# Difference between revisions of "Oja's rule"

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'''Oja's rule''', developed by Finnish computer scientist Erkki Oja in 1982, is a stable version of [[Hebb's rule]].<ref name="Oja82">Oja, Erkki (November 1982). [http://www.springerlink.com/content/u9u6120r003825u1 "Simplified neuron model as a principal component analyzer"]. <em>Journal of Mathematical Biology</em> <strong>15</strong> (3): 267–273</ref> | '''Oja's rule''', developed by Finnish computer scientist Erkki Oja in 1982, is a stable version of [[Hebb's rule]].<ref name="Oja82">Oja, Erkki (November 1982). [http://www.springerlink.com/content/u9u6120r003825u1 "Simplified neuron model as a principal component analyzer"]. <em>Journal of Mathematical Biology</em> <strong>15</strong> (3): 267–273</ref> | ||

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[[Category: Neural computational models]] | [[Category: Neural computational models]] | ||

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## Latest revision as of 03:23, 24 June 2016

**Oja's rule**, developed by Finnish computer scientist Erkki Oja in 1982, is a stable version of Hebb's rule.^{[1]}

## Model

As with Hebb's rule, we use a linear neuron. Given a set of k-dimensional inputs represented as a column vector生成缩略图出错：无法将缩略图保存到目标地点

, and a linear neuron with (initially random) synaptic weights from the inputs 生成缩略图出错：无法将缩略图保存到目标地点

the output the neuron is defined as follows:
生成缩略图出错：无法将缩略图保存到目标地点

Oja's rule gives the update rule which is applied after an input pattern is presented:

生成缩略图出错：无法将缩略图保存到目标地点

生成缩略图出错：无法将缩略图保存到目标地点

ignored for n>1 since η is small.
It can be shown that Oja's rule extracts the first principal component of the data set. If there are many Oja's rule neurons, then all will converge to the same principal component, which is not useful. Sanger's rule was formulated to get around this issue.

## References

- ↑ Oja, Erkki (November 1982). "Simplified neuron model as a principal component analyzer".
*Journal of Mathematical Biology***15**(3): 267–273