University of Groningen
Statistical physics of learning vector quantization
Witoelar, Aree Widya
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Witoelar, A. W. (2010). Statistical physics of learning vector quantization. Groningen: s.n.
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Bibliography
Ahr, M., Biehl, M. and Schloesser, E.: 1999, Weight decay induced phase transitions in multi-layer neural networks, Journal of Physics A: Mathematical and General 32, 5003–5008. Ahr, M., Biehl, M. and Urbanczik, R.: 1999, Statistical physics and practical training of
soft-committee machines, The European Physical Journal B 10, 583–588.
Barber, D. and Sollich, P.: 1998, Online learning from finite training sets, Europhysics Letters
38, 279–302.
Barkai, N., Seung, H. and Sompolinsky, H.: 1993, Scaling laws in learning of classification tasks, Phys. Rev. Lett. 70 70, 3167–3170.
Baum, E. and Haussler, D.: 1989, What size net gives valid generalization?, Neural
Computa-tion 1, 151–160.
Bengio, Y.: 2000, Gradient-based optimization of hyperparameters, Neural Computation
12(8), 1889–1900.
Bermejo, S. and Cabestany, J.: 2000, A batch learning vector quantization algorithm for nearest neighbour classification, Neural Processing Letters 11(3), 173–184.
Bezdek, J.: 1981, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York.
Biehl, M.: 1994, An exactly solvable model of unsupervised learning, Europhysics Letters
25(5), 391–396.
Biehl, M. and Caticha, N.: 2003, The statistical mechanics of on-line learning and generaliza-tion, The handbook of brain theory and neural networks pp. 1095–1098.
Biehl, M., Freking, A., Ghosh, A. and Reents, G.: 2004, A theoretical framework for analysing the dynamics of LVQ: A statistical physics approach, Technical Report
2004-9-02, Mathematics and Computing Science, University of Groningen . Available on-line:
http://www.cs.rug.nl/∼biehl.
Biehl, M., Ghosh, A. and Hammer, B.: 2006, Learning vector quantization: The dynamics of winner-takes-all algorithms, Neurocomputing 69, 660–670.
Biehl, M., Ghosh, A. and Hammer, B.: 2007, Dynamics and generalization ability of LVQ algorithms, Journal of Machine Learning Research 8, 323–360.
Biehl, M. and Mietzner, A.: 1994, Statistical mechanics of unsupervised structure recognition,
J. Phys. A 27, 1885–1897.
Biehl, M., Schl ¨osser, E. and Ahr, M.: 1998, Phase transitions in soft-committee machines,
Eu-rophys. Lett. 44(2), 261–267.
Bojer, T., Hammer, B. and Koers, C.: 2003, Monitoring technical systems with prototype based clustering, in M. Verleysen (ed.), European Symposium on Artificial Neural Networks
(ESANN), d-side, Evere, Belgium, pp. 433–439.
Bojer, T., Hammer, B., Schunk, D. and von Toschanowitz, K. T.: 2001, Relevance determina-tionin learning vector quantization, in M. Verleysen (ed.), European Symposium on
Artifi-cial Neural Networks (ESANN), d-side, Evere, Belgium, pp. 271–276.
Bottou, L.: 1991, Stochastic gradient learning in neural networks, Proceedings of Neuro-Nˆımes
91, EC2, Nimes, France.
Bottou, L. and Bengio, Y.: 1995, Convergence properties of the k-means, NIPS 1994, pp. 585– 592.
Buhmann, J. M.: 1998, Stochastic algorithms for exploratory data analysis: Data clustering and data visualization, In Learning in Graphical Models, Kluwer, pp. 405–420.
Buhot, A., Gordon, M. and Nadal, J.: 2002, Rigorous bounds to retarded learning, Phys. Rev.
Lett. 88(9), 099801.
Carnevali, P. and Patarnello, S.: 1987, Exhaustive thermodynamic analysis of boolean learning networks, Europhys. Lett. pp. 1199–1204.
Cortes, C. and Vapnik, V.: 1995, Support-vector networks, Machine Learning 20(3), 273–297. Cottrell, M., Hammer, B., Hasenfuß, A. and Villmann, T.: 2006, Batch and median neural gas,
Neural Networks 19(6), 762–771.
Crammer, K., Gilad-bachrach, R., Navot, A. and Tishby, N.: 2002, Margin analysis of the lvq algorithm, Advances in Neural Information Processing Systems 2002, MIT press, pp. 462– 469.
del Giudice, P., Franz, S. and Virasoro, M. A.: 1989, Perceptron beyond the limit of capacity,
Journal de Physique 50(2), 121–134.
Duda, R., Hart, P. and Stork, D.: 2000, Pattern Classification, Wiley, New York.
Edwards, S. and P.W, A.: 1975, Theory of spin glasses, Journal of Physics F: Metal Physics
5(5), 965–974.
Engel, A. and van den Broeck, C.: 2001, The Statistical Mechanics of Learning, Cambridge Uni-versity Press, Cambridge, UK.
Gersho, A. and Gray, R. M.: 1991, Vector quantization and signal compression, Kluwer Academic Publishers, Norwell, MA, USA.
Ghosh, A., Biehl, M. and Hammer, B.: 2006, Performance analysis of LVQ algorithms: a sta-tistical physics approach, Neural Networks 19, 817–829.
Hammer, B., Hasenfuss, A., Schleif, F. and Villmann, T.: 2006, Supervised batch neural gas,
Artificial Neural Networks in Pattern Recognition, Vol. 4087, Springer, pp. 33–45.
Hammer, B., Strickert, M. and Villmann, T.: 2003, On the generalization ability of grlvq net-works, Neural Processing Letters, p. 10.
Hammer, B., Strickert, M. and Villmann, T.: 2004, Relevance lvq versus svm, Artificial
Intel-ligence and Softcomputing, volume 3070 of Springer Lecture Notes in Artificial IntelIntel-ligence,
Springer, pp. 592–597.
Hammer, B. and Villmann, T.: 2002, Generalized relevance learning vector quantization,
Neu-ral Networks 15(8-9), 1059 – 1068.
Han, J. and Kamber, M.: 2005, Data Mining: Concepts and Techniques, Morgan Kaufmann Pub-lishers Inc.
Hansel, D. and Sompolinsky, H.: 1990, Learning from examples in a single-layer neural net-work, Europhys. Lett. 11, 687.
Herschkowitz, D. and Opper, M.: 2001, Retarded learning: Rigorous results from statistical mechanics, Phys. Rev. Lett. 86(10), 2174–2177.
Huang, K.: 1987, Statistical mechanics, 2nd ed. edn, Wiley, New York.
Jain, A. K., Murty, M. N. and Flynn, P. J.: 1999, Data clustering: a review, ACM Comput. Surv.
31(3), 264–323.
Kinzel, W.: 1997, Phase transitions of neural networks, Phil. Mag. B 77, 1455–1477.
Kohonen, T.: 1990, Improved versions of learning vector quantization, Neural Networks, 1990.,
1990 IJCNN International Joint Conference on, Vol. 1, pp. 545–550.
Kohonen, T.: 1997, Self Organising Maps, Springer, Berlin 2nd ed.
Kuncheva, L.: 2004, Classifier ensembles for changing environments, in F. Roli, J. Kittler and T. Windeatt (eds), Multiple Classifier Ensembles: 5th International Workshop, MCS 2004,
Cagliari, Italy, Vol. 3077 of Lecture Notes in Computer Science, Springer, Berlin, pp. 1–15.
Levin, E., Tishby, N. and Solla, S.: 1990, A statistical approach to learning and generalization in layered neural networks, Proceedings of the IEEE, Vol. 78, pp. 1568–1574.
Lootens, E. and van den Broeck, C.: 1995, Analysing cluster formation by replica method,
Europhys. Lett. 30, 381–387.
Lyman, P. and Varian, H. R.: 2003, How much information. Retrieved from http://www.sims.berkeley.edu/how-much-info-2003 on 19 Jan 2010.
Martinetz, T., Berkovich, S. and Schulten, K.: 1993, ’neural gas’ network for vector quantiza-tion and its applicaquantiza-tion to time series predicquantiza-tion, IEEE TNN 4(4), 558–569.
Meir, R.: 1995, Empirical risk minimization versus maximum-likelihood estimation: a case study, Neural computation 7, 144–157.
Mezard, M., Parisi, G. and Virasoro, M.: 1987, Spin Glass Theory and Beyond, Singapore: World Scientific.
Neural Networks Research Centre, Helsinki: 2002, Bibliography on the self-organizing maps (SOM) and learning vector quantization (LVQ), Otaniemi: Helsinki Univ. of Technology . Available on-line: http://liinwww.ira.uka.de/bibliography/Neural/SOM.LVQ.html . Opper, M.: 1994, Learning and generalization in a two-layer neural network: The role of the
vapnik-chervonenkis dimension, Phys. Rev. Lett. 72(13), 2113–2116.
Pregenzer, M., Pfurtscheller, G. and Flotzinger, D.: 1996, Automated feature selection with a distinction sensitive learning vector quantizer, Neurocomputing 11(1), 19 – 29.
Rae, H., Sollich, P. and Coolen, A.: 1999, On-line learning with restricted training sets: An exactly solvable case, Journal of Physics A: Mathematical and General 32(18), 3321–3339. Reents, G. and Urbanczik, R.: 1998, Self averaging and on-line learning, Phys. Rev. Letter
80, 5445–5448.
Ripley, B.: 1996, Pattern Recognition and Neural Networks, Cambridge University Press. Saad, D. (ed.): 1999, Online learning in neural networks, Cambridge University Press,
Cam-bridge, UK.
Saad, D. and Rattray, M.: 1997, Globally optimal parameters for on-line learning in multilayer neural networks, Phys. Rev. Lett. 79(13), 2578–2581.
Saad, D. and Solla, S.: 1995, On-line learning in soft committee machines, Phys. Rev. E
52(4), 4225–4243.
Sato, A. and Yamada, K.: 1995, Generalized learning vector quantization, NIPS, pp. 423–429. Schleif, F., Villmann, T. and Hammer, B.: 2006, Local metric adaptation for soft nearest
pro-totype classification to classify proteomic data, International Workshop on Fuzzy Logic and
Applications 3849, 290–296.
Schneider, P., Biehl, M. and Hammer, B.: 2009, Adaptive relevance matrices in learning vector quantization, Neural Computation pp. 1–30. PMID: 19764875.
Schottky, B.: 1995, Phase transitions in the generalization behaviour of multilayer neural net-works, Journal of Physics A: Mathematical and General 28(16), 4515.
Seo, S. and Obermayer, K.: 2003, Soft learning vector quantization, Neural Computation
15, 1589–1604.
Seo, S. and Obermayer, K.: 2006, Dynamic hyperparameter scaling method for lvq algorithms,
International Joint Conference on Neural Networks, pp. 3196–3203.
Seung, H., Sompolinsky, H. and Tishby, N.: 1992, Statistical mechanics of learning from ex-amples, Physical Review A 45(8), 6056–6091.
Solla, S. A. and Levin, E.: 1992, Learning in linear neural networks: The validity of the an-nealed approximation, Physical Review A 46, 2124–2130.
Sompolinsky, H. and Tishby, N.: 1990, Learning in a two-layer neural network of edge detec-tors, Europhys. Lett. 13:6, 567–572.
Strickert, M., Seiffert, U., Sreenivasulu, N., Weschke, W., Villmann, T. and Hammer, B.: 2006, Generalized relevance lvq (grlvq) with correlation measures for gene expression analy-sis, Neurocomputing 69(7-9), 651 – 659. New Issues in Neurocomputing: 13th European Symposium on Artificial Neural Networks.
Sutton, R. and Barto, A.: 1998, Reinforcement learning, an introduction, MIT Press.
Tishby, N., Levin, E. and Solla, S.: 1989, Consistent inference of probabilities in layered net-works: predictions and generalizations, IJCNN International Joint Conference on Neural
Networks, pp. 403–409 vol.2.
Valiant, L. G.: 1984, A theory of the learnable, Commun. ACM 27(11), 1134–1142.
Vapnik, V.: 1995, The nature of statistical learning theory, Springer-Verlag New York, Inc., New York, NY, USA.
Villmann, T., Merenyi, E. and Hammer, B.: 2003, Neural maps in remote sensing image anal-ysis, Neural Networks 16(3-4), 389–403.
Watkin, T. and Nadal, J.: 1994, Optimal unsupervised learning, J. Phys. A 27, 1899–1915. Watkin, T., Rau, A. and Biehl, M.: 1993, The statistical mechanics of learning a rule, Reviews of
Modern Physics 65(2), 499–556.
Witoelar, A. and Biehl, M.: 2008, Equilibrium physics approach in vector quantization.,
Tech-nical Report, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen . Available on-line: http://www.cs.rug.nl/∼aree.
Witoelar, A. and Biehl, M.: 2009, Phase transitions in vector quantization and neural gas,
Neurocomputing 72, 1390–1397.
Witoelar, A., Biehl, M., Ghosh, A. and Hammer, B.: 2008, Learning dynamics and robustness of vector quantization and neural gas, Neurocomputing 71, 1210–1219.