This document provides an overview of neural network analysis, including what neural networks are, their advantages and disadvantages, and two common types - multilayer perceptron and Kohonen networks. It describes how neural networks are trained using cases with input and output data, and how the network parameters are adjusted during training to best fit the data. The training process involves using a portion of cases for training, another portion for verification, and the remainder for testing the network.

1. BASICS OF
NEURAL NETWORK ANALYSIS
Multilayer Perceptron Neural Networks
Kohonen Neural Networks

2. CONTENTS
• What
is
a
Neural
Network?
• What
can
it
do
for
me?
• Advantages
and
Disadvantages
• Two
Common
Types
of
Neural
Networks
– Mul?layer
Perceptron
• A
“black
box”
model
predicts
output
values
– Kohonen
Classifica?on
• Experimental
cases
are
classified
into
groups
• Training
Neural
Networks

3. What
is
a
Neural
Network?
A
neuron
is
a
func?on,
Y=f(X),
with
input
X
and
output
Y:
X
Y
Y
=
f(X)
Neurons
are
connected
by
synapses.
A
synapse
mul?plies
the
output
by
a
weigh?ng
factor,
W:
X
WY
Z
Y
=
f(X)
Z
=
g(WY)

4. The
func?on
in
a
neuron
can
be
linear
or
nonlinear.
A
typical
nonlinear
func?on
is
the
Sigmoid
func?on:

5. Neural
networks
are
trained
with
cases
• What
is
a
case?
– A
case
is
an
experiment
with
one
or
more
inputs
(controlled
variables)
and
one
or
more
outputs
(results
or
observa?ons)
– Example
• Inputs:
temp
298°K,
ini?al
concentra?on
1.0
g/l,
?me
7
days;
Outputs:
final
concentra?on
0.9
g/l,
degrada?on
product
0.15
g/l

6. When
a
neural
network
is
“trained”
with
different
cases,
the
parameters
of
the
neuronal
func?ons
and
synap?c
weigh?ng
factors
are
adjusted
for
the
best
“fit”:
The
inputs
are
x1
thru
xp.
The
outputs
are
y1
thru
ym.
The
w-­‐values
are
the
synap?c
weigh?ng
factors.
The
u-­‐
values
are
sums
of
weigh?ng
factors.

7. What
can
a
neural
network
do
for
me?
• Analyze
data
with
a
large
number
of
variables
with
complex
rela?onships.
• Develop
formula?ons
or
mul?-­‐step
processes.
• Compare
performance
characteris?cs
of
mul?ple
formula?ons
or
processes.
• Analyze
experimental
data
even
when
data
points
are
missing
or
not
in
a
balanced
design.

8. Advantages
• No
need
to
propose
a
model
prior
to
data
analysis.
• Can
handle
variables
with
very
complex
interac?ons.
• No
assump?on
that
inputs
and
outputs
are
normally
distributed.
• More
robust
to
noise.
• No
need
to
pre-­‐determine
important
variables
and
interac?ons
with
a
Design
of
Experiments

9. Disadvantages
• Need
a
lot
of
data.
– (Number
of
Training
Cases)
≈
10
x
(Number
of
Synapses)
• Output
variables
are
not
expressed
as
analy?c
func?ons
of
input
variables.

10. Training
Kohonen
Neural
Networks
and
Mul?layer
Perceptron
Neural
Networks
• A
por?on
of
the
cases
are
randomly
selected
to
be
training
cases
–
typically
about
70%.
• A
por?on
of
the
cases
are
randomly
selected
to
be
verifica?on
cases
–
typically
about
20%.
• The
remainder
are
test
cases
–
typically
about
10%.

11. Teaching
the
neural
network
with
just
the
training
cases
will
result
in
“over-­‐fieng”
the
data:

12. So,
the
verifica?on
cases
are
added:

13. Then
the
network
is
“retrained”
with
the
verifica?on
cases
and
the
final
model
is
the
result:

14. Finally,
the
test
cases
are
used
to
determine
how
well
the
“black
box”
model
predicts
the
outputs.
The
outputs
of
a
Kohonen
Neural
Network
will
be
the
different
“classes”
into
which
the
cases
have
been
classified.
The
outputs
of
a
Mul?layer
Perceptron
Neural
Network
will
be
con?nuous
variables
represen?ng
the
performance
characteris?cs
of
all
the
formula?ons
or
all
the
mul?-­‐step
processes.
(Remember,
each
formula?on
or
process
is
a
“case”.)