Abstract
Principal component analysis (PCA) by neural networks is one of the most frequently used feature extracting methods. To process huge data sets, many learning algorithms based on neural networks for PCA have been proposed. However, traditional algorithms are not globally convergent. In this paper, a new PCA learning algorithm based on cascade recursive least square (CRLS) neural network is proposed. This algorithm can guarantee the network weight vector converges to an eigenvector associated with the largest eigenvalue of the input covariance matrix globally. A rigorous mathematical proof is given. Simulation results show the effectiveness of the algorithm.
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Golub GH, Van Loan CF (1996) Matrix computation. The Johns Hopkins University Press
Anisse T, Gianalvo C (1999) Against the convergence of the minor component analysis neurons. IEEE Trans Neural Netw 10(1):207–210
Baldi P, Hornik K (1995) Learning in linear neural networks: a survey. IEEE Trans Neural Netw 6(4):837–858
Bannour S, Azimi-Sadjadi MR (1995) Principal component extraction using recursive least spares learning. IEEE Trans Neural Netw 6(2):457–469
Chatterjee C, Kung Z, Roychowdhury VP (2000) Algorithms for accelerated convergence of adaptive PCA. IEEE Trans Neural Netw 11(3):338–355
Cichock A, Kasprzak W, Skarbek W (1996) Adaptive learning algorithm for principal component analysis with partial data. Proc Cybern Syst 2:1014–1019
Firori S, Piazaa F (2000) A general class of φ APEX PCA Neural algorithm. IEEE Trans Circuits and Systems, I 47(9):1397–1998
Marko VJ (2003) A new simple ∞OH neuron model as biologically plausible principal component analyzer. IEEE Trans Neural Netw 14(4):853–859
Oja E (1989) Neural networks, principal components, and subspaces. Int J Neural Syst 1:61–68
Ouyang S, Bao Z, Liao G (2000) Robust recursive least squares learning algorithm for principal component analysis. IEEE Trans Neural Netw 11(1):215–221
Sanger TD (1989) Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Netw 2(6):459–473
Weingessels A, Hornik K (2000) Local PCA algorithms. IEEE Trans Neural Netw 11(6):1242–1250
Zhang Q, Leung Y (2000) A class of learning algorithms for principal component analysis and minor component analysis. IEEE Trans Neural Netw 11(1):529–533
Costa S, Fiori S (2001) Image compression using principal component neural networks. Image Vis Comput 19:649–668
Chen T, Hua Y, Yan W (1998) Global convergence of Oja subspace algorithm for principal component extraction. IEEE Trans Neural Netw 9(1):58–67
Xu L (1993) Least mean square error reconstruction principle for self-organizing neural nets. Neural Netw 6(5):627–648
Yan W, Helmke U, Moore JB (1994) Global analysis of Oja’s flow for neural networks. IEEE Trans Neural Netw 5(5):674–683
Zufiria PJ (2002) On the discrete time dynamics of the basic hebbian neural network node. IEEE Trans Neural Netw 13(6):1342–1352
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This work is supported in part by the National Science Foundation of China under grant number A0324638 and Youth Science and Technology Foundation of UESTC YF020801.
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Ye, M., Yi, Z. & Lv, J. A globally convergent learning algorithm for PCA neural networks. Neural Comput & Applic 14, 18–24 (2005). https://doi.org/10.1007/s00521-004-0435-y
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DOI: https://doi.org/10.1007/s00521-004-0435-y