Neural Networks. R & G Chapter 8

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Neural Networks. R & G Chapter 8



8.1
Feed
-
Forward Neural Networks

otherwise known as


The Multi
-
layer Perceptron

or


The Back
-
Propagation Neural Network

Figure 8.1 A fully connected feed
-
forward neural network

A diagramatic representation of a Feed
-
Forward NN

x1=

x2=

x3=

y

Inputs and outputs are numeric.

Inputs and outputs


Must be
numeric
, but can have any range in
general.


However, R &G prefer to consider
constraining to (0
-
1) range inputs and
outputs.

Equation 8.1

Neural Network Input Format


Real input data values

are standardized (scaled) so
that they all have ranges from 0


1.

Categorical input format


We need a way to convert categores to numberical values.


For “hair
-
colour” we might have values: red, blond, brown,
black, grey.

3 APPROACHES:


1. Use of (5) Dummy variables

(
BEST
):

Let XR=1 if hair
-
colour = red, 0 otherwise, etc…


2. Use a binary array
: 3 binary inputs can represent 8
numbers. Hence let red = (0,0,0), blond, (0,0,1), etc…

However, this sets up a
false

associations.


3. VERY BAD
: red = 0.0, blond = 0.25, … , grey = 1.0

Converts nominal scale into
false

interval scale.


Equation 8.2

Calculating Neuron Output:

The neuron threshhold function.

The following sigmoid function, called the standard logistic
function, is often used to model the effect of a neuron.



Consider node i, in the hidden layer. It has inputs x1, x2, and x3,
each with a weight
-
parameter.


Then calculate the output from the following function:

Figure 8.2 The sigmoid function

Note: the output values are in the range (0,1).

This is fine if we want to use our output
to predict a
probability of an event happening.

.


Other output types


If we have a
categorical output

with several values, then
we can
use dummy output notes

for each value of the
attribute.


E.g. if we were predicting one of 5 hair
-
colour classes, we
would have 5 output nodes, with 1 being certain yes, and 0
being certain no..


If we have a real output variable, with values outside the
range (0
-
1), then another transformation would be needed
to get realistic real outputs. Usually the inverse of the
scaling transformation. i.e.


The performance
parameters

of the feed
-
forward neural network are
the
weights.



The weights have to be varied so that the predicted output is close to the
true output value corresponding to the inpute values.


Training
of the ANN (Artificial Neural Net) is effected by:



Starting with artibrary wieghts



Presenting the data, instance by instance



adapting the weights according the error for each instance.


Repeating until convergence.

Training the Feed
-
forward net

8.2 Neural Network Training: A
Conceptual View

Supervised Learning/Training
with Feed
-
Forward Networks



Backpropagation Learning

Calculated error of each instance is used to ammend weights.



Least squares fitting.

All the errors for all instances are squared and summed
(=ESS). All weights are then changed to lower the ESS
.


BOTH METHODS GIVE THE SAME RESULTS.


IGNOR THE R & G GENETIC ALGORITHM STUFF.

Unsupervised Clustering with
Self
-
Organizing Maps

Figure 8.3 A 3x3 Kohonen network
with two input layer nodes

r

x

n

n

n’= n + r*(x
-
n)

Data Instance

8.3 Neural Network Explanation



Sensitivity Analysis



Average Member Technique


8.4 General Considerations




What input attributes will be used to build the network?



How will the network output be represented?



How many hidden layers should the network contain?



How many nodes should there be in each hidden layer?



What condition will terminate network training?


Neural Network Strengths



Work well with noisy data.



Can process numeric and categorical data.



Appropriate for applications requiring a time element.



Have performed well in several domains.



Appropriate for supervised learning and unsupervised

clustering.


Weaknesses



Lack explanation capabilities.



May not provide optimal solutions to problems.



Overtraining can be a problem.



Building Neural Networks with iDA

Chapter 9

9.1 A Four
-
Step Approach for
Backpropagation Learning

1.
Prepare the data to be mined.

2.
Define the network architecture.

3.
Watch the network train.

4.
Read and interpret summary results.

Example 1: Modeling the
Exclusive
-
OR Function

Figure 9.1A graph of the XOR
function

Step 1: Prepare The Data To Be
Mined

Figure 9.2 XOR training data

Step 2: Define The Network
Architecture

Figure 9.3 Dialog box for supervised
learning

Figure 9.4 Training options for
backpropagation learning

Step 3: Watch The Network Train

Figure 9.5 Neural network execution
window

Step 4: Read and Interpret
Summary Results

Figure 9.6 XOR output file for
Experiment 1

Figure 9.7 XOR output file for
Experiment 2

Example 2: The Satellite Image
Dataset

Step 1: Prepare The Data To Be
Mined

Figure 9.8 Satellite image data

Step 2: Define The Network
Architecture

Figure 9.9 Backpropagation learning
parameters for the satellite image
data

Step 3: Watch The Network Train

Step 4: Read And Interpret
Summary Results

Figure 9.10 Statistics for the satellite
image data

Figure 9.11 Satellite image data:
Actual and computed output

9.2 A Four
-
Step Approach for
Neural Network Clustering

Step 1: Prepare The Data To Be
Mined

The Deer Hunter Dataset

Step 2: Define The Network
Architecture

Figure 9.12 Learning parameters for
unsupervised clustering

Step 3: Watch The Network Train

Figure 9.13 Network execution
window

Step 4: Read And Interpret
Summary Results

Figure 9.14 Deer hunter data:
Unsupervised summary statistics

Figure 9.15 Output clusters for the
deer hunter dataset

9.3 ESX for Neural Network
Cluster Analysis