Abstract
The PS is a subspace spanned by all eigenvectors associated with the principal eigenvalues of the autocorrelation matrix of a high-dimensional vector sequence, and the subspace spanned by all eigenvectors associated with the minor eigenvalues is called the MS.
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References
Feng, D. Z., Zheng, W. X., & Jia, Y. (2005). Neural network learning algorithms for tracking minor subspace in high-dimensional data stream. IEEE Transactions on Neural Networks, 16(3), 513–521.
Bannour, S., & Azimi-Sadjadi, R. (1995). Principal component extraction using recursive least squares learning. IEEE Transactions on Neural Networks, 6(2), 457–469.
Cichocki, A., Kasprzak, W., & Skarbek, W. (1996). Adaptive learning algorithm for principal component analysis with partial data. Cybernetics Systems, 2, 1014–1019.
Kung, S., Diamantaras, K., & Taur, J. (1994). Adaptive principal component extraction (APEX) and applications. IEEE Transactions on Signal Processing, 42(5), 1202–1217.
Möller, R., & Könies, A. (2004). Coupled principal component analysis. IEEE Transactions on Neural Networks, 15(1), 214–222.
Oja, E. (1982). A simplified neuron mode as a principal component analyzer. Journal of Mathematics Biology, 15(3), 167–273.
Ouyang, S., Bao, Z., & Liao, G. S. (2000). Robust recursive least squares learning algorithm for principal component analysis. IEEE Transactions on Neural Networks, 11(1), 215–221.
Sanger, T. D. (1989). Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks, 2(6), 459–473.
Xu, L. (1993). Least mean square error reconstruction principle for selforganizing neural-nets. Neural Networks, 6(5), 627–648.
Xu, L., Oja, E., & Suen, C. (1992). Modified Hebbian learning for curve and surface fitting. Neural Networks, 5(3), 441–457.
Oja, E. (1992). Principal component, minor component and linear neural networks. Neural Networks, 5(6), 927–935.
Feng, D. Z., Bao, Z., & Jiao, L. C. (1998). Total least mean squares algorithm. IEEE Transactions on Signal Processing, 46(6), 2122–2130.
Luo, F. L., & Unbehauen, R. (1997). A minor subspace analysis algorithm. IEEE Transactions on Neural Networks, 8(5), 1149–1155.
Cirrincione, G., Cirrincione, M., Herault, J., & Van Huffel, S. (2002). The MCA EXIN neuron for the minor component analysis. IEEE Transactions on Neural Networks, 13(1), 160–187.
Ouyang, S., Bao, Z., Liao, G. S., & Ching, P. C. (2001). Adaptive minor component extraction with modular structure. IEEE Transactions on Signal Processing, 49(9), 2127–2137.
Zhang, Q., & Leung, Y. W. (2000). A class of learning algorithms for principal component analysis and minor component analysis. IEEE Transactions on Neural Networks, 11(2), 529–533.
Möller, R. (2004). A self-stabilizing learning rule for minor component analysis. International Journal of Neural System, 14(1), 1–8.
Douglas, S. C., Kung, S. Y., & Amari, S. (2002). A self-stabilized minor subspace rule. IEEE Signal Processing Letter, 5(12), 1342–1352.
Oja, E. (1989). Neural networks, principal components, and subspaces. International Journal of Neural Systems, 1(1), 61–68.
Williams, R. J. (1985). Feature discovery through error-correction learning. Institute of Cognition Science, University of California, San Diego, Technical Report, 8501.
Baldi, P. (1989). Linear learning: Landscapes and algorithms. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems 1. SanMateo, CA: Morgan Kaufmann.
Miao, Y. F., & Hua, Y. B. (1998). Fast subspace tracking and neural network learning by a novel information criterion. IEEE Transactions on Signal Processing, 46(7), 1967–1978.
Yang, B. (1995). Projection approximation subspace tracking. IEEE Transactions on Signal Processing, 43(1), 95–107.
Fu, Z., & Dowling, E. M. (1995). Conjugate gradient eigenstructure tracking for adaptive spectral estimation. IEEE Transactions on Signal Processing, 43(5), 1151–1160.
Mathew, G., Reddy, V. U., & Dasgupta, S. (1995). Adaptive estimation of eigensubspace. IEEE Transactions on Signal Processing, 43(2), 401–411.
Chen, T. (1997). Modified Oja’s algorithms for principal and minor subspace extraction. Neural Processing Letters, 5(2), 105–110.
Chen, T., & Amari, S. (2001). Unified stabilization approach to principal and minor components extraction. Neural Networks, 14(10), 1377–1387.
Hasan, M. A. (2007). Self-normalizing dual systems for minor and principal component extraction. In Proceedings of the ICASSP 2007 IEEE International Conference on Acoustic, Speech and Signal Processing (Vol. 4, No. 4, pp. 885–888), April 15–20, 2007.
Peng, D. Z., Zhang, Y., & Xiang, Y. (2009). A unified learning algorithm to extract principal and minor components. Digital Signal Processing, 19(4), 640–649.
Chen, T., Amari, S. I., & Lin, Q. (1998). A unified algorithm for principal and minor component extraction. Neural Networks, 11(3), 365–369.
Chen, T., Amari, S. I., & Murata, N. (2001). Sequential extraction of minor components. Neural Processing Letters, 13(3), 195–201.
Jonathan, H. M., Uwe, H., & Iven, M. Y. M. (2005). A dual purpose principal and minor component flow. Systems and Control Letters, 54(8), 759–769.
Karhunen, J., & Joutsensalo, J. (1995). Generalizations of principal component analysis, optimization problems, and neural networks. Neural Networks, 8(4), 549–562.
Chatterjee, C., Kang, Z. J., & Poychowdhury, V. P. (2000). Algorithm for accelerated convergence of adaptive PCA. IEEE Transactions on Neural Networks, 11(2), 338–355.
Chen, T., Hua, Y., & Yan, W. (1998). Global convergence of Oja’s subspace algorithm for principal component extraction. IEEE Transactions on Neural Networks, 9(1), 58–67.
Chauvin, Y. (1989). Principal component analysis by gradient descent on a constrained linear Hebbian cell. In Proceedings of the Joint International Conference on Neural Networks (pp. 373–380). San Diego, CA.
Magnus, J. R., & Neudecker, H. (1991). Matrix differential calculus with applications in statistics and econometrics (2nd ed.). New York: Wiley.
Kushner, H. J., & Clark, D. S. (1976). Stochastic approximation methods for constrained and unconstrained systems. New York: Springer.
Ljung, L. (1977). Analysis of recursive stochastic algorithms. IEEE Transactions on Automatic Control, 22(4), 551–575.
Kong, X. Y., Hu, C. H., & Han, C. Z. (2012). A dual purpose principal and minor subspace gradient flow. IEEE Transactions on Signal Processing, 60(1), 197–210.
LaSalle, J. P. (1976). The stability of dynamical systems. Philadelphia, PA: SIAM.
Kong, X. Y., Hu, C. H., & Han, C. Z. (2010). On the discrete time dynamics of a class of self-stabilizing MCA learning algorithms. IEEE Transactions on Neural Networks, 21(1), 175–181.
Ji, S. H., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346–2356.
Kang, Z. J., Chatterjee, C., & Roychowdhury, V. P. (2000). An adaptive quasi-Newton algorithm for eigensubspace estimation. IEEE Transactions on Signal Processing, 48(12), 3328–3333.
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Kong, X., Hu, C., Duan, Z. (2017). Dual Purpose for Principal and Minor Component Analysis. In: Principal Component Analysis Networks and Algorithms. Springer, Singapore. https://doi.org/10.1007/978-981-10-2915-8_5
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DOI: https://doi.org/10.1007/978-981-10-2915-8_5
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