Chapter 2 Introduction to Neural network
Chapter 2 Introduction to Neural network
Chapter 2 Introduction to Neural network
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<strong>Chapter</strong> 5<br />
Layered Networks of<br />
perceptrons<br />
We have seen that a single perceptron can separate 2 linearly separable<br />
classes. If we put several perceptrons in a multilayer <strong>network</strong><br />
what’s the maximum number of classification regions, i.e. what’s<br />
the capacity of the <strong>network</strong> <br />
Proposition Let R(m, n) denote the number of regions bounded<br />
by m hyper-planes (of dim. n − 1) in a n-dimensional space(all<br />
hyperplane are going through origin), then<br />
where<br />
Example:<br />
R(m, n) = R(m − 1, n) + R(m − 1, n − 1)<br />
R(1, n) = 2 , n 1<br />
R(m, 0) = 0 , ∀m 1<br />
(fig 6.20) R(m, n) is computed recursively.<br />
M\N 0 1 2 3 4 5 6<br />
1 0 2 2 2 2 2 2<br />
2 0 2 4 4 4 4 4<br />
3 0 2 6 8 8 8 8<br />
4 0 2 8 14 16 16 16<br />
5 0 2 10 22 30 32 32<br />
6 0 2 12 32 52 62 64<br />
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