PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
  • Sesja wygasła!
Tytuł artykułu

Aspects in Classification Learning - Review of Recent Developments in Learning Vector Quantization

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Classification is one of the most frequent tasks in machine learning. However, the variety of classification tasks as well as classifier methods is huge. Thus the question is coming up: which classifier is suitable for a given problem or how can we utilize a certain classifier model for different tasks in classification learning. This paper focuses on learning vector quantization classifiers as one of the most intuitive prototype based classification models. Recent extensions and modifications of the basic learning vector quantization algorithm, which are proposed in the last years, are highlighted and also discussed in relation to particular classification task scenarios like imbalanced and/or incomplete data, prior data knowledge, classification guarantees or adaptive data metrics for optimal classification.
Rocznik
Strony
79--105
Opis fizyczny
Bibliogr. 112 poz.
Twórcy
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
autor
  • Computational Intelligence Group at the University of Applied Sciences Mittweida, Dept. of Mathematics, Technikumplatz 17, 09648 Mittweida, Saxonia - Germany
Bibliografia
  • [1] F. Aiolli and A. Sperduti. A re-weighting strategy for improving margins. Artifiical Intelligence, 137:197-216, 2002.
  • [2] N. Aronszajn. Theory of reproducing kernels. Transactions of the American Mathematical Society, 68:337-404, 1950.
  • [3] A. Backhaus and U. Seiffert. Classification in high-dimensional spectral data: Accuracy vs. interpretability vs. model size. Neurocomputing, page in press, 2014.
  • [4] Y. Bengio. Learning deep architectures for AI. Foundations and Trends in Machine Learning, 2(1):1-127, 2009.
  • [5] B.Hammer and A.Hasenfuss. Relational neural gas. Künstliche Intelligenz, pages 190-204, 2007.
  • [6] M. Biehl. Admire LVQ: Adaptive distance measures in relevance Learning Vector Quantization. KI - Künstliche Intelligenz, 26:391-395, 2012.
  • [7] M. Biehl, K. Bunte, and P. Schneider. Analysis of flow cytometry data by matrix relevance learning vector quantization. PLoS ONE, 8(3):e59401, 2013.
  • [8] M. Biehl, A. Ghosh, and B. Hammer. Dynamics and generalization ability of LVQ algorithms. Journal of Machine Learning Research, 8:323-360, 2007.
  • [9] M. Biehl, B. Hammer, and T. Villmann. Distance measures for prototype based classification. In N. Petkov, editor, Proceedings of the International Workshop on Brain-Inspired Computing 2013 (Cetraro/Italy), page in press. Springer, 2014.
  • [10] M. Biehl, M. Kaden, and T. Villmann. Statistical quality measures and ROC-optimization by learning vector quantization classifiers. In H. Kestler, M. Schmid, H. Binder, and B. Bischl, editors, Proceedings of the 46th Workshop on Statistical Computing (Ulm/Reisensburg 2014), number 2014-xxx in Ulmer Informatik-Berichte, page accepted. University Ulm, Germany, 2014.
  • [11] M. Biehl, P. Schneider, D. Smith, H. Stiekema, A. Taylor, B. Hughes, C. Shackleton, P. Stewart, and W. Arlt. Matrix relevance LVQ in steroid metabolomics based classification of adrenal tumors. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2012), pages 423-428, Louvain-La-Neuve, Belgium, 2012. i6doc.com.
  • [12] C. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
  • [13] T. Bojer, B. Hammer, D. Schunk, and T. von Toschanowitz K. Relevance determination in learning vector quantization. In 9th European Symposium on Artificial Neural Networks. ESANN’2001. Proceedings. D-Facto, Evere, Belgium, pages 271-6, 2001.
  • [14] C. Bouveyron, S. Girard, and C. Schmid. High-dimensional data clustering. Computational Statistics and Data Analysis, 57(1):502-519, 2007.
  • [15] A. Bradley. The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition, 30(7):1149-1155, 1997.
  • [16] K. Bunte, P. Schneider, B. Hammer, F.-M. Schleif, T. Villmann, and M. Biehl. Limited rank matrix learning, discriminative dimension reduction and visualization. Neural Networks, 26(1):159-173, 2012.
  • [17] T. Calinski and J. Harabacz. A dendrite method for cluster analysis. Communications in Statistics, 3:1-27, 1974.
  • [18] K. Chidanananda and G. Krishna. The condensed nearest neighbor rule using the concept of mutual nearest neighborhood. IEEE Transactions on Information Theory, 25:488-490, 1979.
  • [19] C. Chow. On optimum recognition error and reject tradeoff. IEEE Transaction on Information Theory, 16(1):41-46, 1970.
  • [20] A. Cichocki, R. Zdunek, A. Phan, and S.-I. Amari. Nonnegative Matrix and Tensor Factorizations. Wiley, Chichester, 2009.
  • [21] R. Cilibrasi and P. Vitányi. Clustering by compression. IEEE Transactions on Information Theory, 51(4):1523-1545, 2005.
  • [22] T. Cover and P. Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13:21-27, 1967.
  • [23] K. Crammer, R. Gilad-Bachrach, A. Navot, and A.Tishby. Margin analysis of the LVQ algorithm. In S. Becker, S. Thrun, and K. Obermayer, editors, Advances in Neural Information Processing (Proc. NIPS 2002), volume 15, pages 462-469, Cambridge, MA, 2003. MIT Press.
  • [24] N. Cristianini and J. Shawe-Taylor. An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press, 2000.
  • [25] J. Davis and M. Goadrich. The relationship between precision-recall and ROC curves. In Proceedings of the 23rd International Conference on Machine Learning, ICML ’06, pages 233-240, New York, NY, USA, 2006. ACM.
  • [26] R. Duda and P. Hart. Pattern Classification and Scene Analysis. Wiley, New York, 1973.
  • [27] T. Fawcett. An introduction to ROC analysis. Pattern Recognition Letters, 27:861-874, 2006.
  • [28] L. Fischer, D. Nebel, T. Villmann, B. Hammer, and H. Wersing. Rejection strategies for learning vector quantization U a comparison of probabilistic and deterministic approaches. In T. Villmann, F.-M. Schleif, M. Kaden, and M. Lange, editors, Advances in Self-Organizing Maps: 10th International Workshop WSOM 2014 Mittweida, Advances in Intelligent Systems and Computing, page accepted, Berlin, 2014. Springer.
  • [29] R. Fisher. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2):179-188, 1936.
  • [30] T. Geweniger, P. Schneider, F.-M. Schleif, M. Biehl, and T. Villmann. Extending RSLVQ to handle data points with uncertain class assignments. Machine Learning Reports, 3(MLR-02-2009):1-17, 2009. ISSN:1865-3960, http://www.uni-leipzig.de/~compint/mlr/mlr_02_2009.pdf.
  • [31] T. Geweniger and T. Villmann. Extending FSNPC to handle data points with fuzzy class assignments. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks (ESANN’2010), pages 399-404, Evere, Belgium, 2010. d-side publications.
  • [32] T. Geweniger, D. Zühlke, B. Hammer, and T. Villmann. Median fuzzy c-means for clustering dissimilarity data. Neurocomputing, 73(7-9):1109-1116, 2010.
  • [33] Z. Gu, M. Shao, L. Li, and Y. Fu. Discriminative metric: Schatten norms vs. vector norm. In Proc. of The 21st International Conference on Pattern Recognition (ICPR 2012), pages 1213-1216, 2012.
  • [34] B. Hammer, M. Strickert, and T. Villmann. Relevance LVQ versus SVM. In L. Rutkowski, J. Siekmann, R. Tadeusiewicz, and L. Zadeh, editors, Artificial Intelligence and Soft Computing (ICAISC 2004), Lecture Notes in Artificial Intelligence 3070, pages 592-597. Springer Verlag, Berlin-Heidelberg, 2004.
  • [35] B. Hammer, M. Strickert, and T. Villmann. On the generalization ability of GRLVQ networks. Neural Processing Letters, 21(2):109-120, 2005.
  • [36] B. Hammer, M. Strickert, and T. Villmann. Supervised neural gas with general similarity measure. Neural Processing Letters, 21(1):21-44, 2005.
  • [37] B. Hammer and T. Villmann. Generalized relevance learning vector quantization. Neural Networks, 15(8-9):1059-1068, 2002.
  • [38] J. Hanley and B. McNeil. The meaning and use of the area under a receiver operating characteristic. Radiology, 143:29-36, 1982.
  • [39] P. Hart. The condensed nearest neighbor rule. IEEE Transactions on Information Theory, 14:515-516, 1968.
  • [40] T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer Verlag, Heidelberg-Berlin, 2001.
  • [41] S. Haykin. Neural Networks - A Comprehensive Foundation. IEEE Press, New York, 1994.
  • [42] R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 2nd edition, 2013.
  • [43] J. Huang and C. X. Ling. Using AUC and accuracy in evaluating learning algorithms. IEEE Transactions on Knowledge and Data Engineering, 17(3):299-310, 2005.
  • [44] M. Kaden, W. Hermann, and T. Villmann. Optimization of general statistical accuracy measures for classification based on learning vector quantization. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2014), pages 47-52, Louvain-La-Neuve, Belgium, 2014. i6doc.com.
  • [45] M. Kaden and T. Villmann. A framework for optimization of statistical classification measures based on generalized learning vector quantization. Machine Learning Reports, 7(MLR-02-2013):69-76, 2013. ISSN:1865-3960, http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_02_2013.pdf.
  • [46] M. Kaden and T. Villmann. Attention based classification learning in GLVQ and asymmetric classification error assessment. In T. Villmann, F.-M. Schleif, M. Kaden, and M. Lange, editors, Advances in Self-Organizing Maps: 10th International Workshop WSOM 2014 Mittweida, Advances in Intelligent Systems and Computing, page accepted, Berlin, 2014. Springer.
  • [47] M. Kästner, D. Nebel, M. Riedel, M. Biehl, and T. Villmann. Differentiable kernels in generalized matrix learning vector quantization. In Proc. of the Internacional Conference of Machine Learning Applications (ICMLA’12), pages 1-6. IEEE Computer Society Press, 2012.
  • [48] M. Kästner, M. Riedel, M. Strickert, W. Hermann, and T. Villmann. Bordersensitive learning in kernelized learning vector quantization. In I. Rojas, G. Joya, and J. Cabestany, editors, Proc. of the 12th International Workshop on Artificial Neural Networks (IWANN), volume 7902 of LNCS, pages 357-366, Berlin, 2013. Springer.
  • [49] M. Kästner, M. Strickert, D. Labudde, M. Lange, S. Haase, and T. Villmann. Utilization of correlation measures in vector quantization for analysis of gene expression data - a review of recent developments. Machine Learning Reports, 6(MLR-04-2012):5-22, 2012. ISSN:1865-3960, http://www.techfak.unibielefeld.de/~fschleif/mlr/mlr_04_2012.pdf.
  • [50] S. Keerthi, O. Chapelle, and D. DeCoste. Building support vector machines with reduced classifier complexity. Journal of Machine Learning Research, 7:1493-1515, 2006.
  • [51] T. Kohonen. Automatic formation of topological maps of patterns in a selforganizing system. In E. Oja and O. Simula, editors, Proc. 2SCIA, Scand. Conf. on Image Analysis, pages 214-220, Helsinki, Finland, 1981. Suomen Hahmontunnistustutkimuksen Seura r. y.
  • [52] T. Kohonen. Self-Organizing Maps, volume 30 of Springer Series in Information Sciences. Springer, Berlin, Heidelberg, 1995. (Second Extended Edition 1997).
  • [53] T. Kohonen, J. Kangas, J. Laaksonen, and K. Torkkola. LVQ_PAK: A program package for the correct application of Learning Vector Quantization algorithms. In Proc. IJCNN’92, International Joint Conference on Neural Networks, volume I, pages 725-730, Piscataway, NJ, 1992. IEEE Service Center.
  • [54] M. Lange. Partielle Korrelationen und Partial Mutual Information zur Analyse von fMRT-Zeitreihen. Master’s thesis, University of Applied Sciences Mittweida, Mittweida, Saxony, Germany, 2012.
  • [55] M. Lange, M. Biehl, and T. Villmann. Non-Euclidean principal component analysis by Hebbian learning. Neurocomputing, page in press, 2014.
  • [56] M. Lange, D. Nebel, and T. Villmann. Non-Euclidean principal component analysis for matrices by Hebbian learning. In L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L. Zadeh, and J. Zurada, editors, Artificial Intelligence and Soft Computing - Proc. the International Conference ICAISC, Zakopane, volume 1 of LNAI 8467, pages 77-88, Berlin Heidelberg, 2014. Springer.
  • [57] M. Lange and T. Villmann. Derivatives of lp-norms and their approximations. Machine Learning Reports, 7(MLR-04-2013):43-59, 2013. ISSN:1865-3960, http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_04_2013.pdf.
  • [58] M. Lange, D. Zühlke, O. Holz, and T. Villmann. Applications of lp-norms and their smooth approximations for gradient based learning vector quantization. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2014), pages 271-276, Louvain-La-Neuve, Belgium, 2014. i6doc.com.
  • [59] T. Martinetz and K. Schulten. Topology representing networks. Neural Networks, 7(2), 1994.
  • [60] T. M. Martinetz, S. G. Berkovich, and K. J. Schulten. ’Neural-gas’ network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks, 4(4):558-569, 1993.
  • [61] C. Micchelli, Y. Xu, and H. Zhang. Universal kernels. Journal of Machine Learning Research, 7:26051-2667, 2006.
  • [62] M.Strickert, B. Labitzke, A. Kolb, and T. Villmann. Multispectral image characterization by partial generalized covariance. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks (ESANN’2011), pages 105-110, Louvain-La-Neuve, Belgium, 2011. i6doc.com.
  • [63] E. Mwebaze, P. Schneider, F.-M. Schleif, J. Aduwo, J. Quinn, S. Haase, T. Villmann, and M. Biehl. Divergence based classification in learning vector quantization. Neurocomputing, 74(9):1429-1435, 2011.
  • [64] D. Nebel, B. Hammer, and T. Villmann. Supervised generative models for learning dissimilarity data. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2014), pages 35-40, Louvain-La-Neuve, Belgium, 2014. i6doc.com.
  • [65] D. Nebel and T. Villmann. About the equivalence of robust soft learning vector quantization and soft nearest prototype classification. Machine Learning Reports, 7(MLR-02-2013):114-118, 2013. ISSN:1865-3960, http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_02_2013.pdf.
  • [66] D. Nebel and T. Villmann. A median variant of generalized learning vector quantization. In M. Lee, A. Hirose, Z.-G. Hou, and R. Kil, editors, Proceedings of International Conference on Neural Information Processing (ICONIP), volume II of LNCS, pages 19-26, Berlin, 2013. Springer-Verlag.
  • [67] N. Niang and G. Saporta. Supervised classification and AUC. In Workshop Franco-Brésilien sur la fouille de données, pages 32-33, 2009.
  • [68] D. Nova and P. Estévez. A review of learning vector quantization classifiers. Neural Computation and Applications, 2013.
  • [69] J. Principe. Information Theoretic Learning. Springer, Heidelberg, 2010.
  • [70] J. C. Principe, J. F. III, and D. Xu. Information theoretic learning. In S. Haykin, editor, Unsupervised Adaptive Filtering. Wiley, New York, NY, 2000.
  • [71] A. Qin and P. Suganthan. Initialization insensitive LVQ algorithm based on cost-function adaptation. Pattern Recognition, 38:773 U-776, 2004.
  • [72] A. Qin and P. Suganthan. A novel kernel prototype-based learning algorithm. In Proceedings of the 17th International Conference on Pattern Recognition (ICPR’04), volume 4, pages 621-624, 2004.
  • [73] M. Riedel, D. Nebel, T. Villmann, and B. Hammer. Generative versus discriminative prototype based classification. In T. Villmann, F.-M. Schleif, M. Kaden, and M. Lange, editors, Advances in Self-Organizing Maps: 10th International Workshop WSOM 2014 Mittweida, Advances in Intelligent Systems and Computing, page accepted, Berlin, 2014. Springer.
  • [74] C. Rijsbergen. Information Retrieval. Butterworths, London, 2nd edition edition, 1979.
  • [75] F. Rosenblatt. The perceptron: A probabilistic model for information storage and organization in the brain. Psych. Rev., 65:386-408, 1958.
  • [76] L. Sachs. Angewandte Statistik. Springer Verlag, 7-th edition, 1992.
  • [77] A. Sato and K. Yamada. Generalized learning vector quantization. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems 8. Proceedings of the 1995 Conference, pages 423-9. MIT Press, Cambridge, MA, USA, 1996.
  • [78] R. Schatten. A Theory of Cross-Spaces, volume 26 of Annals of Mathematics Studies. Princeton University Press, 1950.
  • [79] F.-M. Schleif, T. Villmann, and B. Hammer. Prototype based fuzzy classification in clinical proteomics. International Journal of Approximate Reasoning, 47(1):4-16, 2008.
  • [80] F.-M. Schleif, T. Villmann, B. Hammer, and P. Schneider. Efficient kernelized prototype based classification. International Journal of Neural Systems, 21(6):443-457, 2011.
  • [81] F.-M. Schleif, T. Villmann, M. Kostrzewa, B. Hammer, and A. Gammerman. Cancer informatics by prototype networks in mass spectrometry. Artificial Intelligence in Medicine, 45(2-3):215-228, 2009.
  • [82] F.-M. Schleif, X. Zhu, and B. Hammer. A conformal classifier for dissimilarity data. In L. I. I. Maglogiannis, H. Papadopoulos, K. Karatzas, and S. Siouta, editors, Proceedings of AIAI 2012, Halkidiki, Greece, volume 382 of IFIP Advances in Information and Communication Technology, pages 234-243, Berlin, 2012. Springer.
  • [83] B. Schölkopf and A. Smola. Learning with Kernels. MIT Press, 2002.
  • [84] P. Schneider, K. Bunte, H. Stiekema, B. Hammer, T. Villmann, and M. Biehl. Regularization in matrix relevance learning. IEEE Transactions on Neural Networks, 21(5):831-840, 2010.
  • [85] P. Schneider, T. Geweniger, F.-M. Schleif, M. Biehl, and T. Villmann. Multivariate class labeling in Robust Soft LVQ. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks (ESANN’2011), pages 17-22, Louvain-La-Neuve, Belgium, 2011. i6doc.com.
  • [86] P. Schneider, B. Hammer, and M. Biehl. Adaptive relevance matrices in learning vector quantization. Neural Computation, 21:3532-3561, 2009.
  • [87] P. Schneider, B. Hammer, and M. Biehl. Distance learning in discriminative vector quantization. Neural Computation, 21:2942-2969, 2009.
  • [88] C. Scovel, D. Hush, I. Steinwart, and J. Theiler. Radial kernels and their reproducing kernel Hilbert spaces. Journal of Complexity, 26:641-660, 2010.
  • [89] S. Seo, M. Bode, and K. Obermayer. Soft nearest prototype classification. IEEE Transaction on Neural Networks, 14:390-398, 2003.
  • [90] S. Seo and K. Obermayer. Soft learning vector quantization. Neural Computation, 15:1589-1604, 2003.
  • [91] G. Shafer and V. Vovk. A tutorial on conformal prediction. Journal of Machine Learning Research, 9:371-421, 2008.
  • [92] R. Shaffer, S. Rose-Pehrsson, and R. A. McGill. Probabilistic neural networks for chemical sensor array pattern recognition: Comparison studies, improvements and automated outlier rejection. Technical Report NRL/FR/6110-98-9879, Naval Research Laboratory, Washington, DC, 1998.
  • [93] J. Shawe-Taylor and N. Cristianini. Kernel Methods for Pattern Analysis and Discovery. Cambridge University Press, 2004.
  • [94] I. Steinwart. On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research, 2:67-93, 2001.
  • [95] M. Strickert and K. Bunte. Soft rank neighbor embeddings. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2013), pages 77-82, Louvain- La-Neuve, Belgium, 2013. i6doc.com.
  • [96] M. Strickert, F.-M. Schleif, U. Seiffert, and T. Villmann. Derivatives of Pearson correlation for gradient-based analysis of biomedical data. Inteligencia Artificial, Revista Iberoamericana de Inteligencia Artificial, (37):37-44, 2008.
  • [97] M. Strickert, F.-M. Schleif, T. Villmann, and U. Seiffert. Unleashing pearson correlation for faithful analysis of biomedical data. In M. Biehl, B. Hammer, M. Verleysen, and T. Villmann, editors, Similarity-based Clustering, volume 5400 of LNAI, pages 70-91. Springer, Berlin, 2009.
  • [98] K. Torkkola. Feature extraction by non-parametric mutual information maximization. Journal of Machine Learning Research, 3:1415-1438, 2003.
  • [99] S. Vanderlooy and E. Hüllermeier. A critical analysis of variants of the AUC. Machine Learning, 72:247-262, 2008.
  • [100] V. Vapnik. Statistical Learning Theory. Wiley and Sons, New York, 1998.
  • [101] V. Vapnik and A. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications, 16(2):264-280, 1971.
  • [102] T. Villmann and S. Haase. Divergence based vector quantization. Neural Computation, 23(5):1343-1392, 2011.
  • [103] T. Villmann, S. Haase, and M. Kaden. Kernelized vector quantization in gradient-descent learning. Neurocomputing, page in press, 2014.
  • [104] T. Villmann, S. Haase, and M. Kästner. Gradient based learning in vector quantization using differentiable kernels. In P. Estevez, J. Principe, and P. Zegers, editors, Advances in Self-Organizing Maps: 9th International Workshop WSOM 2012 Santiage de Chile, volume 198 of Advances in Intelligent Systems and Computing, pages 193-204, Berlin, 2013. Springer.
  • [105] T. Villmann, B. Hammer, F.-M. Schleif, T. Geweniger, and W. Herrmann. Fuzzy classification by fuzzy labeled neural gas. Neural Networks, 19:772-779, 2006.
  • [106] T. Villmann, B. Hammer, F.-M. Schleif, W. Hermann, and M. Cottrell. Fuzzy classification using information theoretic learning vector quantization. Neurocomputing, 71:3070-3076, 2008.
  • [107] T. Villmann, F.-M. Schleif, and B. Hammer. Prototype-based fuzzy classification with local relevance for proteomics. Neurocomputing, 69(16-18):2425-2428, October 2006.
  • [108] V. Vovk, A. Gammerman, and G. Shafer. Algorithmic learning in a random world. Springer, Berlin, 2005.
  • [109] A. Witoelar, A. Gosh, J. de Vries, B. Hammer, and M. Biehl. Windowbased example selection in learning vector quantization. Neural Computation, 22(11):2924-2961, 2010.
  • [110] Y. Wu, K. Ianakiev, and V. Govindaraju. Improved k-nearest neighbor classification. Pattern Recognition, 35:2311 - 2318, 2002.
  • [111] D. Zühlke, T. Geweniger, U. Heimann, and T. Villmann. Fuzzy Fleiss-Kappa for comparison of fuzzy classifiers. In M. Verleysen, editor, Proc. of the European Symposium on Artificial Neural Networks (ESANN’2009), pages 269-274, Evere, Belgium, 2009. d-side publications.
  • [112] X. Zhu, F.-M. Schleif, and B. Hammer. Semi-supervised vector quantization for proximity data. In M. Verleysen, editor, Proc. of European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN’2013), pages 89-94, Louvain-La-Neuve, Belgium, 2013. i6doc.com.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7e5357dc-d6e8-4a88-b45c-38cf8e9c7a20
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.