// train the neural network
public void Train(double[] inputsList, double[] targetsList)
{
// Convert inputs and targets list (one-dimensional) to two-dimensional, one-column matrices.
double[,] inputs = new double[inputsList.Length, 1];
inputs.SetColumn(0, inputsList);
// calculate signals into hidden layer
double[,] hiddenInputs = Wih.Dot(inputs);
// calculate the signals emerging from hidden layer
double[,] hiddenOutputs = hiddenInputs.Apply(x => ActivationFunction(x));
// calculate signals into final output layer
double[,] finalInputs = Who.Dot(hiddenOutputs);
// calculate the signals emerging from final output layer
double[,] finalOutputs = finalInputs.Apply(x => ActivationFunction(x));
// output layer error is the (target - actual)
double[] outputError = targetsList.Subtract(finalOutputs.GetColumn(0));
// hidden layer error is the output_errors, split by weights, recombined at hidden nodes
double[] hiddenError = Who.TransposeAndDot(outputError);
// update the weights for the links between the hidden and output layers
UpdateWeigths(hiddenOutputs, finalOutputs, ref Who, outputError);
// update the weights for the links between the input and hidden layers
UpdateWeigths(inputs, hiddenOutputs, ref Wih, hiddenError);
}
// ----------------------------------------------------------------------------------------
// Helper function for updating weight values during backpropagation.
private void UpdateWeigths(double[,] layer1, double[,] layer2, ref double[,] weigths, double[] errorList)
{
// Convert errors list (one-dimensional) to two-dimensional, one-column matrix.
double[,] errors = Matrix.Create <double>(errorList.Length, 1);
errors.SetColumn(0, errorList);
// Calculate delta matrix (differences for updating weight values).
double[,] deltas = Elementwise.Multiply(errors, layer2.Apply(x => x * (1 - x)))
.Dot(layer1.Transpose())
.Apply(x => x * .1);
// Apply delta matrix.
weigths = weigths.Add(deltas);
}
// query the neural network
public double[] Query(double[] inputsList)
{
// Convert inputs list (one-dimensional) to two-dimensional, one-column matrix.
double[,] inputs = Matrix.Create <double>(inputsList.Length, 1);
inputs.SetColumn(0, inputsList);
// calculate signals into hidden layer
double[,] hiddenInputs = Wih.Dot(inputs);
// calculate the signals emerging from hidden layer
double[,] hiddenOutputs = hiddenInputs.Apply(x => ActivationFunction(x));
// calculate signals into final output layer
double[,] finalInputs = Who.Dot(hiddenOutputs);
// calculate the signals emerging from final output layer
double[,] finalOutputs = finalInputs.Apply(x => ActivationFunction(x));
// Convert output node matrix back to a 1-dimensional list of values.
return(finalOutputs.GetColumn(0));
}