Abstract
Switching regression is a powerful tool for revealing intrinsic non-linear dependencies among exploratory variables and objective variables. In this paper, Fuzzy c-Regression Models (FCRM), which is an FCM-type switching regression model, is modified so that it can handle uncertain categorical observations. In data mining applications, we often deal with databases consisting of mixed measurement levels. The alternating least squares method is a technique for mixed measurement situations, in which categorical observations are quantified such that they suit the current model by optimal scaling, and has been applied to FCM-type fuzzy clustering in order to characterize each cluster considering mutual relation among categories. While optimal scaling has been used for handling categorical observations, categorical observations often have ambiguity of natural language categories. In this paper, a modified FCM-type switching regression is performed by considering tolerance of quantified category observations in conjunction with optimal scaling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Quandt, R.E.: The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of the American Statistical Association 53, 873–880 (1958)
Quandt, R.E.: A new approach to estimating switching regressions. Journal of the American Statistical Association 67, 306–310 (1972)
Hathaway, R.J., Bezdek, J.C.: Switching regression models and fuzzy clustering. IEEE Trans. Fuzzy Systems 1(3), 195–204 (1993)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press (1981)
Young, F.W., De Leeuw, J., Takane, Y.: Regression with qualitative and quantitative variables: an alternating least squares method with optimal scaling features. Psychometrika 41, 505–529 (1976)
Takane, Y., Young, F.W., De Leeuw, J.: Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika 42, 7–67 (1977)
Young, F.W., Takane, Y., De Leeuw, J.: Principal components of mixed measurement level multivariate data: an alternating least squares method with optimal scaling features. Psychometrika 43, 279–281 (1978)
Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications. STUDFUZZ, vol. 229. Springer, Heidelberg (2008)
MacQueen, J.B.: Some methods of classification and analysis of multivariate observations. In: Proc. of 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281–297 (1967)
Hamasuna, Y., Endo, Y., Miyamoto, S.: On tolerant fuzzy c-means clustering. Journal of Advanced Computational Intelligence and Intelligent Informatics 13(4), 421–428 (2009)
Endo, Y., Hasegawa, Y., Hamasuna, Y., Kanzawa, Y.: Fuzzy c-means clustering for uncertain data using quadratic penalty-vector regularization. Journal of Advanced Computational Intelligence and Intelligent Informatics 15(1), 76–82 (2011)
Honda, K., Uesugi, R., Ichihashi, H.: FCM-type fuzzy clustering of mixed databases considering nominal variable quantification. Journal of Advanced Computational Intelligence and Intelligent Informatics 11(2), 162–167 (2007)
Honda, K., Ohyama, T., Ichihashi, H., Notsu, A.: FCM-type switching regression with alternating least squares method. In: Proc. 2008 IEEE International Conference on Fuzzy Systems, pp. 122–127 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Iwata, S., Honda, K., Notsu, A. (2014). Fuzzy c-Regression Models Based on Optimal Scaling of Categorical Observation with Tolerance. In: Cho, Y., Matson, E. (eds) Soft Computing in Artificial Intelligence. Advances in Intelligent Systems and Computing, vol 270. Springer, Cham. https://doi.org/10.1007/978-3-319-05515-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-05515-2_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05514-5
Online ISBN: 978-3-319-05515-2
eBook Packages: EngineeringEngineering (R0)