Abstract
Principal component analysis (PCA) is a well-known tool often used for the exploratory analysis of a data set, which can be used to reduce the data dimensionality and also to decrease the dependency among features. The traditional PCA algorithms are designed aiming at numerical data instead of non-numerical data. In this article we propose a generalized PCA algorithm which tackles a problem where data is linguistic variable represented by triangular fuzzy number. Using the information provided by the centroid and fuzzy boundary of triangular fuzzy number, the proposed method starts with translating triangular fuzzy numbers into real numbers, then PCA is carried out on high-dimensional real number data set. Finally, the application of the proposed algorithm to a triangular fuzzy number data set is described.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Johnson, A., Wichern, W.: Applied multivariate analysis. Printice Hall, New Jersey (2003)
Han, J., Kamber, M.: Data miningconcept and technique. Morgan Kaufmann Publishers, San Francisco (2001)
Ross, T.J.: Fuzzy logic with engineering applications. The McGraw-Hill Companies, Inc., New York (2001)
He, X.: The theory and technology of fuzzy knowledge processing. National Defence Industry Press, Beijing (1998)
Gowda, K.C., Diday, E.: Symbolic clustering using a new dissimilarity measure. Pattern Recognition 24(6), 567–578 (1991)
Gao, X., Fan, J., Xie, W.: A novel algorithm of FCM clustering for interval valued data. Journal of Xian University 26(5), 604–609 (1999)
Bock, H.H., Diday, E.: Analysis symbolic data. Springer, Berlin (2000)
Asharaf, S., Murty, M.N., Shevade, S.K.: Rough set based incremental clustering of interval data. Pattern Recognition Letters 27(6), 515–519 (2006)
Falasconi, M., Pardo, M., Vezzoli, M., Sberveglieri, G.: Cluster validation for electronic nose. Data Sensors and Actuators B: Chemical 125(2), 596–606 (2007)
Ozkan, I., Turksen, I.B., Canpolat, N.: A currency crisis and its perception with fuzzy C-means. Information Sciences 178(8), 1923–1934 (2008)
Liu, J., Xu, M.: Kernelized fuzzy attribute C-means clustering algorithm. Fuzzy Sets and Systems 159(18), 2428–2445 (2008)
Cazes, P., Chouakria, A., Diday, E.: Symbolic principal components analysis. In: Bock, H.H., Diday, E. (eds.) Analysis of Symbolic Data. Springer, Berlin (2000)
Durso, P., Giordania, P.: A least squares approach to principal component analysis for interval valued data. Chemometrics and Intelligent Laboratory Systems 70(2), 179–192 (2004)
Giordania, P., Kiersb, A.L.: A comparison of three methods for principal component analysis of fuzzy interval data. Computational Statistics & Data Analysis 51(1), 379–397 (2006)
Xu, D., Wang, Y.: An automated feature extraction and emboli detection system based on the PCA and fuzzy sets. Computers in Biology and Medicine 37(6), 861–871 (2007)
Guo, J., Li, W.: Principal component analysis based on error theory and its application. Application of Statistics and Management 26(4), 636–640 (2007)
Polat, K., Gnes, S.: Principles component analysis fuzzy weighting pre-processing and artificial immune recognition system based diagnostic system for diagnosis of lung cancer. Expert Systems with Applications 34(1), 214–221 (2008)
Luukka, P.: PCA for fuzzy data and similarity classifier in building recognition system for post-operative patient data. Expert Systems with Applications 36(2), 1222–1228 (2009)
Chen, N., Zhang, Z.: Principal component analysis algorithm for interval-valued data. Advances in Information and Systems Sciences 3(2), 496–505 (2009)
Coppi, R., D’Urso, P.: Fuzzy K-means clustering models for triangular fuzzy time trajectories. Statistical Methods & Applications 11, 21–40 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, Nx., Zhang, Yj. (2009). Principal Component Analysis of Triangular Fuzzy Number Data. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_87
Download citation
DOI: https://doi.org/10.1007/978-3-642-03664-4_87
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03663-7
Online ISBN: 978-3-642-03664-4
eBook Packages: EngineeringEngineering (R0)