This Article 
 Bibliographic References 
 Add to: 
Learning Vector Quantization with Training Data Selection
January 2006 (vol. 28 no. 1)
pp. 157-162
In this paper, we propose a method that selects a subset of the training data points to update LVQ prototypes. The main goal is to conduct the prototypes to converge at a more convenient location, diminishing misclassification errors. The method selects an update set composed by a subset of points considered to be at the risk of being captured by another class prototype. We associate the proposed methodology to a weighted norm, instead of the Euclidean, in order to establish different levels of relevance for the input attributes. The technique was implemented on a controlled experiment and on Web available data sets.

[1] A. Gersho, “Asymptotically Optimal Block Quantization,” IEEE Trans. Information Theory, vol. 25, pp. 373-380, 1979.
[2] P. Zador, “Asymptotic Quantization Error of Continuous Signals and the Quantization Dimension,” IEEE Trans. Information Theory, vol. 28, pp. 139-149, 1982.
[3] R.A. Jonson and D.W. Wichern, Applied Multivariable Statistical Analysis. Prentice Hall, 1998.
[4] T. Kohonen, “Self-Organized Formation of Topologically Correct Feature Maps,” Biological Cybernetics, vol. 43, p. 59, 1982.
[5] T. Kohonen, Self-Organizing Maps, third ed. Springer, 2001.
[6] T. Kohonen, “An Introduction to Neural Computing,” Neural Networks 1, pp. 3-16, 1988.
[7] R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, second ed. John Wiley, 2001.
[8] L. Bottou, “Stochastic Learning,” Lecture Notes in Artificial Intelligence, vol. 3176, pp. 146-168, 2004.
[9] T. Kohonen, G. Barna, and R. Chrisley, “Statistical Pattern Recognition with Neural Networks: Benchmarking Studies,” Proc. IEEE Int'l Conf. Neural Networks, 1988.
[10] A.S. Sato and K. Yamada, “Generalized Learning Vector Quantization,” Advances in Neural Information Processing Systems, G. Tesauro, D. Touretzky, and T. Leon, eds., vol. 7, pp. 423-429, 1995.
[11] B. Hammer and T. Villmann, “Generalized Relevance Learning Vector Quantization,” Neural Networks 15, pp. 1059-1068, 2002.
[12] A.K. Qin and P.N. Suganthan, “Initialization Insensitive LVQ Algorithm Based on Cost-Function Adaptation,” Pattern Recognition, 2005.
[13] M.T. Vakil-Baghmisheh and N. Pavesi, “Premature Clustering Phenomenon and New Training Algorithms for LVQ,” Pattern Recognition, vol. 36, no. 8, pp. 1901-1912, 2003.
[14] S. Seo and K. Obermayer, “Soft Learning Vector Quantization,” Neural Computation, vol. 15, no. 7, pp. 1589-1604, 2003.
[15] N.H. Harmon, Modern Factor Analysis. Univ. of Chicago Press, 1967.
[16] E. Oja, “Principal Component Analysis,” The Handbook of Brain Theory and Neural Networks, M. Arbib, ed. pp. 753-756, MIT Press, 1995.
[17] M. Girolami, Self-Organising Neural Networks: Independent Component Analysis and Blind Source Separation. Springer, 1999.
[18] L. Breiman, J.H. Friedman, R.A. Olshen, and C. Stone, Classification and Regression Trees, Belmont, Calif.: Wadsworth, 1984.
[19] R. Setiono and H. Liu, “Neural Network Feature Selector,” IEEE Trans. Neural Networks, vol. 8, pp. 654-661, 1997.
[20] R. Battiti, “Using Mutual Information for Selecting Features in Supervised Neural Net Learning,” IEEE Trans. Neural Networks, vol. 5, pp. 537-550, 1994.
[21] N. Kwak and C. Choi, “Input Feature Selection for Classification Problems,” IEEE Trans. Neural Networks, vol. 13, no. 1, pp. 143-159, 2002.
[22] I. Gath and A.B. Geva, “Unsupervised Optimal Fuzzy Clustering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 773-781, July 1989.
[23] V. Vapnik, The Nature of Statistical Learning Theory. Springer-Verlag, 1995.
[24] K. Crammer, R. Gilad-Bachrach, and A. Tishby, “Marging Analysis of the LVQ Algorithm,” Proc. 15th Ann. Conf. Neural Information Processing Systems, 2002.
[25] S. Haykin, Neural Networks: A Comprehensive Foundation. Prentice-Hall 1998.
[26] R.A. Fisher, “The Use of Multiple Measurements in Taxonomic Problems,” Ann. Eugenics, vol. 7, part II, pp. 179-188, 1936.
[27] R. Detrano, A. Janosi, W. Steinbrunn, M. Pfisterer, J. Schmid, S. Sandhu, K. Guppy, S. Lee, and V. Froelicher, “International Application of a New Probability Algorithm for the Diagnosis of Coronary Artery Disease,” Am. J. Cardiology, pp. 304-310, 1989.
[28] W.H. Wolberg and O.L. Mangasarian, “Multisurface Method of Pattern Separation for Medical Diagnosis Applied to Breast Cytology,” Proc. Nat'l Academy of Sciences, USA, vol. 87, pp. 9193-9196, 1990.
[29] O.L. Mangasarian, “Multisurface Method of Pattern Separation,” IEEE Trans. Information Theory, vol. 14, no. 6, pp. 801-807, Nov. 1968.
[30] F. Berzal, J.C. Cubero, F. Cuenca, and M. Martín-Bautista, “On the Quest for Easy-to-Understand Splitting Rules,” Data and Knowledge Eng., vol. 44, no. 1, pp. 31-48, 2003.

Index Terms:
Index Terms- Learning vector quantization LVQ, pattern classification, clustering, data selection, neural networks.
Carlos E. Pedreira, "Learning Vector Quantization with Training Data Selection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 1, pp. 157-162, Jan. 2006, doi:10.1109/TPAMI.2006.14
Usage of this product signifies your acceptance of the Terms of Use.