Abstract
This paper presents a linear replicator [2][4] based on minimizing the reconstruction error [8][9]. It can be used to study the learning behaviors of the kernel principal component analysis [10], the Hebbian algorithm for the principle component analysis (PCA) [8][9] and the iterative kernel PCA [3].
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References
Boser, B.E., Guyon, I.M., Vapnik, V.N.: A Training Algorithm for Optimal Margin Classifiers. In: COLT 1992: Proceedings of the Fifth Annual Workshop on Computational Learning Theory, pp. 144–152 (1992)
Hecht-Nielsen, R.: Replicator Neural Networks for Universal Optimal Source Coding. Science 269, 1860–1863 (1995)
Kim, K.I., Franz, M.O., Scholkopf, B.: Iterative Kernel Principal Component Analysis for Image Modeling. IEEE Transcations on Pattern Analysis and Machine Intelligence 27, 1351–1366 (2005)
Liou, C.-Y., Chen, H.-T., Huang, J.-C.: Separation of Internal Representations of the Hidden Layer. In: Proceedings of the International Computer Symposium, Workshop on Artificial Intelligence, pp. 26–34 (2000)
Liou, C.-Y., Cheng, W.-C.: Resolving Hidden Representations. In: Ishikawa, M., et al. (eds.) ICONIP 2007, Part II. LNCS, vol. 4985, pp. 254–263. Springer, Heidelberg (2008)
Mercer, J.: Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations. Philosophical Transactions of the Royal Society of London. Series A 209, 415–446 (1909)
Oja, E.: Neural Networks, Principal Components, and Subspaces. International Journal of Neural Systems 1, 61–68 (1989)
Oja, E.: Simplified Neuron Model as a Principal Component Analyzer. Journal of Mathematical Biology 15, 267–273 (1982)
Sanger, T.D.: Optimal Unsupervised Learning in a Single-Layer Linear Feedforward Neural Network. Neural Networks 2, 459–473 (1989)
Scholkopf, B., Smola, A., Müller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)
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Cheng, WC., Liou, CY. (2010). Linear Replicator in Kernel Space. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13318-3_10
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DOI: https://doi.org/10.1007/978-3-642-13318-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13317-6
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