/**
* Calculate the squared error of the neural network.
*
* @param x The input to the neural network.
* @param y The expected output.
* @return The squared error.
*/
public double squaredError(Matrix x, Matrix y) {
Matrix y_ = predict(x);
double sumSquareWeights = 0;
for (Layer layer : layers) sumSquareWeights += layer.weightMatrix.power(2).sum();
double j =
0.5 * y_.subtract(y).power(2).sum() / layers.get(0).getLayerSize().getInputSize()
+ lambda / 2 * sumSquareWeights;
return j;
}
/**
* 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;
}
private Matrix createRandomMatrix(int rows, int cols) {
Matrix random = new Matrix(rows, cols);
return random.map(
new Matrix.Function() {
@Override
public double function(double x) {
return Math.random();
}
});
}
/**
* Calculate the cross entropy error of the neural network.
*
* @param x The input to the neural network.
* @param y The expected output.
* @return The cross entropy error.
*/
public double crossEntropyError(Matrix x, Matrix y) {
Matrix y_ = predict(x);
double j =
y_.multiply(
y.map(
new Matrix.Function() {
@Override
public double function(double x) {
return Math.log(x);
}
}))
.sum();
return -j;
}
/**
* 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;
}
private Matrix applyFunctionDerivative(Matrix input) {
Matrix activated = (Matrix) input.clone();
if (function instanceof Softmax)
activated =
activated.map(
new Matrix.Function() {
@Override
public double function(double x) {
return Math.exp(x);
}
});
else
activated =
activated.map(
new Matrix.Function() {
@Override
public double function(double x) {
return function.derivative(x);
}
});
if (function instanceof Softmax) {
double sum = activated.sum();
if (sum != 0) activated = activated.multiply(1 / sum);
activated = activated.subtract(input);
activated =
activated.map(
new Matrix.Function() {
@Override
public double function(double x) {
return function.activate(x);
}
});
}
return activated;
}
/**
* Processes the input to the layer.
*
* @param input The input to the layer.
* @return The output of the layer.
*/
private Matrix activate(Matrix input) {
inputMatrix = weightMatrix.dot(input).add(biasMatrix);
Matrix y = applyFunction(inputMatrix);
outputMatrix = y;
return y;
}
/**
* 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;
}
/**
* Set the weight matrix of a layer of the neural network.
*
* @param layer The layer number of the neural network.
* @param weights The new weight matrix for the layer.
*/
public void setWeights(int layer, Matrix weights) {
layers.get(layer).weightMatrix = (Matrix) weights.clone();
}
/**
* Get the position of the most probable in an output array.
*
* @param output The output of the neural network (using Softmax)
* @return The position of the most probable class.
*/
public static int argMax(Matrix output) {
double max = output.max();
return output.find(max)[0];
}