Abstract
Nonlinear PCA based on neural networks (NN) have been widely used in different applications in the past decade. There is a difficulty with the determination of the optimal topology for the networks that are used. Principal curves were introduced to nonlinear PCA to separate the original complex five-layer NN into two three-layer RBF networks and eased the above problem. Using the advantage of Fast Recursive Algorithm, where the number of neurons, the location of centers, and the weights between the hidden layer and the output layer can be identified simultaneously for the RBF networks, the topology problem for the nonlinear PCA based on NN can thus be solved. The simulation result shows that the method is excellent for solving nonlinear principal component problems.
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References
Chen, Q., Wyne, R., Goulding, P.R., Sandoz, D.J.: The application of principal component analysis and kernel density estimation to enhance process monitoring. Control Engineering Practice 8(5), 531–543 (2000)
Dong, D., McAvoy, T.J.: Nonlinear principal component analysis-based on principal curves and neural networks. Computers and Chemical Engineering 20(1), 65–78 (1996)
Hastie, T.J., Stuetzle, W.: Principal curves. Journal of American Statistical Association 84, 502–516 (1989)
Hiden, H., Willis, M., Tham, M., Montague, G.: Nonlinear principal components analysis using genetic programming. Computers and Chemical Engineering 23(3), 413–425 (1999)
Hinton, G.E., Salakhutdinov, R.R.: Reducing the dimensionality of data with neural networks. Science 313(5786), 504–507 (2006)
Jackson, J.E.: A Users Guide to Principal Components. Wiley Series in Probability and Mathematical Statistics. John Wiley, New York (1991)
Jia, F., Martin, E.B., Morris, A.J.: Nonlinear principal components analysis with application to process fault detection. International Journal of Systems Science 31(11), 1473–1487 (2000)
Kramer, M.A.: Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal 37(3), 233–243 (1991)
Li, K., Peng, J., Irwin, G.W.: A fast nonlinear model identification method. IEEE Transactions on Automatic Control 50(8), 1211–1216 (2005)
Li, K., Peng, J., Bai, E.: A two-stage algorithm for identification of nonlinear dynamic systems. Automatica 42(7), 1189–1197 (2006)
Tan, S., Mavrovouniotis, M.L.: Reducing data dimensionality through optimizing neural network inputs. AIChE Journal 41(6), 1471–1480 (1995)
Wilson, D.J.H., Irwin, G.W., Lightbody, G.: Rbf principal manifolds for process monitoring. IEEE Transactions on Neural Networks 10(6), 1424–1434 (1999)
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Liu, X., Li, K., McAfee, M., Deng, J. (2010). Improved Nonlinear PCA Based on RBF Networks and Principal Curves. In: Li, K., Fei, M., Jia, L., Irwin, G.W. (eds) Life System Modeling and Intelligent Computing. ICSEE LSMS 2010 2010. Lecture Notes in Computer Science, vol 6328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15621-2_2
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DOI: https://doi.org/10.1007/978-3-642-15621-2_2
Publisher Name: Springer, Berlin, Heidelberg
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