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Volumn 74, Issue 4, 2011, Pages 522-539

Local matrix adaptation in topographic neural maps

Author keywords

Convergence; Matrix learning; Metric adaptation; Neural gas; Topographic maps

Indexed keywords

CONVERGENCE; MATRIX; METRIC ADAPTATION; NEURAL GAS; TOPOGRAPHIC MAP;

EID: 78650239815     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.08.016     Document Type: Article
Times cited : (25)

References (49)
  • 1
    • 78650238917 scopus 로고    scopus 로고
    • Analyzing dissimilarity matrices using Kohonen maps, in: Proceeding of IFCS96
    • C. Ambroise, G. Govaert, Analyzing dissimilarity matrices using Kohonen maps, in: Proceeding of IFCS96, vol. 1, 1996, pp. 425-430.
    • (1996) , vol.1 , pp. 425-430
    • Ambroise, C.1    Govaert, G.2
  • 2
    • 10944268652 scopus 로고    scopus 로고
    • Adaptive second order self-organizing mapping for 2D pattern representation, in: International Joint Conference on Neural Networks 2004,
    • B. Arnonkijpanich, C. Lursinsap, Adaptive second order self-organizing mapping for 2D pattern representation, in: International Joint Conference on Neural Networks 2004, 2004, pp. 775-780.
    • (2004) , pp. 775-780
    • Arnonkijpanich, B.1    Lursinsap, C.2
  • 3
    • 78650240064 scopus 로고    scopus 로고
    • UCI Machine Learning Repository [〈〉], Irvine, CA, University of California, School of Information and Computer Science,
    • A. Asuncion, D.J. Newman, UCI Machine Learning Repository [〈〉], Irvine, CA, University of California, School of Information and Computer Science, 2007. http://www.ics.uci.edu/~mlearn/MLRepository.html.
    • (2007)
    • Asuncion, A.1    Newman, D.J.2
  • 4
    • 85153959666 scopus 로고
    • Convergence properties of the k-means algorithm
    • MIT Press, G. Tesauro, D.S. Touretzky, T.K. Leen (Eds.)
    • Bottou L., Bengio Y. Convergence properties of the k-means algorithm. Neural Information Processing Systems 1994 1995, 585-592. MIT Press. G. Tesauro, D.S. Touretzky, T.K. Leen (Eds.).
    • (1995) Neural Information Processing Systems 1994 , pp. 585-592
    • Bottou, L.1    Bengio, Y.2
  • 6
    • 0345404393 scopus 로고    scopus 로고
    • Theoretical aspects of the SOM algorithm
    • Cottrell M., Fort J.C., Pagès G. Theoretical aspects of the SOM algorithm. Neurocomputing 1999, 21:119-138.
    • (1999) Neurocomputing , vol.21 , pp. 119-138
    • Cottrell, M.1    Fort, J.C.2    Pagès, G.3
  • 7
    • 78650232790 scopus 로고
    • Learning internal representations from grey-scale images: an example of extensional programming, in: Ninth Annual Conference of the Cognitive Science Society, Hillsdale Erlbaum,
    • G. Cottrell, P. Munro, D. Zipser, Learning internal representations from grey-scale images: an example of extensional programming, in: Ninth Annual Conference of the Cognitive Science Society, Hillsdale Erlbaum, 1987, pp. 462-473.
    • (1987) , pp. 462-473
    • Cottrell, G.1    Munro, P.2    Zipser, D.3
  • 9
    • 58549087543 scopus 로고    scopus 로고
    • Pg-means: learning the number of clusters in data, in: NIPS
    • Y. Feng, G. Hamerly, Pg-means: learning the number of clusters in data, in: NIPS, 2006, pp. 393-400.
    • (2006) , pp. 393-400
    • Feng, Y.1    Hamerly, G.2
  • 10
    • 33745902277 scopus 로고    scopus 로고
    • Advantages and drawbacks of the Batch Kohonen algorithm, in: M. Verleysen (Ed.), European Symposium on Artificial Neural Networks'2002, D Facto,
    • J.-C. Fort, P. Letrémy, M. Cottrell, Advantages and drawbacks of the Batch Kohonen algorithm, in: M. Verleysen (Ed.), European Symposium on Artificial Neural Networks'2002, D Facto, 2002, pp. 223-230.
    • (2002) , pp. 223-230
    • Fort, J.-C.1    Letrémy, P.2    Cottrell, M.3
  • 12
    • 0344972928 scopus 로고    scopus 로고
    • Self-organizing maps: generalizations and new optimization techniques
    • Graepel T., Burger M., Obermayer K. Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 1998, 21:173-190.
    • (1998) Neurocomputing , vol.21 , pp. 173-190
    • Graepel, T.1    Burger, M.2    Obermayer, K.3
  • 13
  • 14
    • 78650239486 scopus 로고    scopus 로고
    • Learning the k in k-means, in: NIPS,
    • G. Hamerly, C. Elkan, Learning the k in k-means, in: NIPS, 2003, pp. 281-288.
    • (2003) , pp. 281-288
    • Hamerly, G.1    Elkan, C.2
  • 16
    • 0035506768 scopus 로고    scopus 로고
    • Self-organizing maps, vector quantization, and mixture modeling
    • Heskes T. Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 2001, 12:1299-1305.
    • (2001) IEEE Transactions on Neural Networks , vol.12 , pp. 1299-1305
    • Heskes, T.1
  • 17
    • 84943234961 scopus 로고
    • Error potentials for self-organization
    • San Francisco, IEEE, New York
    • Heskes T., Kappen B. Error potentials for self-organization. International Conference on Neural Networks 1993, vol. 3:1219-1223. San Francisco, IEEE, New York.
    • (1993) International Conference on Neural Networks , vol.3 , pp. 1219-1223
    • Heskes, T.1    Kappen, B.2
  • 19
    • 0348139702 scopus 로고    scopus 로고
    • Dimension reduction by local principal component analysis
    • Kambhatla A., Leen T.K. Dimension reduction by local principal component analysis. Neural Computation 1997, 9(7):1493-1516.
    • (1997) Neural Computation , vol.9 , Issue.7 , pp. 1493-1516
    • Kambhatla, A.1    Leen, T.K.2
  • 21
    • 0003023542 scopus 로고
    • Self-organizing maps: optimization approaches
    • North-Holland, Amsterdam, T. Kohonen (Ed.)
    • Kohonen T. Self-organizing maps: optimization approaches. Artificial Neural Networks 1991, 981-990. North-Holland, Amsterdam. T. Kohonen (Ed.).
    • (1991) Artificial Neural Networks , pp. 981-990
    • Kohonen, T.1
  • 22
    • 0000761101 scopus 로고    scopus 로고
    • Self-organized formation of various invariant-feature filters in the adaptive-subspace SOM
    • Kohonen T., Kaski S., Lappalainen H. Self-organized formation of various invariant-feature filters in the adaptive-subspace SOM. Neural Computation 1997, 9(6):1321-1344.
    • (1997) Neural Computation , vol.9 , Issue.6 , pp. 1321-1344
    • Kohonen, T.1    Kaski, S.2    Lappalainen, H.3
  • 23
    • 0344972931 scopus 로고    scopus 로고
    • Self-organizing maps of symbol strings
    • Kohonen T., Somervuo P. Self-organizing maps of symbol strings. Neurocomputing 1998, 21(1-3):19-30.
    • (1998) Neurocomputing , vol.21 , Issue.1-3 , pp. 19-30
    • Kohonen, T.1    Somervuo, P.2
  • 24
    • 0031382558 scopus 로고    scopus 로고
    • Vector quantization using genetic K-means algorithm for image compression, in: International Conference on Information, Communications and Signal Processing,
    • K. Krishna, K.R. Ramakrishnan, M.A.L. Thathachar, Vector quantization using genetic K-means algorithm for image compression, in: International Conference on Information, Communications and Signal Processing, vol. 3, 1997, pp. 1585-1587.
    • (1997) , vol.3 , pp. 1585-1587
    • Krishna, K.1    Ramakrishnan, K.R.2    Thathachar, M.A.L.3
  • 25
    • 0345257348 scopus 로고    scopus 로고
    • Topological local principal component analysis
    • Liu Z.-Y., Xu L. Topological local principal component analysis. Neurocomputing 2003, 55:739-745.
    • (2003) Neurocomputing , vol.55 , pp. 739-745
    • Liu, Z.-Y.1    Xu, L.2
  • 27
    • 0024900153 scopus 로고
    • Self-organisation: a derivation from first principles of a class of learning algorithms
    • IEEE Computer Society Press
    • Luttrell S. Self-organisation: a derivation from first principles of a class of learning algorithms. International Joint Conference on Neural Networks 1989, vol. 2:495-498. IEEE Computer Society Press.
    • (1989) International Joint Conference on Neural Networks , vol.2 , pp. 495-498
    • Luttrell, S.1
  • 28
    • 78650251644 scopus 로고    scopus 로고
    • Matlab Toolbox for Dimensionality Reduction, MICC, Maastricht University, [〈〉]
    • L.J.P. van der Maaten, E.O. Postma, H.J. van den Herik, Matlab Toolbox for Dimensionality Reduction, MICC, Maastricht University, [〈〉], 2007. http://www.cs.unimaas.nl/l.vandermaaten/Laurens_van_der_Maaten/Matlab_Toolbox_for_Dimensionality_Reduction.html.
    • (2007)
    • van der Maaten, L.J.P.1    Postma, E.O.2    van den Herik, H.J.3
  • 29
    • 78650232372 scopus 로고
    • Selbstorganisierende neuronale Netzwerkmodelle zur Bewegungssteuerung, Sankt Augustin, 1992, Dissertationen zur künstlichen Intelligenz,
    • T. Martinetz, Selbstorganisierende neuronale Netzwerkmodelle zur Bewegungssteuerung, Sankt Augustin, 1992, Dissertationen zur künstlichen Intelligenz, 1992.
    • (1992)
    • Martinetz, T.1
  • 30
    • 0027632248 scopus 로고
    • 'Neural gas' network for vector quantization and its application to time series prediction
    • Martinetz T., Berkovich S., Schulten K. 'Neural gas' network for vector quantization and its application to time series prediction. IEEE Transactions on Neural networks 1993, 4(4):558-569.
    • (1993) IEEE Transactions on Neural networks , vol.4 , Issue.4 , pp. 558-569
    • Martinetz, T.1    Berkovich, S.2    Schulten, K.3
  • 32
    • 33746111259 scopus 로고    scopus 로고
    • Learning an optimal distance metric in a linguistic vector space
    • Mochihashi D., Kikui G., Kita K. Learning an optimal distance metric in a linguistic vector space. Systems and Computers in Japan 2006, 37(9):12-21.
    • (2006) Systems and Computers in Japan , vol.37 , Issue.9 , pp. 12-21
    • Mochihashi, D.1    Kikui, G.2    Kita, K.3
  • 33
    • 8644270422 scopus 로고    scopus 로고
    • An extension of neural gas to local PCA
    • Möller R., Hoffmann H. An extension of neural gas to local PCA. Neurocomputing 2004, 62:305-326.
    • (2004) Neurocomputing , vol.62 , pp. 305-326
    • Möller, R.1    Hoffmann, H.2
  • 35
    • 9144260753 scopus 로고    scopus 로고
    • Improved learning of Riemannian metrics for exploratory analysis
    • Peltonen J., Klami A., Kaski S. Improved learning of Riemannian metrics for exploratory analysis. Neural Networks 2004, 17:1087-1100.
    • (2004) Neural Networks , vol.17 , pp. 1087-1100
    • Peltonen, J.1    Klami, A.2    Kaski, S.3
  • 36
    • 0032202775 scopus 로고    scopus 로고
    • Deterministic annealing for clustering, compression, classification, regression, and related optimization problems
    • Rose K. Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proceedings of the IEEE 1998, 86(11):2210-2239.
    • (1998) Proceedings of the IEEE , vol.86 , Issue.11 , pp. 2210-2239
    • Rose, K.1
  • 37
    • 0024883243 scopus 로고
    • Optimal unsupervised learning in a single-layer linear feedforward neural network
    • Sanger T.D. Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks 1989, 2(6):459-473.
    • (1989) Neural Networks , vol.2 , Issue.6 , pp. 459-473
    • Sanger, T.D.1
  • 38
    • 9144234927 scopus 로고    scopus 로고
    • Self organizing maps and clustering for matrix data
    • Seo S., Obermayer K. Self organizing maps and clustering for matrix data. Neural Networks 2004, 17(8-9):1211-1229.
    • (2004) Neural Networks , vol.17 , Issue.8-9 , pp. 1211-1229
    • Seo, S.1    Obermayer, K.2
  • 40
    • 38449091680 scopus 로고    scopus 로고
    • Relevance matrices in LVQ, in: M. Verleysen (Ed.), European Symposium on Neural Networks 2007
    • P. Schneider, M. Biehl, B. Hammer, Relevance matrices in LVQ, in: M. Verleysen (Ed.), European Symposium on Neural Networks 2007, 2007, pp. 37-42.
    • (2007) , pp. 37-42
    • Schneider, P.1    Biehl, M.2    Hammer, B.3
  • 41
    • 33745899587 scopus 로고    scopus 로고
    • Growing hierarchical principal components analysis self-organizing map, in: Advances in Neural Networks-ISNN 2006, Lecture Notes in Computer Science, Springer,
    • L.Z. Stones, Y. Zhang, C.L. Jian, Growing hierarchical principal components analysis self-organizing map, in: Advances in Neural Networks-ISNN 2006, Lecture Notes in Computer Science, vol. 3971, Springer, 2006, pp. 701-706.
    • (2006) , vol.3971 , pp. 701-706
    • Stones, L.Z.1    Zhang, Y.2    Jian, C.L.3
  • 42
    • 33846486102 scopus 로고    scopus 로고
    • A unified continuous optimization framework for center-based clustering methods
    • Teboulle M. A unified continuous optimization framework for center-based clustering methods. Journal of Machine Learning Research 2007, 8:65-102.
    • (2007) Journal of Machine Learning Research , vol.8 , pp. 65-102
    • Teboulle, M.1
  • 43
    • 0033556788 scopus 로고    scopus 로고
    • Mixtures of probabilistic principal component analyzers
    • Tipping M.E., Bishop C.M. Mixtures of probabilistic principal component analyzers. Neural Computation 1999, 11:443-482.
    • (1999) Neural Computation , vol.11 , pp. 443-482
    • Tipping, M.E.1    Bishop, C.M.2
  • 44
    • 0025608647 scopus 로고
    • An analysis of Kohonens self-organizing maps using a system of energy functions
    • Tolat V. An analysis of Kohonens self-organizing maps using a system of energy functions. Biological Cybernetics 1990, 64:155-164.
    • (1990) Biological Cybernetics , vol.64 , pp. 155-164
    • Tolat, V.1
  • 45
    • 0031097231 scopus 로고    scopus 로고
    • Topology preservation in self-organizing feature maps: exact definition and measurement
    • Villmann T., Der R., Herrmann M., Martinetz T. Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Transactions on Neural Networks 1997, 8(2):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
  • 46
    • 0034187075 scopus 로고    scopus 로고
    • Probabilistic principal component subspaces: a hierarchical finite mixture model for data visualization
    • Wang Y., Freedman M.I., Kung S.-K. Probabilistic principal component subspaces: a hierarchical finite mixture model for data visualization. IEEE Transactions on Neural Networks 2000, 11(3):625-636.
    • (2000) IEEE Transactions on Neural Networks , vol.11 , Issue.3 , pp. 625-636
    • Wang, Y.1    Freedman, M.I.2    Kung, S.-K.3
  • 48
    • 0035272084 scopus 로고    scopus 로고
    • Self-organizing mixture networks for probability density estimation
    • Yin H., Allinson N.M. Self-organizing mixture networks for probability density estimation. IEEE Transactions on Neural Networks 2001, 12(2):405-411.
    • (2001) IEEE Transactions on Neural Networks , vol.12 , Issue.2 , pp. 405-411
    • Yin, H.1    Allinson, N.M.2


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