, University of Pennsylvania, July 2006.
-
(2006)
Local multidimensional scaling for nonlinear dimensionality reduction, graph layout, and proximity analysis
-
-
Chen, L.1
-
7
-
-
84980028038
-
Vector quantization and projection neural network
-
Springer, New York
-
P. Demartines, J. Hérault, Vector quantization and projection neural network, in: Lecture Notes in Computer Science, vol. 686, Springer, New York, 1993, pp. 328-333.
-
(1993)
Lecture Notes in Computer Science
, vol.686
, pp. 328-333
-
-
Demartines, P.1
Hérault, J.2
-
8
-
-
0030736375
-
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
-
Demartines P., and Hérault J. Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets. IEEE Transactions on Neural Networks 8 1 (1997) 148-154
-
(1997)
IEEE Transactions on Neural Networks
, vol.8
, Issue.1
, pp. 148-154
-
-
Demartines, P.1
Hérault, J.2
-
9
-
-
0004061989
-
-
Prentice-Hall, Englewood-Cliffs, NJ
-
Di Battista G., Eades P., Tamassia R., and Tollis I. Graph Drawing: Algorithms for the Visualization of Graphs (1999), Prentice-Hall, Englewood-Cliffs, NJ
-
(1999)
Graph Drawing: Algorithms for the Visualization of Graphs
-
-
Di Battista, G.1
Eades, P.2
Tamassia, R.3
Tollis, I.4
-
11
-
-
0004494388
-
Intrinsic dimensionality extraction
-
Krishnaiah P., and Kanal L. (Eds), Elsevier, Amsterdam
-
Fukunaga K. Intrinsic dimensionality extraction. In: Krishnaiah P., and Kanal L. (Eds). Classification, Pattern Recognition and Reduction of Dimensionality, Handbook of Statistics vol. 2 (1982), Elsevier, Amsterdam 347-360
-
(1982)
Classification, Pattern Recognition and Reduction of Dimensionality, Handbook of Statistics
, vol.2
, pp. 347-360
-
-
Fukunaga, K.1
-
12
-
-
1542535868
-
Curvilinear component analysis for high dimensional data representation: I. Theoretical aspects and practical use in the presence of noise
-
Mira J., and Sánchez J. (Eds), Springer, Alicante, Spain
-
Hérault J., Jaussions-Picaud C., and Guérin-Dugué A. Curvilinear component analysis for high dimensional data representation: I. Theoretical aspects and practical use in the presence of noise. In: Mira J., and Sánchez J. (Eds). Proceedings of IWANN'99 vol. II (1999), Springer, Alicante, Spain 635-644
-
(1999)
Proceedings of IWANN'99
, vol.II
, pp. 635-644
-
-
Hérault, J.1
Jaussions-Picaud, C.2
Guérin-Dugué, A.3
-
14
-
-
0020068152
-
Self-organization of topologically correct feature maps
-
Kohonen T. Self-organization of topologically correct feature maps. Biological Cybernetics 43 (1982) 59-69
-
(1982)
Biological Cybernetics
, vol.43
, pp. 59-69
-
-
Kohonen, T.1
-
16
-
-
0026113980
-
Nonlinear principal component analysis using autoassociative neural networks
-
Kramer M. Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal 37 2 (1991) 233-243
-
(1991)
AIChE Journal
, vol.37
, Issue.2
, pp. 233-243
-
-
Kramer, M.1
-
17
-
-
0041654220
-
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 29 (1964) 1-28
-
(1964)
Psychometrika
, vol.29
, pp. 1-28
-
-
Kruskal, J.1
-
18
-
-
21744458509
-
Locally linear embedding versus isotop
-
M. Verleysen Ed, Bruges, Belgium
-
J. Lee, C. Archambeau, M. Verleysen, Locally linear embedding versus isotop, in: M. Verleysen (Ed.), Proceedings of 11th European Symposium on Artificial Neural Networks, ESANN 2003, d-side, Bruges, Belgium, 2003, pp. 527-534.
-
(2003)
Proceedings of 11th European Symposium on Artificial Neural Networks, ESANN 2003, d-side
, pp. 527-534
-
-
Lee, J.1
Archambeau, C.2
Verleysen, M.3
-
19
-
-
0037818078
-
Curvilinear distances analysis versus isomap
-
M. Verleysen Ed, Bruges, Belgium
-
J. Lee, A. Lendasse, M. Verleysen, Curvilinear distances analysis versus isomap, in: M. Verleysen (Ed.), Proceedings of 10th European Symposium on Artificial Neural Networks, ESANN 2002, d-side, Bruges, Belgium, 2002, pp. 185-192.
-
(2002)
Proceedings of 10th European Symposium on Artificial Neural Networks, ESANN 2002, d-side
, pp. 185-192
-
-
Lee, J.1
Lendasse, A.2
Verleysen, M.3
-
20
-
-
1542680971
-
Curvilinear distance analysis versus isomap
-
Lee J., and Verleysen M. Curvilinear distance analysis versus isomap. Neurocomputing 57 (2004) 49-76
-
(2004)
Neurocomputing
, vol.57
, pp. 49-76
-
-
Lee, J.1
Verleysen, M.2
-
21
-
-
21744433228
-
Nonlinear dimensionality reduction of data manifolds with essential loops
-
Lee J., and Verleysen M. Nonlinear dimensionality reduction of data manifolds with essential loops. Neurocomputing 67 (2005) 29-53
-
(2005)
Neurocomputing
, vol.67
, pp. 29-53
-
-
Lee, J.1
Verleysen, M.2
-
23
-
-
84887013766
-
Rank-based quality assessment of nonlinear dimensionality reduction
-
M. Verleysen Ed, Bruges
-
J. Lee, M. Verleysen, Rank-based quality assessment of nonlinear dimensionality reduction, in: M. Verleysen (Ed.), Proceedings of 16th European Symposium on Artificial Neural Networks, ESANN 2008, d-side, Bruges, 2008, pp. 49-54.
-
(2008)
Proceedings of 16th European Symposium on Artificial Neural Networks, ESANN 2008, d-side
, pp. 49-54
-
-
Lee, J.1
Verleysen, M.2
-
24
-
-
0029270805
-
Artificial neural networks for feature extraction and multivariate data projection
-
Mao J., and Jain A. Artificial neural networks for feature extraction and multivariate data projection. IEEE Transactions on Neural Networks 6 2 (1995) 296-317
-
(1995)
IEEE Transactions on Neural Networks
, vol.6
, Issue.2
, pp. 296-317
-
-
Mao, J.1
Jain, A.2
-
25
-
-
84864071145
-
Diffusion maps, spectral clustering and eigenfunction of Fokker-Planck operators
-
Weiss Y., Schölkopf B., and Platt J. (Eds), MIT Press, Cambridge, MA
-
Nadler B., Lafon S., Coifman R., and Kevrekidis I. Diffusion maps, spectral clustering and eigenfunction of Fokker-Planck operators. In: Weiss Y., Schölkopf B., and Platt J. (Eds). Advances in Neural Information Processing Systems (NIPS 2005) vol. 18 (2006), MIT Press, Cambridge, MA
-
(2006)
Advances in Neural Information Processing Systems (NIPS 2005)
, vol.18
-
-
Nadler, B.1
Lafon, S.2
Coifman, R.3
Kevrekidis, I.4
-
26
-
-
0000621817
-
Data compression, feature extraction, and autoassociation in feedforward neural networks
-
Kohonen T., Mäkisara K., Simula O., and Kangas J. (Eds), Elsevier Science Publishers, B.V., North-Holland
-
Oja E. Data compression, feature extraction, and autoassociation in feedforward neural networks. In: Kohonen T., Mäkisara K., Simula O., and Kangas J. (Eds). Artificial Neural Networks vol. 1 (1991), Elsevier Science Publishers, B.V., North-Holland 737-745
-
(1991)
Artificial Neural Networks
, vol.1
, pp. 737-745
-
-
Oja, E.1
-
27
-
-
0034704222
-
Nonlinear dimensionality reduction by locally linear embedding
-
Roweis S., and Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science 290 5500 (2000) 2323-2326
-
(2000)
Science
, vol.290
, Issue.5500
, pp. 2323-2326
-
-
Roweis, S.1
Saul, L.2
-
28
-
-
22944459214
-
The principal components analysis of a graph, and its relationships to spectral clustering
-
Proceedings of the 15th European Conference on Machine Learning ECML, Pisa, Italy
-
M. Saerens, F. Fouss, L. Yen, P. Dupont, The principal components analysis of a graph, and its relationships to spectral clustering, in: Proceedings of the 15th European Conference on Machine Learning (ECML 2004), Lecture Notes in Artificial Intelligence, vol. 3201, Pisa, Italy, 2004.
-
(2004)
Lecture Notes in Artificial Intelligence
, vol.3201
-
-
Saerens, M.1
Fouss, F.2
Yen, L.3
Dupont, P.4
-
29
-
-
84887006810
-
A nonlinear mapping algorithm for data structure analysis
-
Sammon J. A nonlinear mapping algorithm for data structure analysis. IEEE Transactions on Computers CC-18 5 (1969) 401-409
-
(1969)
IEEE Transactions on Computers
, vol.CC-18
, Issue.5
, pp. 401-409
-
-
Sammon, J.1
-
30
-
-
2342517502
-
Think globally, fit locally: unsupervised learning of nonlinear manifolds
-
Saul L., and Roweis S. Think globally, fit locally: unsupervised learning of nonlinear manifolds. Journal of Machine Learning Research 4 (2003) 119-155
-
(2003)
Journal of Machine Learning Research
, vol.4
, pp. 119-155
-
-
Saul, L.1
Roweis, S.2
-
31
-
-
0347243182
-
Nonlinear component analysis as a kernel eigenvalue problem
-
Schölkopf B., Smola A., and Müller K.-R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10 (1998) 1299-1319
-
(1998)
Neural Computation
, vol.10
, pp. 1299-1319
-
-
Schölkopf, B.1
Smola, A.2
Müller, K.-R.3
-
32
-
-
34250926052
-
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 27 (1962) 125-140 219-249
-
(1962)
Psychometrika
, vol.27
, pp. 125-140
-
-
Shepard, R.1
-
33
-
-
34250297158
-
Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features
-
Takane Y., Young F., and de Leeuw J. Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika 42 (1977) 7-67
-
(1977)
Psychometrika
, vol.42
, pp. 7-67
-
-
Takane, Y.1
Young, F.2
de Leeuw, J.3
-
34
-
-
0034704229
-
A global geometric framework for nonlinear dimensionality reduction
-
Tenenbaum J., de Silva V., and Langford J. A global geometric framework for nonlinear dimensionality reduction. Science 290 5500 (2000) 2319-2323
-
(2000)
Science
, vol.290
, Issue.5500
, pp. 2319-2323
-
-
Tenenbaum, J.1
de Silva, V.2
Langford, J.3
-
35
-
-
84950351930
-
Multidimensional scaling, I: theory and method
-
Torgerson W. Multidimensional scaling, I: theory and method. Psychometrika 17 (1952) 401-419
-
(1952)
Psychometrika
, vol.17
, pp. 401-419
-
-
Torgerson, W.1
-
36
-
-
61849108315
-
-
Ph.D. Thesis, Helsinki University of Technology, Espoo, Finland, June
-
J. Venna, Dimensionality reduction for visual exploration of similarity structures, Ph.D. Thesis, Helsinki University of Technology, Espoo, Finland, June 2007.
-
(2007)
Dimensionality reduction for visual exploration of similarity structures
-
-
Venna, J.1
-
37
-
-
84958976659
-
Neighborhood preservation in nonlinear projection methods: an experimental study
-
Dorffner G., Bischof H., and Hornik K. (Eds), Springer, Berlin
-
Venna J., and Kaski S. Neighborhood preservation in nonlinear projection methods: an experimental study. In: Dorffner G., Bischof H., and Hornik K. (Eds). Proceedings of ICANN 2001 (2001), Springer, Berlin 485-491
-
(2001)
Proceedings of ICANN 2001
, pp. 485-491
-
-
Venna, J.1
Kaski, S.2
-
38
-
-
33746617306
-
Local multidimensional scaling
-
Venna J., and Kaski S. Local multidimensional scaling. Neural Networks 19 (2006) 889-899
-
(2006)
Neural Networks
, vol.19
, pp. 889-899
-
-
Venna, J.1
Kaski, S.2
-
39
-
-
61849130212
-
Nonlinear dimensionality reduction as information retrieval
-
M. Meila, X. Shen Eds, San Juan, Puerto Rico
-
J. Venna, S. Kaski, Nonlinear dimensionality reduction as information retrieval, in: M. Meila, X. Shen (Eds.), Proceedings of the 11th International Conference on Artificial Intelligence and Statistics (AISTATS 2007), San Juan, Puerto Rico, 2007, pp. 568-575.
-
(2007)
Proceedings of the 11th International Conference on Artificial Intelligence and Statistics (AISTATS
, pp. 568-575
-
-
Venna, J.1
Kaski, S.2
-
40
-
-
0031097231
-
Topology preservation in self-organizing feature maps: exact definition and measurement
-
Villmann T., Der R., Herrmann M., and Martinetz T. Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Transactions on Neural Networks 8 2 (1997) 256-266
-
(1997)
IEEE Transactions on Neural Networks
, vol.8
, Issue.2
, pp. 256-266
-
-
Villmann, T.1
Der, R.2
Herrmann, M.3
Martinetz, T.4
-
41
-
-
33744949513
-
-
K. Weinberger, L. Saul, Unsupervised learning of image manifolds by semidefinite programming, International Journal of Computer Vision 70 (1) (2006) 77-90, in: A. Bobick, R. Chellappa, L. Davis (Guest Eds.), Special Issue: Computer Vision and Pattern Recognition-CVPR 2004.
-
K. Weinberger, L. Saul, Unsupervised learning of image manifolds by semidefinite programming, International Journal of Computer Vision 70 (1) (2006) 77-90, in: A. Bobick, R. Chellappa, L. Davis (Guest Eds.), Special Issue: Computer Vision and Pattern Recognition-CVPR 2004.
-
-
-
-
42
-
-
14344251006
-
Learning a kernel matrix for nonlinear dimensionality reduction
-
Banff, Canada
-
K. Weinberger, F. Sha, L. Saul, Learning a kernel matrix for nonlinear dimensionality reduction, in: Proceedings of the 21st International Conference on Machine Learning (ICML-04), Banff, Canada, 2004.
-
(2004)
Proceedings of the 21st International Conference on Machine Learning (ICML-04)
-
-
Weinberger, K.1
Sha, F.2
Saul, L.3
-
43
-
-
0001295575
-
Differentiable manifolds
-
Whitney H. Differentiable manifolds. Annals of Mathematics 37 3 (1936) 645-680
-
(1936)
Annals of Mathematics
, vol.37
, Issue.3
, pp. 645-680
-
-
Whitney, H.1
-
44
-
-
0002361037
-
Discussion of a set of points in terms of their mutual distances
-
Young G., and Householder A. Discussion of a set of points in terms of their mutual distances. Psychometrika 3 (1938) 19-22
-
(1938)
Psychometrika
, vol.3
, pp. 19-22
-
-
Young, G.1
Householder, A.2
|