A First Course in FUZZY and NEURAL CONTROL

5.1. WHAT IS A NEURAL NETWORK? 167

so that the activation of that neuron is

f

√n

X

i=1

wixi−b

!

=

(

1 if

Pn

i=1wixi≥b

0 if

Pn

i=1wixi<b

This is depicted in Figure 5.1.
An artificial neuron is characterized by the parameters

θ=(w 1 ,w 2 ,...,wn,b,f)

The biasbcan be treated as another ìweightî by adding an input nodex 0 that
always takes the input valuex 0 =+1and settingw 0 =−b(see Figure 5.2).
With this representation, adjusting bias and adjusting weights can be done in
thesamemanner.

Figure 5.2. Artificial neuron with bias as weight

We will consider here onlyfeedforward neural networksñthatis,in-
formation propagates only forward as indicated by the direction of the arrows.
Mathematically speaking, a feedforward neural network is an acyclic weighted,
directed graph.
Viewing artificial neurons as elementary units for information processing, we
arrive at simple neural networks by considering several neurons at a time. The
neural network in Figure 5.3 consists of aninput layerñ a layer of input nodes
ñandoneoutput layerconsisting of neurons. This is referred to as asingle-
layer neural networkbecause the input layer is not a layer of neurons, that
is, no computations occur at the input nodes. This single-layer neural network
is called aperceptron.
Amulti-layer neural networkis a neural network with more than one
layer of neurons. Note that the activation functions of the different neurons can
be different. The neurons from one layer have weighted connections with neurons
in the next layer, but no connections between neurons of the same layer. A two-
layer neural network is depicted in Figure 5.4. Note that activation functions of
different neurons can be different. The input layer (or layer 0 )hasn+1nodes,