Heterogeneous distance functions for prototype rules : influence of parameters on probability estimation

• Autorzy: Blachnik M. , Duch W. , Wieczorek T.
• Języki publikacji: EN

Abstrakty

EN

An interesting and little explored way to understand data is based on prototype rules (P-rules). The goal of this approach is to find optimal similarity (or distance) functions and position of prototypes to which unknown vectors are compared. In real applications similarity functions frequently involve different types of attributes, such as continuous, discrete, binary or nominal. Heterogeneous distance functions that may handle such diverse information are usually based on probability distance measure, such as the Value Difference Metrics (VDM). For continuous attributes calculation of probabilities requires estimations of probability density functions. This process requires careful selection of several parameters that may have important impact on the overall classification of accuracy. In this paper, various heterogeneous distance function based on VDM measure are presented, among them some new heterogeneous distance functions based on different types of probability estimation. Results of many numerical experiments with such distance functions are presented on artificial and real datasets, and quite simple P-rules for several heterogeneous databases extracted.

Słowa kluczowe

EN

prototype rules; probability estimation; heterogeneous distance functions; similarity-based methods; classification; data mining

• Wydawca: Wydawnictwo Uniwersytetu Przyrodniczo-Humanistycznego w Siedlcach
• Czasopismo: Studia Informatica : systems and information technology
• Rocznik: 2006
• Tom: Vol. 1(7)
• Strony: 19--30
• Opis fizyczny: Bibliogr. 14 poz., tab.

Twórcy

autor

Blachnik M.

• Division of Engineering Informatics, Department of Electrotechnology, Faculty of Materials Engineering and Metallurgy, Silesian University of Technology Krasińskiego 8, 40-019 Katowice, Poland

autor

Duch W.

• Department of Informatics, Nicolaus Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland
• School of Computer Engineering, Nanyang Technological University Singapore

autor

Wieczorek T.

• Division of Engineering Informatics, Department of Electrotechnology, Faculty of Materials Engineering and Metallurgy, Silesian University of Technology Krasińskiego 8, 40-019 Katowice, Poland

Bibliografia

• 1. Duch W., Visualization of hidden node activity in neural networks: Visualization methods. Lecture Notes in AI Vol. 3070 (2004) 38-43; Application to RBF networks. Lecture Notes in AI Vol. 3070 (2004) 44-49.
• 2. Duch W., Coloring black boxes: visualization of neural network decisions. International Joint Conference on Neural Networks, Portland, Oregon, 2003, IEEE Press, Vol. I, pp. 1735-1740.
• 3. Duch W., Setiono R., Żurada J., (2004). Computational intelligence methods for rule-based data understanding, Proceedings of the IEEE, 92(5): 771- 805.
• 4. Hastie T., Tibshirani R. and Friedman J., The Elements of Statistical Learning. Springer, 2001.
• 5. Grąbczewski K., Duch W., (2000). The separability of split value criterion, 5’th Conf. on Neural Network and Soft Computing, Zakopane, Poland, pp. 201-208.
• 6. D. Nauck, F. Klawonn and R. Kruse, Foundations on Neuro-Fuzzy Systems. Wiley, Chichester, 1997.
• 7. Duch W., Grudziński K., (2001). Prototype based rules - a new way to understand the data. IEEE International Joint Conference on Neural Networks, Washington D.C., IEEE Press, pp. 1858-1863.
• 8. Duch W., Blachnik M., (2004). Fuzzy rule-based system derived from similarity to prototypes, Lecture Notes in Computer Science, 3316, 912-917.
• 9. Blanzieri E., Ricci F., (1999). Probability Based Metrics for Nearest Neighbor Classification and Case-Based reasoning. In: Case-Based reasoning and development. Althoff K., Bergmann R., Branting K. (eds), Springer, pp. 14-28.
• 10. Dubois D., Prade H. (eds.), (2000). Measurements of Membership Functions: Theoretical and Empirical Work, Fundamentals of Fuzzy Sets. Kluwer.
• 11. Duch W., (2000). Similarity based methods: a general framework for classification, approximation and association. Control and Cybernetics 29(4), 937-968.
• 12. Wilson R.T., Martinez T.R., (1997). Improved Heterogeneous Distance Function, Journal of Artificial Intelligence Research, vol. 6, 1-34.
• 13. Haykin S., Neural networks: a comprehensive foundations. New York: MacMillian Publishing, 1994.
• 14. Mertz C.J., Murphy P.M., UCI repository of machine learning databases, http://www.ics.uci.edu/~mlearn/MLRepository.html