Java and Web Technologies
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NEURAL NETWORKS
Ivan F Wilde
Mathematics Department
King’s College London
London, WC2R 2LS, UK
ivan.wilde@kcl.ac.uk
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
Contents
1 Matrix Memory . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2 Adaptive Linear Combiner
....................
21
3 Artificial Neural Networks
....................
35
..........................
45
5 Multilayer Feedforward Networks . . . . . . . . . . . . . . . . .
75
6 Radial Basis Functions
95
4 The Perceptron
......................
7 Recurrent Neural Networks . . . . . . . . . . . . . . . . . . . . 103
8 Singular Value Decomposition
Bibliography
. . . . . . . . . . . . . . . . . . 115
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
Chapter 1
Matrix Memory
We wish to construct a system which possesses so-called associative memory.
This is definable generally as a process by which an input, considered as a
“key”, to a memory system is able to evoke, in a highly selective fashion, a specific response associated with that key, at the system output. The signalresponse association should be “robust”, that is, a “noisy” or “incomplete” input signal should none the less invoke the correct response—or at least an acceptable response. Such a system is also called a content addressable memory. 3
mapping
stimulus
response
Figure 1.1: A content addressable memory.
The idea is that the association should not be defined so much between the individual stimulus-response pairs, but rather embodied as a whole collection of such input-output patterns—the system is a distributive associative memory (the input-output pairs are “distributed” throughout the system memory rather than the particular input-output pairs being somehow represented individually in various different parts of the
www.jwjobs.net
NEURAL NETWORKS
Ivan F Wilde
Mathematics Department
King’s College London
London, WC2R 2LS, UK
ivan.wilde@kcl.ac.uk
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
Contents
1 Matrix Memory . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2 Adaptive Linear Combiner
....................
21
3 Artificial Neural Networks
....................
35
..........................
45
5 Multilayer Feedforward Networks . . . . . . . . . . . . . . . . .
75
6 Radial Basis Functions
95
4 The Perceptron
......................
7 Recurrent Neural Networks . . . . . . . . . . . . . . . . . . . . 103
8 Singular Value Decomposition
Bibliography
. . . . . . . . . . . . . . . . . . 115
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
Chapter 1
Matrix Memory
We wish to construct a system which possesses so-called associative memory.
This is definable generally as a process by which an input, considered as a
“key”, to a memory system is able to evoke, in a highly selective fashion, a specific response associated with that key, at the system output. The signalresponse association should be “robust”, that is, a “noisy” or “incomplete” input signal should none the less invoke the correct response—or at least an acceptable response. Such a system is also called a content addressable memory. 3
mapping
stimulus
response
Figure 1.1: A content addressable memory.
The idea is that the association should not be defined so much between the individual stimulus-response pairs, but rather embodied as a whole collection of such input-output patterns—the system is a distributive associative memory (the input-output pairs are “distributed” throughout the system memory rather than the particular input-output pairs being somehow represented individually in various different parts of the