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Villmann T, Claussen JC (2005) Magnification Control in Self-Organizing Maps and Neural Gas Neural Comput 18:446-469


References and models cited by this paper		References and models that cite this paper
Ahalt SC, Krishnamurthy AK, Chen P, Melton DE (1990) Competitive learning algorithms for vector quantization Neural Netw 3:277-290 Amari S (1980) Topographic organization of nerve fields. Bull Math Biol 42:339-64 [PubMed] Bauer H, Herrmann M, Villmann T (1999) Neural maps and topographic vector quantization. Neural Netw 12:659-676 [PubMed] Bauer HU, Der R, Herrmann M (1996) Controlling the magnification factor of self-organizing feature maps. Neural Comput 8:757-771 Bauer HU, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans Neural Netw 3:570-9 [Journal] [PubMed] Bishop CM, Svensen M, Williams CKI (1998) GTM: The Generative Topographic Mapping Neural Comput 10:215-235 Brause R (1992) Optimal information distribution and performance in neighbourhood-conserving maps for robot control Int J Computers And Artificial Intelligence 11:173-199 Brause RW (1994) An approximation network with maximal transinformation International Conference On Artificial Neural Networks, Marinaro M:Morasso PG, ed. pp.701 Bruske J, Sommer G (1998) Intrinsic dimensionality estimation with optimally topology preserving maps IEEE Transactions On Pattern Analysis And Machine Intelligence 20:572-575 Camastra F, Vinciarelli A (2001) Intrinsic dimension estimation of data: An approach based on Grassberger-Procaccia's algorithm Neural Proc Lett 14:27-34 Claussen JC (2003) Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner Complexity 8:15-22 Claussen JC (2005) Winner-relaxing self-organizing maps Neural Comput 17:997-1009 Claussen JC, Schuster HG (2002) Asymptotic level density of the elastic net self-organizing feature map Proc. International Conf. on Artificial Neural Networks (ICANN), Dorronsoro JR, ed. pp.939 Claussen JC, Villmann TH (2005) Magnification control in winner-relaxing neural gas Neurocomputing 63:125-137 Claussen JC, Villmann TH (2003) Magnification control in winner relaxing neural gas Proc. of European Symposium on Artificial Neural Networks (ESANN2003) :93-98 Claussen JC, Villmann TH (2003) Magnification control in neural gas by winner relaxing learning: Independence of a diagonal term Proc. International Conference on Artificial Neural Networks (ICANN2003), Kaynak O:Alpaydin E:Oja E:Xu L, ed. pp.58 Cottrell M, Fort JC, Pages G (1998) Theoretical aspects of the SOM algorithm Neurocomputing 21:119-138 de_Bodt E, Cottrell M, Letremy P, Verleysen M (2004) On the use of self-orgainzing maps to accelerate vector quantization Neurocomputing 17:187-203 Der R, Herrmann M (1992) Attention based partitioning Bericht des Status-Seminar des BMFT Neuroinformatik, van_der_Meer M, ed. pp.441 Dersch DR, Tavan P (1995) Asymptotic level density in topological feature maps. IEEE Trans Neural Netw 6:230-6 [Journal] [PubMed] Desieno D (1988) Adding a conscience to competitive learning Proc Icnn88, International Conference On Neural Networks :117-124 Duda RO, Hart PE (1973) Pattern Classification and Scene Analysis Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689-91 [Journal] [PubMed] Eckmann JP, Ruelle D (1992) Fundamental limitations for estimating dimensions and lyaponov exponents in dynamic systems Phys D 56:185-187 Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47-55 [PubMed] Fritzke B (1993) Vector quantization with a growing and splitting elastic net Proc. ICANN93, International Conference on Artificial Neural Networks, Gielen S:Kappen B, ed. pp.580 Galanopoulos AS, Ahalt SC (1996) Codeword distribution for frequency sensitive competitive learning with one-dimensional input data. IEEE Trans Neural Netw 7:752-6 [Journal] [PubMed] Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors Physica 9:189-208 Hammer B, Villmann TH (2003) Mathematical aspects of neural networks Proc. of European Symposium on Artificial Neural Networks (ESANN2003), Verleysen M, ed. pp.59 Haykin S (1994) Neural Networks: A Comprehensive Foundation :363-370 Herrmann M, Bauer HU, Der R (1994) The fiperceptual magnetfi effect: A model based on self-organizing feature maps. Neural computation and psychology, Smith LS:Hancock PJB, ed. pp.107 Herrmann M, Villmann TH (1997) Vector quantization by optimal neural gas Artificial Neural Networks-Proceedings of International Conference on Artificial Neural Networks (ICANN97), Gerstner W:Germond A:Hasler M:Nicoud JD, ed. pp.625 Hertz J, Krogh A, Palmer RG (1991) Introduction to the Theory of Neural Computation. Heskes T (1999) Energy functions for self-organizing maps Kohonen maps, Oja E:Kaski S, ed. pp.303 Jain A, Merenyi E (2004) Forbidden magnification? I European symposium on artificial neural networks 2004, Verleysen M, ed. pp.51 Kohonen T (1991) Self-organizing maps: Optimization approaches Artificial Neural Networks, Kohonen T:Makisara K:Simula O:Kangas J, ed. pp.981 Kohonen T (1995) Self-organizing Maps Kohonen T (1999) Comparison of SOM point densities based on different criteria. Neural Comput 11:2081-95 [PubMed] Kuhl PK (1991) Human adults and human infants show a "perceptual magnet effect" for the prototypes of speech categories, monkeys do not. Percept Psychophys 50:93-107 [PubMed] Kuhl PK, Williams KA, Lacerda F, Stevens KN, Lindblom B (1992) Linguistic experience alters phonetic perception in infants by 6 months of age. Science 255:606-8 [PubMed] Liebert W (1991) Chaos und Herzdynamik Linde Y, Buzo A, Gray RM (1980) An algorithm for vector Quantizer design Ieee Transactions On Communications 28:84-95 Linsker R (1989) How to generate maps by maximizing the mutual information between input and output signals Neural Comput 1:402-411 Luttrell SP (1991) Code vector density in topographic mappings: Scalar case. IEEE Trans Neural Netw 2:427-36 [Journal] [PubMed] Martinetz TH, Schulten K (1994) Topology representing networks Neural Networks 7:507-522 Martinetz TM, Berkovich SG, Schulten KJ (1993) ;Neural-gas' network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4:558-69 [Journal] [PubMed] Merenyi E, Jain A (2004) Forbidden magnification? II European Symposium on Artificial Neural Networks 2004, Verleysen M, ed. pp.57 Ripley BD (1996) Pattern recognition and neural networks Ritter H (1989) Asymptotic level density for a class of vector quantization processes Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Netw 2:173-5 [Journal] [PubMed] Ritter H, Martinetz T, Schulten K (1992) Neural Computation and Self-Organizing Maps: An Introduction. Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping Biol Cybern 54:99-106 Takens F (1985) On the numerical determination of the dimension of an attractor Dynamical systems and bifurcations, Braaksma B:Broer H:Takens F, ed. pp.99 Theiler J (1990) Statistical precision of dimension estimators. Phys Rev A 41:3038-3051 [PubMed] Van_hulle MM (2000) Faithful representations and topographic maps from distortion- to information-based self-organization Villmann T, Merényi E, Hammer B (2003) Neural maps in remote sensing image analysis. Neural Netw 16:389-403 [Journal] [PubMed] Villmann TH (1999) Benefits and limits of the self-organizing map and its variants in the area of satellite remote sensoring processing Proc. of European Symposium on Artificial Neural Networks (ESANN99) :111-116 Villmann TH (2000) Controlling strategies for the magnification factor in the neural gas network Neural Network World 10:739-750 Villmann TH (2002) Neural maps for faithful data modelling in medicine-state of the art and exemplary applications Neurocomputing 48:229-250 Villmann TH, Heinze A (2000) pplication of magnification control for the neural gas network in a sensorimotor architecture for robot navigation Proceedings of Selbstorganisation Von Adaptivem Verfahren (SOAVE2000) Ilmenau, Gross HM:Debes K:Bohme HJ, ed. pp.125 Villmann TH, Hermann W, Geyer M (2000) Variants of self-organizing maps for data mining and data visualization in medicine Neural Network World 10:751-762 Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc R Soc Lond B Biol Sci 194:431-45 [Journal] [PubMed] Zador PL (1982) Asymptotic quantization error of continuous signals and the quantization dimension IEEE Transaction On Information Theory 28:149-159 Zheng Y, Greenleaf JF (1996) The effect of concave and convex weight adjustments on self-organizing maps. IEEE Trans Neural Netw 7:87-96 [Journal] [PubMed]		Aoki T, Aoyagi T (2007) Self-organizing maps with asymmetric neighborhood function. Neural Comput 19:2515-35 [Journal] [PubMed]

References and models cited by this paper

References and models that cite this paper

Ahalt SC, Krishnamurthy AK, Chen P, Melton DE (1990) Competitive learning algorithms for vector quantization Neural Netw 3:277-290

Amari S (1980) Topographic organization of nerve fields. Bull Math Biol 42:339-64 [PubMed]

Bauer H, Herrmann M, Villmann T (1999) Neural maps and topographic vector quantization. Neural Netw 12:659-676 [PubMed]

Bauer HU, Der R, Herrmann M (1996) Controlling the magnification factor of self-organizing feature maps. Neural Comput 8:757-771

Bauer HU, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans Neural Netw 3:570-9 [Journal] [PubMed]

Bishop CM, Svensen M, Williams CKI (1998) GTM: The Generative Topographic Mapping Neural Comput 10:215-235

Brause R (1992) Optimal information distribution and performance in neighbourhood-conserving maps for robot control Int J Computers And Artificial Intelligence 11:173-199

Brause RW (1994) An approximation network with maximal transinformation International Conference On Artificial Neural Networks, Marinaro M:Morasso PG, ed. pp.701

Bruske J, Sommer G (1998) Intrinsic dimensionality estimation with optimally topology preserving maps IEEE Transactions On Pattern Analysis And Machine Intelligence 20:572-575

Camastra F, Vinciarelli A (2001) Intrinsic dimension estimation of data: An approach based on Grassberger-Procaccia's algorithm Neural Proc Lett 14:27-34

Claussen JC (2003) Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner Complexity 8:15-22

Claussen JC (2005) Winner-relaxing self-organizing maps Neural Comput 17:997-1009

Claussen JC, Schuster HG (2002) Asymptotic level density of the elastic net self-organizing feature map Proc. International Conf. on Artificial Neural Networks (ICANN), Dorronsoro JR, ed. pp.939

Claussen JC, Villmann TH (2005) Magnification control in winner-relaxing neural gas Neurocomputing 63:125-137

Claussen JC, Villmann TH (2003) Magnification control in winner relaxing neural gas Proc. of European Symposium on Artificial Neural Networks (ESANN2003) :93-98

Claussen JC, Villmann TH (2003) Magnification control in neural gas by winner relaxing learning: Independence of a diagonal term Proc. International Conference on Artificial Neural Networks (ICANN2003), Kaynak O:Alpaydin E:Oja E:Xu L, ed. pp.58

Cottrell M, Fort JC, Pages G (1998) Theoretical aspects of the SOM algorithm Neurocomputing 21:119-138

de_Bodt E, Cottrell M, Letremy P, Verleysen M (2004) On the use of self-orgainzing maps to accelerate vector quantization Neurocomputing 17:187-203

Der R, Herrmann M (1992) Attention based partitioning Bericht des Status-Seminar des BMFT Neuroinformatik, van_der_Meer M, ed. pp.441

Dersch DR, Tavan P (1995) Asymptotic level density in topological feature maps. IEEE Trans Neural Netw 6:230-6 [Journal] [PubMed]

Desieno D (1988) Adding a conscience to competitive learning Proc Icnn88, International Conference On Neural Networks :117-124

Duda RO, Hart PE (1973) Pattern Classification and Scene Analysis

Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689-91 [Journal] [PubMed]

Eckmann JP, Ruelle D (1992) Fundamental limitations for estimating dimensions and lyaponov exponents in dynamic systems Phys D 56:185-187

Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47-55 [PubMed]

Fritzke B (1993) Vector quantization with a growing and splitting elastic net Proc. ICANN93, International Conference on Artificial Neural Networks, Gielen S:Kappen B, ed. pp.580

Galanopoulos AS, Ahalt SC (1996) Codeword distribution for frequency sensitive competitive learning with one-dimensional input data. IEEE Trans Neural Netw 7:752-6 [Journal] [PubMed]

Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors Physica 9:189-208

Hammer B, Villmann TH (2003) Mathematical aspects of neural networks Proc. of European Symposium on Artificial Neural Networks (ESANN2003), Verleysen M, ed. pp.59

Haykin S (1994) Neural Networks: A Comprehensive Foundation :363-370

Herrmann M, Bauer HU, Der R (1994) The fiperceptual magnetfi effect: A model based on self-organizing feature maps. Neural computation and psychology, Smith LS:Hancock PJB, ed. pp.107

Herrmann M, Villmann TH (1997) Vector quantization by optimal neural gas Artificial Neural Networks-Proceedings of International Conference on Artificial Neural Networks (ICANN97), Gerstner W:Germond A:Hasler M:Nicoud JD, ed. pp.625

Hertz J, Krogh A, Palmer RG (1991) Introduction to the Theory of Neural Computation.

Heskes T (1999) Energy functions for self-organizing maps Kohonen maps, Oja E:Kaski S, ed. pp.303

Jain A, Merenyi E (2004) Forbidden magnification? I European symposium on artificial neural networks 2004, Verleysen M, ed. pp.51

Kohonen T (1991) Self-organizing maps: Optimization approaches Artificial Neural Networks, Kohonen T:Makisara K:Simula O:Kangas J, ed. pp.981

Kohonen T (1995) Self-organizing Maps

Kohonen T (1999) Comparison of SOM point densities based on different criteria. Neural Comput 11:2081-95 [PubMed]

Kuhl PK (1991) Human adults and human infants show a "perceptual magnet effect" for the prototypes of speech categories, monkeys do not. Percept Psychophys 50:93-107 [PubMed]

Kuhl PK, Williams KA, Lacerda F, Stevens KN, Lindblom B (1992) Linguistic experience alters phonetic perception in infants by 6 months of age. Science 255:606-8 [PubMed]

Liebert W (1991) Chaos und Herzdynamik

Linde Y, Buzo A, Gray RM (1980) An algorithm for vector Quantizer design Ieee Transactions On Communications 28:84-95

Linsker R (1989) How to generate maps by maximizing the mutual information between input and output signals Neural Comput 1:402-411

Luttrell SP (1991) Code vector density in topographic mappings: Scalar case. IEEE Trans Neural Netw 2:427-36 [Journal] [PubMed]

Martinetz TH, Schulten K (1994) Topology representing networks Neural Networks 7:507-522

Martinetz TM, Berkovich SG, Schulten KJ (1993) ;Neural-gas' network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4:558-69 [Journal] [PubMed]

Merenyi E, Jain A (2004) Forbidden magnification? II European Symposium on Artificial Neural Networks 2004, Verleysen M, ed. pp.57

Ripley BD (1996) Pattern recognition and neural networks

Ritter H (1989) Asymptotic level density for a class of vector quantization processes

Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Netw 2:173-5 [Journal] [PubMed]

Ritter H, Martinetz T, Schulten K (1992) Neural Computation and Self-Organizing Maps: An Introduction.

Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping Biol Cybern 54:99-106

Takens F (1985) On the numerical determination of the dimension of an attractor Dynamical systems and bifurcations, Braaksma B:Broer H:Takens F, ed. pp.99

Theiler J (1990) Statistical precision of dimension estimators. Phys Rev A 41:3038-3051 [PubMed]

Van_hulle MM (2000) Faithful representations and topographic maps from distortion- to information-based self-organization

Villmann T, Merényi E, Hammer B (2003) Neural maps in remote sensing image analysis. Neural Netw 16:389-403 [Journal] [PubMed]

Villmann TH (1999) Benefits and limits of the self-organizing map and its variants in the area of satellite remote sensoring processing Proc. of European Symposium on Artificial Neural Networks (ESANN99) :111-116

Villmann TH (2000) Controlling strategies for the magnification factor in the neural gas network Neural Network World 10:739-750

Villmann TH (2002) Neural maps for faithful data modelling in medicine-state of the art and exemplary applications Neurocomputing 48:229-250

Villmann TH, Heinze A (2000) pplication of magnification control for the neural gas network in a sensorimotor architecture for robot navigation Proceedings of Selbstorganisation Von Adaptivem Verfahren (SOAVE2000) Ilmenau, Gross HM:Debes K:Bohme HJ, ed. pp.125

Villmann TH, Hermann W, Geyer M (2000) Variants of self-organizing maps for data mining and data visualization in medicine Neural Network World 10:751-762

Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc R Soc Lond B Biol Sci 194:431-45 [Journal] [PubMed]

Zador PL (1982) Asymptotic quantization error of continuous signals and the quantization dimension IEEE Transaction On Information Theory 28:149-159

Zheng Y, Greenleaf JF (1996) The effect of concave and convex weight adjustments on self-organizing maps. IEEE Trans Neural Netw 7:87-96 [Journal] [PubMed]

Aoki T, Aoyagi T (2007) Self-organizing maps with asymmetric neighborhood function. Neural Comput 19:2515-35 [Journal] [PubMed]

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