- Volume 14 Issue 5
DOI QR Code
An Improved Robust Fuzzy Principal Component Analysis
잡음 민감성이 개선된 퍼지 주성분 분석
- Heo, Gyeong-Yong (Computer and Information Science and Engineering, University of Florida) ;
- Woo, Young-Woon ;
- Kim, Seong-Hoon
- Received : 2010.01.26
- Accepted : 2010.02.12
- Published : 2010.05.31
Principal component analysis (PCA) is a well-known method for dimension reduction while maintaining most of the variation in data. Although PCA has been applied to many areas successfully, it is sensitive to outliers. Several variants of PCA have been proposed to resolve the problem and, among the variants, robust fuzzy PCA (RF-PCA) demonstrated promising results. RF-PCA uses fuzzy memberships to reduce the noise sensitivity. However, there are also problems in RF-PCA and the convergence property is one of them. RF-PCA uses two different objective functions to update memberships and principal components, which is the main reason of the lack of convergence property. The difference between two functions also slows the convergence and deteriorates the solutions of RF-PCA. In this paper, a variant of RF-PCA, called RF-PCA2, is proposed. RF-PCA2 uses an integrated objective function both for memberships and principal components. By using alternating optimization, RF-PCA2 is guaranteed to converge on a local optimum. Furthermore, RF-PCA2 converges faster than RF-PCA and the solutions found are more similar to the desired solutions than those of RF-PCA. Experimental results also support this.
- I. T. Jolliffe, Principal Component Analysis, 2nd Edition, Springer, 2002.
- P. Rousseeuw, "Multivariate estimation with high breakdown point," Mathematical Statistics and Applications B, pp. 283-297, 1985.
- C.-D. Lu, T.-Y. Zhang, X.-Z. Du, and C.-P. Li, "A robust kernel PCA algorithm," Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 3084-3087, 2004.
- C. Lu, T. Zhang, R. Zhang, and C. Zhang, "Adaptive robust kernel PCA algorithm," Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. VI621-624, 2003.
- G. Heo, P. Gader, and H. Frigui, "RKF-PCA: Robust kernel fuzzy PCA," Neural Networks Vol. 22, No. 5-6, pp. 642-650, 2009. https://doi.org/10.1016/j.neunet.2009.06.013
- T.-N. Yang and S.-D. Wang, "Fuzzy auto-associative neural networks for principal component extraction of noisy data," IEEE Transaction on Neural Networks, Vol. 11, No. 3, pp. 808-810, 2000 https://doi.org/10.1109/72.846752
- T. R. Cundari, C. Sarbu, and H. F. Pop, "Robust fuzzy principal component analysis (FPCA). A comparative study concerning interaction of carbonhydrogen bonds with molybdenum-oxo bonds," Journal of Chemical Information and Computer Sciences, Vol. 42, No. 6, pp. 1363-1369, 2002. https://doi.org/10.1021/ci025524s
- J. C. Bezdekand R. J. Hathaway, "Convergence of alternating optimization," Neural, Parallel and Scientific Computations, Vol. 11, No. 4, pp. 351-368, 2003.
- G. Heo and P. Gader, "Fuzzy SVM for noisy data: A robust membership calculation method," Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, pp. 431-436, 2009.
- H. Ichihashi, K. Honda, and N. Tani, "Gaussian mixture PDF approximation and fuzzy c-means clustering with entropy regularization," Proceedings of the 4th Asian Symposium, pp. 217-221, 2000.
- P. J. Huber, Robust Statistics, Wiley-Interscience, 1981.