LYAPUNOV FUNCTIONS FOR CONVERGENCE OF PRINCIPAL COMPONENT ALGORITHMS
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PLUMBLEY, MD (1995) LYAPUNOV FUNCTIONS FOR CONVERGENCE OF PRINCIPAL COMPONENT ALGORITHMS NEURAL NETWORKS, 8 (1). pp. 11-23.
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Plumbley95-nn_accepted_notice.pdf - Accepted version Manuscript Available under License : See the attached licence file. Download (414kB) | Preview |
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Abstract
Recent theoretical analyses of a class of unsupervized Hebbian principal component algorithms have identified its local stability conditions. The only locally stable solution for the subspace P extracted by the network is the principal component subspace P∗. In this paper we use the Lyapunov function approach to discover the global stability characteristics of this class of algorithms. The subspace projection error, least mean squared projection error, and mutual information I are all Lyapunov functions for convergence to the principal subspace, although the various domains of convergence indicated by these Lyapunov functions leave some of P-space uncovered. A modification to I yields a principal subspace information Lyapunov function I′ with a domain of convergence that covers almost all of P-space. This shows that this class of algorithms converges to the principal subspace from almost everywhere.
| Item Type: | Article | ||||||
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| Subjects : | Electronic Engineering | ||||||
| Divisions : | Faculty of Engineering and Physical Sciences > Electronic Engineering | ||||||
| Authors : |
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| Date : | 1 January 1995 | ||||||
| DOI : | 10.1016/0893-6080(95)91644-9 | ||||||
| Copyright Disclaimer : | © 1995. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | ||||||
| Uncontrolled Keywords : | Science & Technology, Technology, Computer Science, Artificial Intelligence, Computer Science, COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE, NEUROSCIENCES, NEURAL NETWORKS, UNSUPERVIZED LEARNING, PRINCIPAL COMPONENT ANALYSIS, INFORMATION THEORY, HEBBIAN ALGORITHMS, LYAPUNOV FUNCTIONS, OJA RULE | ||||||
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| Depositing User : | Symplectic Elements | ||||||
| Date Deposited : | 02 Nov 2016 17:03 | ||||||
| Last Modified : | 31 Oct 2017 18:40 | ||||||
| URI: | http://epubs.surrey.ac.uk/id/eprint/812060 |
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