In Brazil, one of the ways for a person to enter university consists of taking an exam and if he/she achieves the minimum grade for the course that he/she is seeking, then he/she can enroll. To demonstrate the backpropagation algorithm, let us consider this scenario. The data shown in the table was collected from a university database. The second column represents the person's gender (one means female and zero means male); the third column has grades scaled by 100 and the last column is formed by two neurons (1,0 means performed enrollment and 0,1 means waiver enrollment):
|
Sample |
Gender |
Grade |
Enrollment Status |
|---|---|---|---|
|
1 |
1 |
0.73 |
1 0 |
|
2 |
1 |
0.81 |
1 0 |
|
3 |
1 |
0.86 |
1 0 |
|
4 |
0 |
0.65 |
1 0 |
|
5 |
0 |
0.45 |
1 0 |
|
6 |
1 |
0.70 |
0 1 |
|
7 |
0 |
0.51 |
0 1 |
|
8 |
1 |
0.89 |
0 1 |
|
9 |
1 |
0.79 |
0 1 |
|
10 |
0 |
0.54 |
0 1 |
Double[][] _neuralDataSet = {
{1.0, 0.73, 1.0, -1.0}
, {1.0, 0.81, 1.0, -1.0}
, {1.0, 0.86, 1.0, -1.0}
, {0.0, 0.65, 1.0, -1.0}
, {0.0, 0.45, 1.0, -1.0}
, {1.0, 0.70, -1.0, 1.0}
, {0.0, 0.51, -1.0, 1.0}
, {1.0, 0.89, -1.0, 1.0}
, {1.0, 0.79, -1.0, 1.0}
, {0.0, 0.54, -1.0, 1.0}
};
int[] inputColumns = {0,1};
int[] outputColumns = {2,3};
NeuralDataSet neuralDataSet = new NeuralDataSet(_neuralDataSet,inputColumns,outputColumns);We create a neural network containing three neurons in the hidden layer, as shown in the following figure:
int numberOfInputs = 2;
int numberOfOutputs = 2;
int[] numberOfHiddenNeurons={5};
Linear outputAcFnc = new Linear(1.0);
Sigmoid hdAcFnc = new Sigmoid(1.0);
IActivationFunction[] hiddenAcFnc={hdAcFnc };
NeuralNet nnlm = new NeuralNet(numberOfInputs,numberOfOutputs
,numberOfHiddenNeurons,hiddenAcFnc,outputAcFnc);
NeuralNet nnelm = new NeuralNet(numberOfInputs,numberOfOutputs
,numberOfHiddenNeurons,hiddenAcFnc,outputAcFnc);We've also set up the learning algorithms Levenberg-Marquardt and extreme learning machines:
LevenbergMarquardt lma = new LevenbergMarquardt(nnlm,
neuralDataSet,
LearningAlgorithm.LearningMode.BATCH);
lma.setDamping(0.001);
lma.setMaxEpochs(100);
lma.setMinOverallError(0.0001);
ELM elm = new ELM(nnelm,neuralDataSet);
elm.setMinOverallError(0.0001);
elm.printTraining=true;Running the training, we find that the training was successful. For the Levenberg-Marquardt algorithm, the minimum satisfied error was found after nine epochs:
And the extreme learning machine found an error near to zero:
