CSUMS Summer 11

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