Relevance learning in unsupervised vector quantization based on divergences

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6731 LNCS, Issue , 2011, Pages 90-100

  Kästner, Marika ^a   Backhaus, Andreas ^b   Geweniger, Tina ^a   Haase, Sven ^a   Seiffert, Udo ^b   Villmann, Thomas ^a  

^a UNIVERSITY OF APPLIED SCIENCES MITTWEIDA   (Germany)

^b FRAUNHOFER INSTITUTE FOR FACTORY OPERATION AND AUTOMATION IFF   (Germany)

Author keywords

divergence learning; relevance learning; vector quantization

Indexed keywords

DATA VECTORS; DIVERGENCE LEARNING; FUZZY C MEAN; NEURAL GAS ALGORITHMS; QUANTIZATION SCHEMES; RELEVANCE LEARNING; SIMILARITY MEASURE; STOCHASTIC GRADIENT DESCENT; VECTOR QUANTIZATION ALGORITHMS;

ALGORITHMS; C (PROGRAMMING LANGUAGE); CONFORMAL MAPPING; SELF ORGANIZING MAPS; VECTORS; COST FUNCTIONS; STOCHASTIC SYSTEMS;

VECTOR QUANTIZATION;

EID: 79959294295     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-21566-7_9     Document Type: Conference Paper

References (37)

1. Arnonkijpanich, B., Hasenfuss, A., Hammer, B.: Local matrix adaptation in topographic neural maps. Neurocomputing 74(4), 522-539 (2011).
2. Backhaus, A., Kuwabara, A., Bauch, M., Monk, N., Sanguinetti, G., Fleming, A.: LEAFPROCESSOR: a new leaf phenotyping tool using contour bending energy and shape cluster analysis. New Phytologist 187(1), 251-261 (2010).
3. Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981).
4. Bouveyron, C., Girard, S., Schmid, C.: High-dimensional data clustering. Computational Statistics and Data Analysis 57(1), 502-519 (2007). (Pubitemid 47331728)
5. Bunte, K., Hammer, B., Wism̈uller, A., Biehl, M.: Adaptive local dissimilarity measures for discriminative dimension reduction of labeled data. Neurocomputing 73, 1074-1092 (2010).
6. Camps-Valls, G., Bruzzone, L.: Kernel-based methods for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing 43(6), 1351-1362 (2005). (Pubitemid 40811944)
7. Cesar, R.M., da Fontoura Costa, L.: Application and assessment of multiscale bending energy for morphometric characterization of neural cells. Rev. Sci. Instrum. 68(5), 2177-2186 (1997). (Pubitemid 127639163)
8. Cichocki, A., Amari, S.-I.: Families of alpha- beta- and gamma- divergences: Flexible and robust measures of similarities. Entropy 12, 1532-1568 (2010).
9. Dunn, J.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics 3, 32-57 (1973).
10. Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15(8-9), 1059-1068 (2002).
11. Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen Maps, pp. 303-316. Elsevier, Amsterdam (1999).
12. Izakian, H., Abraham, A.: Fuzzy c-means and fuzzy swarm for fuzzy clustering problem. Expert Systems with Applications 38(3), 1835-1838 (2011).
13. Kass, M., Witkin, A., Terzopoulos, D.: Snakes - Active Contour models. International Journal of Computer Vision 1(4), 321-331 (1987).
14. Kato, T.: On the adiabatic theorem of quantum mechanics. Journal of the Physical Society of Japan 5(6), 435-439 (1950).
15. Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995), 2nd extended edn. (1997).
16. Landgrebe, D.: Signal Theory Methods in Multispectral Remote Sensing. Wiley, Hoboken, New Jersey (2003).
17. Lee, J., Verleysen, M.: Generalization of the lp norm for time series and its application to self-organizing maps. In: Cottrell, M. (ed.) Proc. of Workshop on Self- Organizing Maps (WSOM) 2005, Paris, Sorbonne, pp. 733-740 (2005).
18. Liu, Z.-Y., Xu, L.: Topological local principal component analysis. Neurocomputing 55(3-4), 739-745 (2003). (Pubitemid 37455486)
19. Ĺopez-Rubio, E., noz Ṕerez, J.M., Ǵomez-Ruiz, J.: A principal components analysis self-organizing map. Neural Networks 2(2), 261-270 (2004). (Pubitemid 38230223)
20. Martinetz, T.M., Berkovich, S.G., Schulten, K.J.: 'Neuralgas' network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4(4), 558-569 (1993).
21. M̈oller, R., Hoffmann, H.: An extension of neural gas to local PCA. Neurocomputing 62, 305-326 (2004). (Pubitemid 39504668)
22. Mwebaze, E., Schneider, P., Schleif, F.-M., Aduwo, J., Quinn, J., Haase, S., Villmann, T., Biehl, M.: Divergence based classification in learning vector quantization. Neurocomputing 74(9), 1429-1435 (2011).
23. Oja, E., Lampinen, J.: Unsupervised learning for feature extraction. In: Zurada, J.M., Marks II, R.J., Robinson, C.J. (eds.) Computational Intelligence Imitating Life, pp. 13-22. IEEE Press, Los Alamitos (1994).
24. Principe, J.C., III, J.F., Xu, D.: Information theoretic learning. In: Haykin, S. (ed.) Unsupervised Adaptive Filtering, Wiley, New York (2000).
25. Rubner, J., Tavan, P.: A self-organizing network for principle-component analysis. Europhys. Letters 7(10), 693-698 (1989).
26. Schneider, P., Hammer, B., Biehl, M.: Adaptive relevance matrices in learning vector quantization. Neural Computation 21, 3532-3561 (2009).
27. Tipping, M., Bishop, C.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443-482 (1999).
28. Van Hulle, M.M.: Faithful representations with topographic maps. Neural Networks 12(6), 803-823 (1999). (Pubitemid 29359220)
29. Villmann, T., Cichocki, A., Principe, J.: Information theory related learning. In: Verleysen, M. (ed.) Proc. of European Symposium on Artificial Neural Networks (ESANN 2011), Evere, Belgium, d-side publications (2011) (page in press).
30. Villmann, T., Der, R., Herrmann, M., Martinetz, T.: Topology Preservation in Self-Organizing Feature Maps: Exact Definition and Measurement. IEEE Transactions on Neural Networks 8(2), 256-266 (1997). (Pubitemid 127765121)
31. Villmann, T., Haase, S.: Divergence based vector quantization. Neural Computation 23(5), 1343-1392 (2011).
32. Villmann, T., Hammer, B.: Theoretical aspects of kernel GLVQ with differentiable kernel. IfI Technical Report Series (IfI-09-12), pp. 133-141 (2009).
33. Villmann, T., Schleif, F.-M.: Functional vector quantization by neural maps. In: Chanussot, J. (ed.) Proceedings of First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2009), pp. 1-4. IEEE Press, Los Alamitos (2009); ISBN 978-1-4244-4948-4.
34. Xie, X., Beni, G.: A validity measure for fuzzy clustering. IEEE Transactions on Pat 13(8), 841-847 (1991). (Pubitemid 21704193)
35. Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645-678 (2005). (Pubitemid 40718010)
36. Young, I.T., Walker, J.E., Bowie, J.E.: An analysis technique for biological shape. i. Information and Control 25(4), 357-370 (1974).
37. Zalik, K., Zalik, B.: Validity index for clusters of different sizes and densities. Pattern Recognition Letters 32, 221-234 (2011)