/**
* Train the neural network to predict an output given some input.
*
* @param input The input to the neural network.
* @param output The target output for the given input.
* @param learningRate The rate at which the neural network learns. This is normally 0.01.
* @return The error of the network as an mean cross entropy.
*/
public double train(Matrix input, Matrix output, double learningRate) {
double totalError = 0;
if (input.getNumRows() == output.getNumRows()) {
for (int i = 0; i < input.getNumRows(); i++) {
Matrix inputRow = new Matrix(new double[][] {input.getRow(i)}).transpose();
Matrix outputRow = new Matrix(new double[][] {output.getRow(i)}).transpose();
Matrix netOutput = this.predict(inputRow);
// Output layer
Matrix previousDelta =
outputRow
.subtract(netOutput)
.multiply(-1)
.multiply(
layers
.get(layers.size() - 1)
.applyFunctionDerivative(layers.get(layers.size() - 1).inputMatrix));
Matrix change =
previousDelta
.dot(layers.get(layers.size() - 2).outputMatrix.transpose())
.add(layers.get(layers.size() - 1).weightMatrix.multiply(lambda));
layers.get(layers.size() - 1).weightMatrix =
layers.get(layers.size() - 1).weightMatrix.subtract(change.multiply(learningRate));
// Hidden layers
for (int l = layers.size() - 2; l > 0; l--) {
previousDelta =
layers
.get(l + 1)
.weightMatrix
.transpose()
.dot(previousDelta)
.multiply(layers.get(l).applyFunctionDerivative(layers.get(l).inputMatrix));
change =
previousDelta
.dot(layers.get(l - 1).outputMatrix.transpose())
.add(layers.get(l).weightMatrix.multiply(lambda));
layers.get(l).weightMatrix =
layers.get(l).weightMatrix.subtract(change.multiply(learningRate));
}
double error = squaredError(inputRow, outputRow);
totalError += error;
}
}
return totalError;
}
/**
* Give a prediction based on some input.
*
* @param input The input to the neural network which is equal in size to the number of input
* neurons.
* @return The output of the neural network.
*/
public Matrix predict(Matrix input) {
if (input.getNumRows() != layers.get(0).getLayerSize().getInputSize()) {
throw new InvalidParameterException(
"Input size did not match the input size of the first layer");
}
Matrix modInput = (Matrix) input.clone();
for (Layer l : layers) {
modInput = l.activate(modInput);
}
return modInput;
}
/**
* Applies the activation function to the processed input.
*
* @param input The input to the activation function.
* @return The output of the activation function.
*/
private Matrix applyFunction(Matrix input) {
Matrix activated = (Matrix) input.clone();
for (int row = 0; row < input.getNumRows(); row++)
for (int col = 0; col < input.getNumCols(); col++)
activated.set(row, col, function.activate(input.get(row, col)));
if (function instanceof Softmax) {
double sum = activated.sum();
if (sum != 0) activated = activated.multiply(1 / sum);
}
return activated;
}