Abstract
We review a recently proposed family of functions for finding principal and minor components of a data set. We extend the family so that the Principal Subspace of the data set is found by using a method similar to that known as the Bigradient algorithm. We then amend the method in a way which was shown to change a Principal Component Analysis (PCA) rule to a rule for performing Factor Analysis (FA) and show its power on a standard problem. We find in both cases that, whereas the one Principal Component family all have similar convergence and stability properties, the multiple output networks for both PCA and FA have different properties.
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References
D. Charles and C. Fyfe. Discovering independent sources with an adapted pca network. In Proceedings of The Second International Conference on Soft Computing, SOCO97, Sept. 1997.
P. Földiák. Models of Sensory Coding. PhD thesis, University of Cambridge, 1992.
C. Fyfe. Introducing asymmetry into interneuron learning. Neural Computation, 7(6):1167–1181, 1995.
C. Fyfe. A neural net for pca and beyond. Neural Processing Letters, 6(1):33–41, 1997.
E. Oja. A simplified neuron model as a principal component analyser. Journal of Mathematical Biology, 16:267–273, 1982.
E. Oja. Neural networks, principal components and subspaces. International Journal of Neural Systems, 1:61–68, 1989.
E. Oja, H. Ogawa, and J. Wangviwattana. Principal component analysis by homogeneous neural networks, part 1: The weighted subspace criterion. IEICE Trans. Inf. & Syst., E75-D:366–375, May 1992.
Erkki Oja and Juha Karhunen. On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Mathematical Analysis and Applications, 106:69–84, 1985.
J. Rubner and P. Tavan. A self-organising network for principal-component analysis. Europhysics Letters, 10(7):693–698, Dec 1989.
T. D. Sanger. Analysis of the two-dimensional receptive fields learned by the generalized hebbian algorithm in response to random input. Biological Cybernetics, 1990.
L. Wang and J. Karhunen. A unified neural bigradient algorithm for robust pca and mca. International Journal of Neural Systems, 1995.
Qingfu Zhang and Yiu-Wing Leung. A class of learning algorithms for principal component analysis and minor component analysis. IEEE Transactions on Neural Networks, 11(1):200–204, Jan 2000.
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Han, Y., Fyfe, C. (2000). A General Class of Neural Networks for Principal Component Analysis and Factor Analysis. In: Leung, K.S., Chan, LW., Meng, H. (eds) Intelligent Data Engineering and Automated Learning — IDEAL 2000. Data Mining, Financial Engineering, and Intelligent Agents. IDEAL 2000. Lecture Notes in Computer Science, vol 1983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44491-2_24
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DOI: https://doi.org/10.1007/3-540-44491-2_24
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