Abstract
A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived. It is shown that the model neuron tends to extract the principal component from a stationary input vector sequence.
This is a preview of subscription content, access via your institution.
Reference
Anderson, T. W.: An introduction to multivariate statistical analysis. New York: Wiley 1958
Cooper, L. N., Liberman, F., Oja, E.: A theory for the acquisition and loss of neuron specificity in visual cortex. Biol. Cyb. 33, 9–28 (1979)
Hale, J. K.: Ordinary differential equations. New York: Wiley 1969
Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cyb. 43, 59–69 (1982)
Kohonen, T., Lehtiö, P., Oja, E.: Storage and processing of information in distributed associative memory systems. In: Hinton, G., Anderson, J. A. (eds.). Parallel models of associative memory, pp. 105–143. Hillsdale: Erlbaum 1981
Kushner, H., Clark, D.: Stochastic approximation methods for constrained and unconstrained systems. New York: Springer 1978
Ljung, L.: Analysis of recursive stochastic algorithms. IEEE Trans. Automatic Control AC-22, 551–575 (1977)
von der Malsburg, C.: Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14, 85–100 (1973)
McCulloch, W. S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophysics 5, 115–133 (1943)
Nass, M., Cooper, L. N.: A theory for the development of feature detecting cells in visual cortex. Biol. Cyb. 19, 1–18 (1975)
Oja, E., Karhunen, J.: On stochastic approximation of eigenvectors and eigenvalues of the expectation of a random matrix. Helsinki University of Technology, Report TKK-F-A458 (1981)
Perez, R., Glass, L., Shlaer, R. J.: Development of specificity in the cat visual cortex. J. Math. Biol. 1, 275–288 (1975)
Stent, G. S.: A psychological mechanism for Hebb's postulate of learning. Proc. Natl. Acad. Sciences 70, 997–1001 (1973)
Takeuchi, A., Amari, S.: Formation of topographic maps and columnar microstructures in nerve fields. Biol. Cyb. 35, 63–72 (1979)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oja, E. Simplified neuron model as a principal component analyzer. J. Math. Biology 15, 267–273 (1982). https://doi.org/10.1007/BF00275687
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00275687
Key words
- Neuron models
- Synaptic plasticity
- Stochastic approximation