Abstract
In this paper, we introduce a new multivariate statistical process control chart for outliers detection using kernel local linear embedding algorithm. The proposed control chart is effective in the detection of outliers, and its control limits are derived from the eigen-analysis of the kernel matrix in the Hilbert feature space. Our experimental results show the much improved performance of the proposed control chart in comparison with existing multivariate monitoring and controlling charts.
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.
References
D.C. Montgomery, Introduction to Statistical Quality Control, John Wiley & Sons, 2005.
K. Yang and J. Trewn, Multivariate Statistical Methods in Quality Management, Mc Graw Hill Professional, 2004.
K.H. Chen, D.S. Boning, and R.E. Welch, “Multivariate statistical process control and signature analysis using eigenfactor detection methods,” Proc. Symposium on the Interface of Computer Science and Statistics, Costa Mesa, CA, 2001.
I.T. Jolliffe, Principal Component Analysis, New York: Springer, 1986.
J.A. Vargas, “Robust estimation in multivariate control charts for individual observations,” Journal of Quality Technology, vol. 35, no. 4, pp. 367-376, 2003
N.D. Tracy, J.C. Young, and R.L. Mason, “Multivariate quality control charts for individual observations,” Journal of Quality Technology, vol. 24, no. 22, pp. 88-95, 1992.
J.H. Sullivan and W.H. Woodall, “A comparison of multivariate control charts for individual observations,” Journal of Quality Technology, vol. 28, no. 24, pp. 398-408, 1996.
F.A. Alqallaf, K.P. Konis, and R.D. Martin, and R.H. Zamar, “Scalable robust covariance and correlation estimates for data mining,” Proc. ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 14-23, 2002.
S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice Hall, 2nd edition, 1998.
B. Scholkopf, A. Smola, and K-R. Muller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation, vol. 10, pp. 1299-1319, 1998.
J. Shawe-Taylor and C. Williams, “The stability of kernel principal components analysis and its relation to the process eigenspectrum.,” Advances in neural information processing systems, vol. 15, 2003.
S. Roweis and L. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V.
About this paper
Cite this paper
Tsagaroulis, T., Hamza, A.B. (2008). Kernel Locally Linear Embedding Algorithm for Quality Control. In: Sobh, T., Elleithy, K., Mahmood, A., Karim, M.A. (eds) Novel Algorithms and Techniques In Telecommunications, Automation and Industrial Electronics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8737-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8737-0_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8736-3
Online ISBN: 978-1-4020-8737-0
eBook Packages: EngineeringEngineering (R0)