| public setValue ( int index, double value ) : void | ||
| index | int | |
| value | double | |
| return | void | |
public void testFeedForwardAndBAckLoopWorksWithMomentum()
{
// example 11.14 of Neural Network Design by Hagan, Demuth and Beale
Matrix hiddenLayerWeightMatrix = new Matrix(2, 1);
hiddenLayerWeightMatrix.set(0, 0, -0.27);
hiddenLayerWeightMatrix.set(1, 0, -0.41);
Vector hiddenLayerBiasVector = new Vector(2);
hiddenLayerBiasVector.setValue(0, -0.48);
hiddenLayerBiasVector.setValue(1, -0.13);
Vector input = new Vector(1);
input.setValue(0, 1);
Matrix outputLayerWeightMatrix = new Matrix(1, 2);
outputLayerWeightMatrix.set(0, 0, 0.09);
outputLayerWeightMatrix.set(0, 1, -0.17);
Vector outputLayerBiasVector = new Vector(1);
outputLayerBiasVector.setValue(0, 0.48);
Vector error = new Vector(1);
error.setValue(0, 1.261);
double learningRate = 0.1;
double momentumFactor = 0.5;
FeedForwardNeuralNetwork ffnn = new FeedForwardNeuralNetwork(
hiddenLayerWeightMatrix, hiddenLayerBiasVector,
outputLayerWeightMatrix, outputLayerBiasVector);
ffnn.setTrainingScheme(new BackPropLearning(learningRate,
momentumFactor));
ffnn.processInput(input);
ffnn.processError(error);
Matrix finalHiddenLayerWeights = ffnn.getHiddenLayerWeights();
Assert.AreEqual(-0.2675, finalHiddenLayerWeights.get(0, 0), 0.001);
Assert.AreEqual(-0.4149, finalHiddenLayerWeights.get(1, 0), 0.001);
Vector hiddenLayerBias = ffnn.getHiddenLayerBias();
Assert.AreEqual(-0.4775, hiddenLayerBias.getValue(0), 0.001);
Assert.AreEqual(-0.1349, hiddenLayerBias.getValue(1), 0.001);
Matrix finalOutputLayerWeights = ffnn.getOutputLayerWeights();
Assert.AreEqual(0.1304, finalOutputLayerWeights.get(0, 0), 0.001);
Assert.AreEqual(-0.1235, finalOutputLayerWeights.get(0, 1), 0.001);
Vector outputLayerBias = ffnn.getOutputLayerBias();
Assert.AreEqual(0.6061, outputLayerBias.getValue(0), 0.001);
}
public Vector plus(Vector v)
{
Vector result = new Vector(size());
for (int i = 0; i < size(); i++)
{
result.setValue(i, getValue(i) + v.getValue(i));
}
return result;
}
public Vector copyVector()
{
Vector result = new Vector(getRowDimension());
for (int i = 0; i < getRowDimension(); i++)
{
result.setValue(i, getValue(i));
}
return result;
}
public Vector plus(Vector v)
{
Vector result = new Vector(size());
for (int i = 0; i < size(); i++)
{
result.setValue(i, getValue(i) + v.getValue(i));
}
return(result);
}
public Vector copyVector()
{
Vector result = new Vector(getRowDimension());
for (int i = 0; i < getRowDimension(); i++)
{
result.setValue(i, getValue(i));
}
return(result);
}
public void testFeedForward()
{
// example 11.14 of Neural Network Design by Hagan, Demuth and Beale
// lots of tedious tests necessary to ensure nn is fundamentally correct
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
Vector expected = new Vector(2);
expected.setValue(0, 0.321);
expected.setValue(1, 0.368);
Vector result1 = layer1.feedForward(inputVector1);
Assert.AreEqual(expected.getValue(0), result1.getValue(0), 0.001);
Assert.AreEqual(expected.getValue(1), result1.getValue(1), 0.001);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
Vector result2 = layer2.feedForward(inputVector2);
Assert.AreEqual(0.446, result2.getValue(0), 0.001);
}
public void testSensitivityMatrixCalculationFromErrorVector()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
Matrix sensitivityMatrix = layer2Sensitivity.getSensitivityMatrix();
Assert.AreEqual(-2.522, sensitivityMatrix.get(0, 0), 0.0001);
}
public Vector feedForward(Vector inputVector) {
lastInput = inputVector;
Matrix inducedField = weightMatrix.times(inputVector).plus(biasVector);
Vector inducedFieldVector = new Vector(numberOfNeurons());
for (int i = 0; i < numberOfNeurons(); i++) {
inducedFieldVector.setValue(i, inducedField.get(i, 0));
}
lastInducedField = inducedFieldVector.copyVector();
Vector resultVector = new Vector(numberOfNeurons());
for (int i = 0; i < numberOfNeurons(); i++) {
resultVector.setValue(i, activationFunction
.activation(inducedFieldVector.getValue(i)));
}
// set the result as the last activation value
lastActivationValues = resultVector.copyVector();
return resultVector;
}
public void testWeightsAndBiasesUpdatedCorrectly()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
layer1Sensitivity
.sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);
BackPropLearning.calculateWeightUpdates(layer2Sensitivity, layer1
.getLastActivationValues(), 0.1);
BackPropLearning.calculateBiasUpdates(layer2Sensitivity, 0.1);
BackPropLearning.calculateWeightUpdates(layer1Sensitivity,
inputVector1, 0.1);
BackPropLearning.calculateBiasUpdates(layer1Sensitivity, 0.1);
layer2.updateWeights();
Matrix newWeightMatrix2 = layer2.getWeightMatrix();
Assert.AreEqual(0.171, newWeightMatrix2.get(0, 0), 0.001);
Assert.AreEqual(-0.0772, newWeightMatrix2.get(0, 1), 0.001);
layer2.updateBiases();
Vector newBiasVector2 = layer2.getBiasVector();
Assert.AreEqual(0.7322, newBiasVector2.getValue(0), 0.00001);
layer1.updateWeights();
Matrix newWeightMatrix1 = layer1.getWeightMatrix();
Assert.AreEqual(-0.265, newWeightMatrix1.get(0, 0), 0.001);
Assert.AreEqual(-0.419, newWeightMatrix1.get(1, 0), 0.001);
layer1.updateBiases();
Vector newBiasVector1 = layer1.getBiasVector();
Assert.AreEqual(-0.475, newBiasVector1.getValue(0), 0.001);
Assert.AreEqual(-0.139, newBiasVector1.getValue(1), 0.001);
}
public void testBiasUpdateMatrixesFormedCorrectly()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
layer1Sensitivity
.sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);
Vector biasUpdateVector2 = BackPropLearning.calculateBiasUpdates(
layer2Sensitivity, 0.1);
Assert.AreEqual(0.2522, biasUpdateVector2.getValue(0), 0.001);
Vector lastBiasUpdateVector2 = layer2.getLastBiasUpdateVector();
Assert.AreEqual(0.2522, lastBiasUpdateVector2.getValue(0), 0.001);
Vector penultimateBiasUpdateVector2 = layer2
.getPenultimateBiasUpdateVector();
Assert.AreEqual(0.0, penultimateBiasUpdateVector2.getValue(0),
0.001);
Vector biasUpdateVector1 = BackPropLearning.calculateBiasUpdates(
layer1Sensitivity, 0.1);
Assert.AreEqual(0.00495, biasUpdateVector1.getValue(0), 0.001);
Assert.AreEqual(-0.00997, biasUpdateVector1.getValue(1), 0.001);
Vector lastBiasUpdateVector1 = layer1.getLastBiasUpdateVector();
Assert.AreEqual(0.00495, lastBiasUpdateVector1.getValue(0), 0.001);
Assert.AreEqual(-0.00997, lastBiasUpdateVector1.getValue(1), 0.001);
Vector penultimateBiasUpdateVector1 = layer1
.getPenultimateBiasUpdateVector();
Assert.AreEqual(0.0, penultimateBiasUpdateVector1.getValue(0),
0.001);
Assert.AreEqual(0.0, penultimateBiasUpdateVector1.getValue(1),
0.001);
}
private static void initializeVector(Vector aVector, double lowerLimit,
double upperLimit) {
for (int i = 0; i < aVector.size(); i++) {
double random = Util.generateRandomDoubleBetween(lowerLimit,
upperLimit);
aVector.setValue(i, random);
}
}
public void updateBiases() {
Matrix biasMatrix = biasVector.plusEquals(lastBiasUpdateVector);
Vector result = new Vector(biasMatrix.getRowDimension());
for (int i = 0; i < biasMatrix.getRowDimension(); i++) {
result.setValue(i, biasMatrix.get(i, 0));
}
biasVector = result;
}
public Vector calculateBiasUpdates(LayerSensitivity layerSensitivity,
double alpha, double momentum)
{
Layer layer = layerSensitivity.getLayer();
Matrix biasUpdateMatrixWithoutMomentum = layerSensitivity
.getSensitivityMatrix().times(alpha).times(-1.0);
Matrix biasUpdateMatrixWithMomentum = layer.getLastBiasUpdateVector()
.times(momentum).plus(
biasUpdateMatrixWithoutMomentum.times(1.0 - momentum));
Vector result = new Vector(biasUpdateMatrixWithMomentum
.getRowDimension());
for (int i = 0; i < biasUpdateMatrixWithMomentum.getRowDimension(); i++)
{
result.setValue(i, biasUpdateMatrixWithMomentum.get(i, 0));
}
layer.acceptNewBiasUpdate(result.copyVector());
return result;
}
public static Vector calculateBiasUpdates(
LayerSensitivity layerSensitivity, double alpha)
{
Layer layer = layerSensitivity.getLayer();
Matrix biasUpdateMatrix = layerSensitivity.getSensitivityMatrix()
.times(alpha).times(-1.0);
Vector result = new Vector(biasUpdateMatrix.getRowDimension());
for (int i = 0; i < biasUpdateMatrix.getRowDimension(); i++)
{
result.setValue(i, biasUpdateMatrix.get(i, 0));
}
layer.acceptNewBiasUpdate(result.copyVector());
return result;
}
