Artificial Neural Networks. The Brain Brain vs. Computers The Perceptron Multilayer networks Some Applications. Artificial Neural Networks. Other terms/names connectionist parallel distributed processing neural computation adaptive networks.. History
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The Brain
Brain vs. Computers
The Perceptron
Multilayer networks
Some Applications
A neuron has a cell body, a branching input
structure (the dendrIte) and a branching output structure (the axOn)
y1
w1j
w2j
y2
w3j
O
y3
yi
wij
A Simple Model of a Neuron (Perceptron)
y1
w1j
w2j
y2
w3j
f(x)
O
y3
yi
wij
An Artificial Neuron
1 if wi xi >t
Output=
0 otherwise
{
i=0
1 if wixi >t
output=
0 otherwise
{
i=0
AND with a Biased input
1
W1 = 1.5
X
t = 0.0
W2 = 1
W3 = 1
Y
Simple networkWhile epoch produces an error
Present network with next inputs from epoch
Error = T – O
If Error <> 0 then
Wj = Wj + LR * Ij * Error
End If
End While
Epoch : Presentation of the entire training set to the neural network. In the case of the AND function an epoch consists of four sets of inputs being presented to the network (i.e. [0,0], [0,1], [1,0], [1,1])
Error: The error value is the amount by which the value output by the network differs from the target value. For example, if we required the network to output 0 and it output a 1, then Error = 1
Target Value, T: When we are training a network we not only present it with the input but also with a value that we require the network to produce. For example, if we present the network with [1,1] for the AND function the target value will be 1
Output , O: The output value from the neuron
Ij : Inputs being presented to the neuron
Wj: Weight from input neuron (Ij) to the output neuron
LR : The learning rate. This dictates how quickly the network converges. It is set by a matter of experimentation. It is typically 0.1
A B Output
0 0 0
0 1 0
1 0 0
1 1 1
1
W1 = ?
x
t = 0.0
W2 = ?
W3 = ?
y
Training PerceptronsW1 = 0.3
x
t = 0.0
W2 = 0.5
W3 =0.4
y
Training PerceptronsFor AND
A B Output
0 0 0
0 1 0
1 0 0
1 1 1
x2
+
+
+


x1
+


Decision Surface of a Perceptronx2
+

x1
+

Linearly separable
NonLinearly separable
B
B
A
B
A
A
B
B
A
B
A
A
B
B
A
B
A
Different NonLinearlySeparable Problems
Types of
Decision Regions
ExclusiveOR
Problem
Classes with
Meshed regions
Most General
Region Shapes
Structure
SingleLayer
Half Plane
Bounded By
Hyperplane
TwoLayer
Convex Open
Or
Closed Regions
Arbitrary
(Complexity
Limited by No.
of Nodes)
ThreeLayer
Input Signals (External Stimuli)
Multilayer Perceptron (MLP)
Output Layer
Adjustable
Weights
Input Layer
f(x) =
1 + e ax
Standard activation functions
Drives 70 mph on a public highway
30 outputs
for steering
30x32 weights
into one out of
four hidden
unit
4 hidden
units
30x32 pixels
as inputs