Learning Algorithms of Neural Networks and

ApplicationsJonathan Reagan

Umass Dartmouth CSUMS Summer 11

August 3rd 2011

Outline What is a Neural Network? How does it work? Why do we care? Results Issues encountered Future work

Neural Network

InputLayers

HiddenLayers

OutputLayers

Idea of Learning Not realistic to study every possible

case Smaller sample can be used to model

the entire case Assume connections hold

Learning Methods (input)=[age, income, credit

score, etc] (output)=[dependability]

We want weights of α’s X*α(Hidden)=Y

iXiY

yxSign ii )(

Learning Methods-Cont. Use the learning method to find α

I Y-Xα I=0

tttttt XYXSign ))((2

11

Preliminary ResultsPerceptron Least Square

N AccuracysFailed 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

Speed of Convergence

1 2 3 4 5 6 7 8 9 10 110

100

200

300

400

500

600

700

800

900f(x) = 0.00314824074223472 exp( 1.37608992318393 x )R² = 0.943699577315672

Time vs. N

100 TrialsExponential (100 Trials)

Speed of Convergence-cont.

5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.50

100

200

300

400

500

600

700

800

900

f(x) = 197.05 x − 1176.92R² = 0.986531193868044

Time vs. N

100 TrialsLinear (100 Trials)

Why have limits on Iterations?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

Data Testing 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

Future Work Increase the speed of the Neural

Network Find more applicable data for testing

of the Neural Network Try multiple layer Neural Networks

and Compare

Questions?