Abstract
This paper presents a new extension of AdaBoost algorithm based on interval-valued fuzzy sets. This extension is for the weights used in samples of the training sets. The original weights are the real number from the interval [0, 1]. In our approach the weights are represented by the interval-valued fuzzy set, that is any weight has a lower and upper membership function. The same value of lower and upper membership function has a weight of the appropriate weak classifier. In our study we use the boosting by the reweighting method where each weak classifier is based on the recursive partitioning method. The described algorithm was tested on two generation data sets and two sets from UCI repository. The obtained results are compared with the original AdaBoost algorithm.
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References
Kearns, M., Valiant, L.: Cryptographic limitations on learning boolean formulae and finite automata. J. Assoc. Comput. Mach. 41(1), 67–95 (1994)
Chunhua, S., Hanxi, L.: On the Dual Formulation of Boosting Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(12), 2216–2231 (2010)
Oza, N.C.: Boosting with Averaged Weight Vectors. In: Windeatt, T., Roli, F. (eds.) MCS 2003. LNCS, vol. 2709, pp. 15–24. Springer, Heidelberg (2003)
Freund, Y., Schapire, R.: Experiments with a new boosting algorithm. In: Proceedings of the Thirteenth International Conference on Machine Learning, Bari, Italy, pp. 148–156 (1996)
Wozniak, M.: Proposition of Boosting Algorithm for Probabilistic Decision Support System. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004, Part I. LNCS, vol. 3036, pp. 675–678. Springer, Heidelberg (2004)
Wozniak, M.: Boosted Decision Trees for Diagnosis Type of Hypertension. In: Oliveira, J.L., Maojo, V., Martín-Sánchez, F., Pereira, A.S. (eds.) ISBMDA 2005. LNCS (LNBI), vol. 3745, pp. 223–230. Springer, Heidelberg (2005)
Freund, Y., Schapire, R.: A decision-theoretic generalization of on-line learning and an application to boostin. Journal of Computer and System Scienses 55(1), 119–139 (1997)
Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)
Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18(1), 145–174 (1967)
Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Information Science 8, 199–249 (1975)
Burduk, R.: Imprecise information in Bayes classifier. Pattern Analysis and Applications 15(2), 147–153 (2012)
Mitchell, H.B.: Pattern recognition using type-II fuzzy sets. Information Science 170, 409–418 (2005)
Melin, P.: Image Processing and Pattern Recognition with Mamdani Interval Type-2 Fuzzy Inference Systems. In: Trillas, E., Bonissone, P.P., Magdalena, L., Kacprzyk, J. (eds.) Combining Experimentation and Theory. STUDFUZZ, vol. 271, pp. 179–190. Springer, Heidelberg (2011)
Dmitrienko, A., Chuang-Stein, C.: Pharmaceutical Statistics Using SAS: A Practical Guide. SAS Press (2007)
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Burduk, R. (2012). New AdaBoost Algorithm Based on Interval-Valued Fuzzy Sets. In: Yin, H., Costa, J.A.F., Barreto, G. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2012. IDEAL 2012. Lecture Notes in Computer Science, vol 7435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32639-4_94
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DOI: https://doi.org/10.1007/978-3-642-32639-4_94
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