Abstract
This paper presents the comparison between mini-models method based on multidimensional polytopes and k-nearest neighbor method. Both algorithms are similar, and both methods use samples only from the local neighborhood of the query point. The mini-models method can on the defined local area use any approximation algorithm to compute the model answer. The paper describes the learning technique of mini-models and presents the results of experiments that compare the effectiveness of two examined algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bronshtein, I., Semendyayev, K., Musiol, G., Muhlig, H.: Handbook of Mathematics. Springer (2007). ISBN 9783540721215
Fix, E., Hodges, J.L.: Discriminatory analysis, nonparametric discrimination: Consistency properties. Randolph Field, pp. 1–21. Texas (1951)
Flasinski, M.: Wstep do Sztucznej Inteligencji. PWN, Warszawa (2011)
Hollash, S.R.: Four-space Visualization of 4d Objects. MSc. Thesis, Arizona State Univeristy (1991). http://steve.hollasch.net/thesis/
Kordos, M., Blachnik, M., Strzempa, D.: Do we need whatever more than k-NN? In: Proceedings of 10th International Conference on Artificial Intelligence and Soft Computing, Zakopane (2010)
Moon, P., Spencer, D.: Field Theory Handbook: Including Coordinate Systems, Differential Equations, and Their Solutions. Springer (1988). ISBN 9780387027326
Piegat, A., Wasikowska, B., Korzeń, M.: Application of the self-learning, 3-point mini-model for modelling of unemployment rate in Poland [in Polish]. Studia Informatica, University of Szczecin, No. 27, pp. 59–69 (2010)
Piegat, A., Wasikowska, B., Korzeń, M.: Differences between the method of mini-models and the k-nearest neighbors an example of modeling unemployment rate in Poland. In: Information Systems in Management IX-Business Intelligence and Knowledge Management. WULS Press, Warsaw (2011)
Pietrzykowski, M.: Comparison of effectiveness of linear mini-models with some methods of modelling. Młodzi Naukowcy dla Polskiej Nauki. CREATIVETIME, pp. 113–123. Krakw (2011)
Pietrzykowski, M.: Mini-models working in 3D space based on polar coordinate system. Nowe trendy w naukach inzynieryjnych 4. Tom II, CREATIVETIME, pp. 117–125. Krakw (2013)
Pietrzykowski, M.: Effectiveness of mini-models method when data modelling within a 2D-space in an information deficiency situation. J. Theor. Appl. Comput. Sci. 6(3), 21–27 (2012)
Pluciński, M.: Mini-models—Local regression models for the function approximation learning. In: Rutkowski L., et al. (eds.) Proceedings of ICAISC 2012, Part II. LNCS, vol. 7268, pp. 160–167. Springer, Berlin (2012)
Pluciński, M.: Nonlinear ellipsoidal mini-models—application for the function approximation task. Przeglad Elektrotechniczny (Electrical Review), R. 88 NR 10b, pp. 247–251 (2012)
Polyanin, A., Manzhirov, A.: Handbook of Mathematics for Engineers and Scientists. Taylor & Francis (2010). ISBN 9781584885023
Rejer, I.: Metody modelowanie wielkowymiarowego systemu z użyciem metod sztucznej inteligencji na przykładzie bezrobocia w Polsce. Szczecin, Wydawnictwo Naukowe Uniwersytetu Szczecińskiego (2003)
Rutkowski, L.: Metody i techniki sztucznej inteligencji. PWN, Warszawa (2009)
UCI Machine LEARNING REPOSITORY: http://archive.ics.uci.edu/ml/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Pietrzykowski, M. (2015). Comparison Between Mini-models Based on Multidimensional Polytopes and k-nearest Neighbor Method: Case Study of 4D and 5D Problems. In: Wiliński, A., Fray, I., Pejaś, J. (eds) Soft Computing in Computer and Information Science. Advances in Intelligent Systems and Computing, vol 342. Springer, Cham. https://doi.org/10.1007/978-3-319-15147-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-15147-2_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15146-5
Online ISBN: 978-3-319-15147-2
eBook Packages: EngineeringEngineering (R0)