Jonathan Reagan
Umass
Dartmouth
CSUMS Summer 11
August 3
rd
2011
What is a Neural Network?
How does it work?
Why do we care?
Results
Issues encountered
Future work
Input
Layers
Hidden
Layers
Output
Layers
Not realistic to study every possible case
Smaller sample can be used to model the
entire case
Assume connections hold
(input)=[age, income, credit score, etc]
(output)=[dependability]
We want weights of
α
’s
X*
α
(Hidden)=Y
Use the learning method to find
α
I Y
-
X
α
I=0
Perceptron
Least Square
N
Accuracys
Failed
Trials
N
Accuracys
Failed
Trials
Min
AVG
Max
N/Total
Min
AVG
Max
N/Total
2
0.4048
0.5296
0.6081
0/100
2
.4081
.5310
.6306
0/100
3
0.3968
0.5247
0.6161
0/100
3
.4000
.5248
.6177
0/100
4
0.3968
0.5292
0.6306
0/100
4
.3984
.5195
.6194
0/100
5
0.4081
0.5312
0.6274
0/100
5
.4048
.5154
.6306
0/100
6
0.3984
0.5446
0.6161
2/100
6
.4081
.5248
.6226
0/100
7
0.4145
0.5312
0.6194
9/100
7
.3645
.5308
.6306
0/100
8
0.4194
0.544
0.6177
20/100
8
.3790
.5374
.6306
0/100
9
0.3952
0.5444
0.621
34/100
9
.3742
.5410
.6323
0/100
10
0.4048
0.5465
0.629
49/100
10
.3726
.5412
.6371
0/100
y = 0.0031e
1.3761x
R² = 0.9437
0
500
1000
1500
2000
2500
3000
3500
0
2
4
6
8
10
12
Time vs. N
100 Trials
Expon. (100 Trials)
y = 197.05x
-
1176.9
R² = 0.9865
0
100
200
300
400
500
600
700
800
900
0
2
4
6
8
10
12
Time vs. N
100 Trials
Linear (100 Trials)
2 million
Convergence
Failed Trials
4 million convergence
Failed Trials
N
T(Time)Seconds
N/Total
N
T(Time)Seconds
N/Total
2
0.03
0/50
2
0.03
0/50
3
0.04
0/50
3
0.05
0/50
4
0.23
0/50
4
0.24
0/50
5
0.93
0/50
5
0.88
0/50
6
10.49
0/50
6
10.4
0/50
7
50.24
.2/50
7
79.8
.2/50
8
143.07
.8/50
8
260.2
.7/50
9
259.8
15/50
9
484.7
14/50
10
363.6
22/50
10
727.5
22/50
11
483.9
28/50
11
928.2
28/50
12
560.1
34/50
12
1096.1
33/50
13
661.7
40/50
13
1287.2
38/50
14
732.7
43/50
14
1416.2
42/50
15
750.4
44/50
15
1463.7
44/50
16
778.1
46/50
16
1508.9
46/50
17
819.3
48/50
17
1607.7
48/50
18
832
50/50
18
1665.4
50/50
Random Data can’t be learned
Deterministic Data can be learned
Adding Random variance decreases
Accuracy
More values of N the Better
But more values of N take Longer
Increase the speed of the Neural Network
Find more applicable data for testing of
the Neural Network
Try multiple layer Neural Networks and
Compare
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