Abstract
The basic nearest neighbour algorithm has been designed to work with complete data vectors. Moreover, it is assumed that each reference sample as well as classified sample belong to one and the only one class. In the paper this restriction has been dismissed. Through incorporation of certain elements of rough set and fuzzy set theories into k-nn classifier we obtain a sample based classifier with new features. In processing incomplete data, the proposed classifier gives answer in the form of rough set, i.e. indicated lower or upper approximation of one or more classes. The basic nearest neighbour algorithm has been designed to work with complete data vectors and assumed that each reference sample as well as classified sample belongs to one and the only one class. Indication of more than one class is a result of incomplete data processing as well as final reduction operation.
Keywords
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References
Aldahdooh, R.T., Ashour, W.: DSMK-means ”Density-based split-and-merge k-means clustering algorithm”. Journal of Artificial Intelligence and Soft Computing Research 3(1), 51–71 (2013)
Anguita, D., Ghelardoni, L., Ghio, A., Ridella, S.: A survey of old and new results for the test error estimation of a classifier. Journal of Artificial Intelligence and Soft Computing Research 3(4), 229–242 (2013)
Bao, Y., Du, X., Ishii, N.: Improving performance of the k-nearest neighbor classifier by tolerant rough sets. In: Proceedings of the Third International Symposium on Cooperative Database Systems for Advanced Applications, CODAS 2001, pp. 167–171 (2001)
Bilski, J., Smolag, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Transactions on Parallel and Distributed Systems PP(99) (2014)
Bilski, J., Smoląg, J., Galushkin, A.I.: The parallel approach to the conjugate gradient learning algorithm for the feedforward neural networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 12–21. Springer, Heidelberg (2014)
Bilski, J.: Momentum modification of the RLS algorithms. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 151–157. Springer, Heidelberg (2004)
Chang, Y., Wang, Y., Chen, C., Ricanek, K.: Improved image-based automatic gender classification by feature selection. Journal of Artificial Intelligence and Soft Computing Research 1(3), 241–253 (2011)
collective work: UCI machine learning repository, http://archive.ics.uci.edu/ml/datasets.html
Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Transactions on Information Theory 13(1), 21–27 (1967)
Cpałka, K., Rutkowski, L.: Flexible Takagi-Sugeno fuzzy systems. In: Proceedings of IEEE International Joint Conference on Neural Networks, IJCNN 2005, vol. 3, pp. 1764–1769. IEEE (2005)
Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomputing 135, 203–217 (2014)
Cpałka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. International Journal of General Systems 42(6), 706–720 (2013)
Gabryel, M., Korytkowski, M., Scherer, R., Rutkowski, L.: Object detection by simple fuzzy classifiers generated by boosting. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 540–547. Springer, Heidelberg (2013)
Gabryel, M., Rutkowski, L.: Evolutionary learning of mamdani-type neuro-fuzzy systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 354–359. Springer, Heidelberg (2006)
Gabryel, M., Rutkowski, L.: Evolutionary designing of logic-type fuzzy systems. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 143–148. Springer, Heidelberg (2010)
Gaweda, A.E., Scherer, R.: Fuzzy number-based hierarchical fuzzy system. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 302–307. Springer, Heidelberg (2004)
He, M., Ping Du, Y.: Research on attribute reduction using rough neighborhood model. In: International Seminar on Business and Information Management, ISBIM 2008, vol. 1, pp. 268–270 (December 2008)
Ishii, N., Torii, I., Bao, Y., Tanaka, H.: Modified reduct: Nearest neighbor classification. In: 2012 IEEE/ACIS 11th International Conference on Computer and Information Science (ICIS), pp. 310–315 (May 2012)
Ishii, N., Torii, I., Bao, Y., Tanaka, H.: Mapping of nearest neighbor for classification. In: 2013 IEEE/ACIS 12th International Conference on Computer and Information Science (ICIS), pp. 121–126 (June 2013)
Jaworski, M., Duda, P., Pietruczuk, L.: On fuzzy clustering of data streams with concept drift. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 82–91. Springer, Heidelberg (2012)
Keller, J., Gray, M., Givens, J.: A fuzzy k-nearest neighbor algorithm. IEEE Transactions on Systems, Man and Cybernetics SMC-15(4), 580–585 (1985)
Kohavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Prceedings on the International Join Conference on Artficial Intelligence (IJCAI), Montreal, Canada, pp. 1137–1143 (1995)
Korytkowski, M., Rutkowski, L., Scherer, R.: From ensemble of fuzzy classifiers to single fuzzy rule base classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008)
Laskowski, Ł.: Objects auto-selection from stereo-images realised by self-correcting neural network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 119–125. Springer, Heidelberg (2012)
Laskowski, L.: A novel hybrid-maximum neural network in stereo-matching process. Neural Computing and Applications 23(7-8), 2435–2450 (2013)
Laskowski, L., Jelonkiewicz, J.: Self-correcting neural network for stereo-matching problem solving. Fundamenta Informaticae 138, 1–26 (2015)
Laskowski, L., Laskowska, M.: Functionalization of SBA-15 mesoporous silica by cu-phosphonate units: Probing of synthesis route. Journal of Solid State Chemistry 220, 221–226 (2014)
Laskowski, L., Laskowska, M., Balanda, M., Fitta, M., Kwiatkowska, J., Dzilinski, K., Karczmarska, A.: Mesoporous silica SBA-15 functionalized by nickel-phosphonic units: Raman and magnetic analysis. Microporous and Mesoporous Materials 200, 253–259 (2014)
Laskowski, Ł., Laskowska, M., Jelonkiewicz, J., Boullanger, A.: Spin-glass implementation of a Hopfield neural structure. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 89–96. Springer, Heidelberg (2014)
Nowicki, R.: On combining neuro-fuzzy architectures with the rough set theory to solve classification problems with incomplete data. IEEE Transactions on Knowledge and Data Engineering 20(9), 1239–1253 (2008)
Nowicki, R.: Rough neuro-fuzzy structures for classification with missing data. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39(6), 1334–1347 (2009)
Nowicki, R.: On classification with missing data using rough-neuro-fuzzy systems. International Journal of Applied Mathematics and Computer Science 20(1), 55–67 (2010)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)
Pedrycz, W., Bargiela, A.: Granular clustering: a granular signature of data. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 32(2), 212–224 (2002)
Pietruczuk, L., Duda, P., Jaworski, M.: A new fuzzy classifier for data streams. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 318–324. Springer, Heidelberg (2012)
Pietruczuk, L., Duda, P., Jaworski, M.: Adaptation of decision trees for handling concept drift. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 459–473. Springer, Heidelberg (2013)
Romaszewski, M., Gawron, P., Opozda, S.: Dimensionality reduction of dynamic mesh animations using ho-svd. Journal of Artificial Intelligence and Soft Computing Research 3(4), 277–289 (2013)
Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the gaussian approximation. IEEE Transactions on Knowledge and Data Engineering 26(1), 108–119 (2014)
Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the mcdiarmid’s bound. IEEE Transactions on Knowledge and Data Engineering 25(6), 1272–1279 (2013)
Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Information Sciences 266, 1–15 (2014)
Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online speed profile generation for industrial machine tool based on neuro-fuzzy approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 645–650. Springer, Heidelberg (2010)
Sarkar, M.: Fuzzy-rough nearest neighbors algorithm. In: 2000 IEEE International Conference on Systems, Man, and Cybernetics, vol. 5, pp. 3556–3561 (2000)
Scherer, R., Rutkowski, L.: A fuzzy relational system with linguistic antecedent certainty factors. In: Rutkowski, L., Kacprzyk, J. (eds.) Proceedings of the Sixth International Conference on Neural Network and Soft Computing. Advances in Soft Computing, pp. 563–569. Springer, Heidelberg (2003)
Scherer, R.: Neuro-fuzzy relational systems for nonlinear approximation and prediction. Nonlinear Analysis 71, e1420–e1425 (2009)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Verbiest, N., Cornelis, C., Jensen, R.: Fuzzy rough positive region based nearest neighbour classification. In: 2012 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–7 (June 2012)
Villmann, T., Schleif, F., Hammer, B.: Fuzzy labeled soft nearest neighbor classification with relevance learning. In: Proceedings of the Fourth International Conference on Machine Learning and Applications, pp. 11–15 (December 2005)
Woźniak, M., Marszałek, Z., Gabryel, M., Nowicki, R.K.: Modified merge sort algorithm for large scale data sets. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 612–622. Springer, Heidelberg (2013)
Woźniak, M., Marszałek, Z., Gabryel, M., Nowicki, R.K.: On quick sort algorithm performance for large data sets. In: Skulimowski, A.M.J. (ed.) Looking into the Future of Creativity and Decision Support Systems, pp. 647–656. Progress & Business Publishers, Cracow (2013)
Woźniak, M., Marszałek, Z., Gabryel, M., Nowicki, R.K.: Triple heap sort algorithm for large data sets. In: Skulimowski, A.M.J. (ed.) Looking into the Future of Creativity and Decision Support Systems, pp. 657–665. Progress & Business Publishers, Cracow (2013)
Yager, R.: Using fuzzy methods to model nearest neighbor rules. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 32(4), 512–525 (2002)
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Nowak, B.A., Nowicki, R.K., Woźniak, M., Napoli, C. (2015). Multi-class Nearest Neighbour Classifier for Incomplete Data Handling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_42
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