public void MulticlassTest1()
{
Accord.Math.Tools.SetupGenerator(0);
// Neuron.RandGenerator = new ThreadSafeRandom(0);
int numberOfInputs = 3;
int numberOfClasses = 4;
int hiddenNeurons = 5;
double[][] input =
{
new double[] { -1, -1, -1 }, // 0
new double[] { -1, 1, -1 }, // 1
new double[] { 1, -1, -1 }, // 1
new double[] { 1, 1, -1 }, // 0
new double[] { -1, -1, 1 }, // 2
new double[] { -1, 1, 1 }, // 3
new double[] { 1, -1, 1 }, // 3
new double[] { 1, 1, 1 } // 2
};
int[] labels =
{
0,
1,
1,
0,
2,
3,
3,
2,
};
double[][] outputs = Accord.Statistics.Tools
.Expand(labels, numberOfClasses, -1, 1);
var function = new BipolarSigmoidFunction(2);
var network = new ActivationNetwork(function,
numberOfInputs, hiddenNeurons, numberOfClasses);
new NguyenWidrow(network).Randomize();
var teacher = new LevenbergMarquardtLearning(network);
double error = Double.PositiveInfinity;
for (int i = 0; i < 10; i++)
error = teacher.RunEpoch(input, outputs);
for (int i = 0; i < input.Length; i++)
{
int answer;
double[] output = network.Compute(input[i]);
double response = output.Max(out answer);
int expected = labels[i];
Assert.AreEqual(expected, answer);
}
}
/// <summary>
/// Constructs a new Gaussian Weight initialization.
/// </summary>
///
/// <param name="network">The activation network whose weights will be initialized.</param>
/// <param name="stdDev">The standard deviation to be used. Common values lie in the 0.001-
/// 0.1 range. Default is 0.1.</param>
///
public GaussianWeights(ActivationNetwork network, double stdDev = 0.1)
{
this.network = network;
this.random = new NormalDistribution(0, stdDev);
this.UpdateThresholds = false;
}
/// <summary>
/// Constructs a new Nguyen-Widrow Weight initialization.
/// </summary>
///
/// <param name="network">The activation network whose weights will be initialized.</param>
///
public NguyenWidrow(ActivationNetwork network)
{
this.network = network;
int hiddenNodes = network.Layers[0].Neurons.Length;
int inputNodes = network.Layers[0].InputsCount;
randRange = new Range(-0.5f, 0.5f);
beta = 0.7 * Math.Pow(hiddenNodes, 1.0 / inputNodes);
}
/// <summary>
/// Constructs a new Nguyen-Widrow Weight initialization.
/// </summary>
///
/// <param name="network">The activation network whose weights will be initialized.</param>
///
public NguyenWidrow(ActivationNetwork network)
{
this.network = network;
int hiddenNodes = network.Layers[0].Neurons.Length;
int inputNodes = network.Layers[0].InputsCount;
randRange = new Range(-0.5f, 0.5f);
beta = 0.7 * Math.Pow(hiddenNodes, 1.0 / inputNodes);
}
public void RunEpochTest1()
{
Accord.Math.Tools.SetupGenerator(0);
double[][] input =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
double[][] output =
{
new double[] { -1 },
new double[] { 1 },
new double[] { 1 },
new double[] { -1 }
};
//Neuron.RandGenerator = new ThreadSafeRandom(0);
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 2, 1);
var teacher = new ParallelResilientBackpropagationLearning(network);
double error = 1.0;
while (error > 1e-5)
error = teacher.RunEpoch(input, output);
for (int i = 0; i < input.Length; i++)
{
double actual = network.Compute(input[i])[0];
double expected = output[i][0];
Assert.AreEqual(expected, actual, 0.01);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void ZeroLambdaTest()
{
Accord.Math.Random.Generator.Seed = 0;
double[,] data = null;
// open selected file
using (TextReader stream = new StringReader(Properties.Resources.ZeroLambda))
using (CsvReader reader = new CsvReader(stream, false))
{
data = reader.ToTable().ToMatrix(System.Globalization.CultureInfo.InvariantCulture);
}
// number of learning samples
int samples = data.GetLength(0);
var ranges = data.GetRange(dimension: 0);
Assert.AreEqual(2, ranges.Length);
var rangeX = ranges[0];
var rangeY = ranges[1];
// data transformation factor
double yFactor = 1.7 / rangeY.Length;
double yMin = rangeY.Min;
double xFactor = 2.0 / rangeX.Length;
double xMin = rangeX.Min;
// prepare learning data
double[][] input = new double[samples][];
double[][] output = new double[samples][];
for (int i = 0; i < samples; i++)
{
input[i] = new double[1];
output[i] = new double[1];
input[i][0] = (data[i, 0] - xMin) * xFactor - 1.0; // set input
output[i][0] = (data[i, 1] - yMin) * yFactor - 0.85; // set output
}
// Neuron.RandGenerator = new ThreadSafeRandom(0);
Accord.Math.Random.Generator.Seed = 0;
// create multi-layer neural network
var network = new ActivationNetwork(
new BipolarSigmoidFunction(5),
1, 12, 1);
// create teacher
var teacher = new LevenbergMarquardtLearning(network, true);
teacher.LearningRate = 1;
// iterations
int iteration = 1;
int iterations = 2000;
// solution array
double[,] solution = new double[samples, 2];
double[] networkInput = new double[1];
bool needToStop = false;
double learningError = 0;
// loop
while (!needToStop)
{
Assert.AreNotEqual(0, teacher.LearningRate);
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output) / samples;
// calculate solution
for (int j = 0; j < samples; j++)
{
networkInput[0] = (solution[j, 0] - xMin) * xFactor - 1.0;
solution[j, 1] = (network.Compute(networkInput)[0] + 0.85) / yFactor + yMin;
}
// calculate error
learningError = 0.0;
for (int j = 0; j < samples; j++)
{
networkInput[0] = input[j][0];
learningError += Math.Abs(data[j, 1] - ((network.Compute(networkInput)[0] + 0.85) / yFactor + yMin));
}
// increase current iteration
iteration++;
// check if we need to stop
if ((iterations != 0) && (iteration > iterations))
break;
}
Assert.IsTrue(learningError < 0.13);
}
private static double computeError(double[][] inputs, double[][] outputs, ActivationNetwork ann)
{
// Compute the machine outputs
int miss = 0;
for (int i = 0; i < inputs.Length; i++)
{
var y = System.Math.Sign(ann.Compute(inputs[i])[0]);
var o = outputs[i][0];
if (y != o) miss++;
}
return (double)miss / inputs.Length;
}
// Worker thread
void SearchSolution()
{
// number of learning samples
int samples = sourceMatrix.GetLength(0);
// prepare learning data
double[][] inputs = sourceMatrix.Submatrix(null, 0, 1).ToArray();
double[][] outputs = sourceMatrix.GetColumn(2).Transpose().ToArray();
// create multi-layer neural network
ann = new ActivationNetwork(
new BipolarSigmoidFunction(sigmoidAlphaValue),
2, neuronsInFirstLayer, 1);
if (useNguyenWidrow)
{
if (useSameWeights)
Accord.Math.Random.Generator.Seed = 0;
NguyenWidrow initializer = new NguyenWidrow(ann);
initializer.Randomize();
}
// create teacher
LevenbergMarquardtLearning teacher = new LevenbergMarquardtLearning(ann, useRegularization);
// set learning rate and momentum
teacher.LearningRate = learningRate;
// iterations
iteration = 1;
var ranges = sourceMatrix.GetRange(0);
double[][] map = Matrix.Mesh(ranges[0], ranges[1], 0.05, 0.05);
var sw = Stopwatch.StartNew();
// loop
while (!needToStop)
{
// run epoch of learning procedure
error = teacher.RunEpoch(inputs, outputs) / samples;
var result = map.Apply(ann.Compute).GetColumn(0).Apply(Math.Sign);
var graph = map.ToMatrix().InsertColumn(result.ToDouble());
this.Invoke((Action)(() =>
{
zedGraphControl2.DataSource = graph;
}));
// increase current iteration
iteration++;
elapsed = sw.Elapsed;
updateStatus();
// check if we need to stop
if ((iterations != 0) && (iteration > iterations))
break;
}
sw.Stop();
// enable settings controls
EnableControls(true);
}
// Worker thread
void SearchSolution()
{
// prepare learning data
double[][] input = new double[samples][];
double[][] output = new double[samples][];
for (int i = 0; i < samples; i++)
{
input[i] = new double[variables];
output[i] = new double[1];
// copy input
for (int j = 0; j < variables; j++)
input[i][j] = data[i, j];
// copy output
output[i][0] = classes[i];
}
// create perceptron
ActivationNetwork network = new ActivationNetwork(new ThresholdFunction(), variables, 1);
ActivationNeuron neuron = network.Layers[0].Neurons[0] as ActivationNeuron;
// create teacher
PerceptronLearning teacher = new PerceptronLearning(network);
// set learning rate
teacher.LearningRate = learningRate;
// iterations
int iteration = 1;
// statistic files
StreamWriter errorsFile = null;
StreamWriter weightsFile = null;
try
{
// check if we need to save statistics to files
if (saveStatisticsToFiles)
{
// open files
errorsFile = File.CreateText("errors.csv");
weightsFile = File.CreateText("weights.csv");
}
// erros list
ArrayList errorsList = new ArrayList();
// loop
while (!needToStop)
{
// save current weights
if (weightsFile != null)
{
for (int i = 0; i < variables; i++)
{
weightsFile.Write(neuron.Weights[i] + ",");
}
weightsFile.WriteLine(neuron.Threshold);
}
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output);
errorsList.Add(error);
// show current iteration
SetText(iterationsBox, iteration.ToString());
// save current error
if (errorsFile != null)
{
errorsFile.WriteLine(error);
}
// show classifier in the case of 2 dimensional data
if ((neuron.InputsCount == 2) && (neuron.Weights[1] != 0))
{
double k = -neuron.Weights[0] / neuron.Weights[1];
double b = -neuron.Threshold / neuron.Weights[1];
double[,] classifier = new double[2, 2] {
{ chart.RangeX.Min, chart.RangeX.Min * k + b },
{ chart.RangeX.Max, chart.RangeX.Max * k + b }
};
// update chart
chart.UpdateDataSeries("classifier", classifier);
}
// stop if no error
if (error == 0)
break;
iteration++;
}
// show perceptron's weights
ListViewItem item = null;
ClearList(weightsList);
for (int i = 0; i < variables; i++)
{
item = AddListItem(weightsList, string.Format("Weight {0}", i + 1));
AddListSubitem(item, neuron.Weights[i].ToString("F6"));
}
item = AddListItem(weightsList, "Threshold");
AddListSubitem(item, neuron.Threshold.ToString("F6"));
// show error's dynamics
double[,] errors = new double[errorsList.Count, 2];
for (int i = 0, n = errorsList.Count; i < n; i++)
{
errors[i, 0] = i;
errors[i, 1] = (double)errorsList[i];
}
errorChart.RangeX = new Range(0, errorsList.Count - 1);
errorChart.RangeY = new Range(0, samples);
errorChart.UpdateDataSeries("error", errors);
}
catch (IOException)
{
MessageBox.Show("Failed writing file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
finally
{
// close files
if (errorsFile != null)
errorsFile.Close();
if (weightsFile != null)
weightsFile.Close();
}
// enable settings controls
EnableControls(true);
}
// Worker thread
void SearchSolution()
{
// number of learning samples
int samples = data.Length - predictionSize - windowSize;
// data transformation factor
double factor = 1.7 / chart.RangeY.Length;
double yMin = chart.RangeY.Min;
// prepare learning data
double[][] input = new double[samples][];
double[][] output = new double[samples][];
for (int i = 0; i < samples; i++)
{
input[i] = new double[windowSize];
output[i] = new double[1];
// set input
for (int j = 0; j < windowSize; j++)
{
input[i][j] = (data[i + j] - yMin) * factor - 0.85;
}
// set output
output[i][0] = (data[i + windowSize] - yMin) * factor - 0.85;
}
// create multi-layer neural network
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(sigmoidAlphaValue),
windowSize, windowSize * 2, 1);
// create teacher
var teacher = new ParallelResilientBackpropagationLearning(network);
teacher.Reset(initialStep);
// run at least one backpropagation epoch
//teacher2.RunEpoch(input, output);
// iterations
int iteration = 1;
// solution array
int solutionSize = data.Length - windowSize;
double[,] solution = new double[solutionSize, 2];
double[] networkInput = new double[windowSize];
// calculate X values to be used with solution function
for (int j = 0; j < solutionSize; j++)
{
solution[j, 0] = j + windowSize;
}
// loop
while (!needToStop)
{
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output) / samples;
// calculate solution and learning and prediction errors
double learningError = 0.0;
double predictionError = 0.0;
// go through all the data
for (int i = 0, n = data.Length - windowSize; i < n; i++)
{
// put values from current window as network's input
for (int j = 0; j < windowSize; j++)
{
networkInput[j] = (data[i + j] - yMin) * factor - 0.85;
}
// evalue the function
solution[i, 1] = (network.Compute(networkInput)[0] + 0.85) / factor + yMin;
// calculate prediction error
if (i >= n - predictionSize)
{
predictionError += Math.Abs(solution[i, 1] - data[windowSize + i]);
}
else
{
learningError += Math.Abs(solution[i, 1] - data[windowSize + i]);
}
}
// update solution on the chart
chart.UpdateDataSeries("solution", solution);
// set current iteration's info
SetText(currentIterationBox, iteration.ToString());
SetText(currentLearningErrorBox, learningError.ToString("F3"));
SetText(currentPredictionErrorBox, predictionError.ToString("F3"));
// increase current iteration
iteration++;
// check if we need to stop
if ((iterations != 0) && (iteration > iterations))
break;
}
// show new solution
for (int j = windowSize, k = 0, n = data.Length; j < n; j++, k++)
{
AddSubItem(dataList, j, solution[k, 1].ToString());
}
// enable settings controls
EnableControls(true);
}
// Worker thread
void SearchSolution()
{
// prepare learning data
double[][] input = new double[samples][];
double[][] output = new double[samples][];
for (int i = 0; i < samples; i++)
{
input[i] = new double[2];
output[i] = new double[classesCount];
// set input
input[i][0] = data[i, 0];
input[i][1] = data[i, 1];
// set output
output[i][classes[i]] = 1;
}
// create perceptron
ActivationNetwork network = new ActivationNetwork(new ThresholdFunction(), 2, classesCount);
ActivationLayer layer = network.Layers[0] as ActivationLayer;
// create teacher
PerceptronLearning teacher = new PerceptronLearning(network);
// set learning rate
teacher.LearningRate = learningRate;
// iterations
int iteration = 1;
// statistic files
StreamWriter errorsFile = null;
StreamWriter weightsFile = null;
try
{
// check if we need to save statistics to files
if (saveStatisticsToFiles)
{
// open files
errorsFile = File.CreateText("errors.csv");
weightsFile = File.CreateText("weights.csv");
}
// erros list
ArrayList errorsList = new ArrayList();
// loop
while (!needToStop)
{
// save current weights
if (weightsFile != null)
{
for (int i = 0; i < classesCount; i++)
{
weightsFile.Write("neuron" + i + ",");
weightsFile.Write(layer.Neurons[i].Weights[0] + ",");
weightsFile.Write(layer.Neurons[i].Weights[1] + ",");
weightsFile.WriteLine(((ActivationNeuron)layer.Neurons[i]).Threshold);
}
}
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output);
errorsList.Add(error);
// save current error
if (errorsFile != null)
{
errorsFile.WriteLine(error);
}
// show current iteration
SetText(iterationsBox, iteration.ToString());
// stop if no error
if (error == 0)
break;
// show classifiers
for (int j = 0; j < classesCount; j++)
{
double k = (layer.Neurons[j].Weights[1] != 0) ? (-layer.Neurons[j].Weights[0] / layer.Neurons[j].Weights[1]) : 0;
double b = (layer.Neurons[j].Weights[1] != 0) ? (-((ActivationNeuron)layer.Neurons[j]).Threshold / layer.Neurons[j].Weights[1]) : 0;
double[,] classifier = new double[2, 2] {
{ chart.RangeX.Min, chart.RangeX.Min * k + b },
{ chart.RangeX.Max, chart.RangeX.Max * k + b }
};
// update chart
chart.UpdateDataSeries(string.Format("classifier" + j), classifier);
}
iteration++;
}
// show perceptron's weights
ClearList(weightsList);
for (int i = 0; i < classesCount; i++)
{
string neuronName = string.Format("Neuron {0}", i + 1);
// weight 0
ListViewItem item = AddListItem(weightsList, neuronName);
AddListSubitem(item, "Weight 1");
AddListSubitem(item, layer.Neurons[i].Weights[0].ToString("F6"));
// weight 1
item = AddListItem(weightsList, neuronName);
AddListSubitem(item, "Weight 2");
AddListSubitem(item, layer.Neurons[i].Weights[1].ToString("F6"));
// threshold
item = AddListItem(weightsList, neuronName);
AddListSubitem(item, "Threshold");
AddListSubitem(item, ((ActivationNeuron)layer.Neurons[i]).Threshold.ToString("F6"));
}
// show error's dynamics
double[,] errors = new double[errorsList.Count, 2];
for (int i = 0, n = errorsList.Count; i < n; i++)
{
errors[i, 0] = i;
errors[i, 1] = (double)errorsList[i];
}
errorChart.RangeX = new Range(0, errorsList.Count - 1);
errorChart.UpdateDataSeries("error", errors);
}
catch (IOException)
{
MessageBox.Show("Failed writing file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
finally
{
// close files
if (errorsFile != null)
errorsFile.Close();
if (weightsFile != null)
weightsFile.Close();
}
// enable settings controls
EnableControls(true);
}
public void BlockHessianTest1()
{
// Network with no hidden layers: 3-1
Accord.Math.Tools.SetupGenerator(0);
double[][] input =
{
new double[] {-1, -1 },
new double[] {-1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
double[][] output =
{
new double[] {-1 },
new double[] { 1 },
new double[] { 1 },
new double[] {-1 }
};
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 1);
var teacher1 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByFiniteDifferences);
var teacher2 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByBackpropagation);
teacher2.Blocks = 2;
// Set lambda to lambda max so no iterations are performed
teacher1.LearningRate = 1e30f;
teacher2.LearningRate = 1e30f;
teacher1.RunEpoch(input, output);
teacher2.RunEpoch(input, output);
var hessian1 = teacher1.Hessian;
var hessian2 = teacher1.Hessian;
for (int i = 0; i < hessian1.Length; i++)
{
for (int j = 0; j < hessian1[i].Length; j++)
{
double j1 = hessian1[i][j];
double j2 = hessian2[i][j];
Assert.AreEqual(j1, j2, 1e-4);
Assert.IsFalse(Double.IsNaN(j1));
Assert.IsFalse(Double.IsNaN(j2));
}
}
Assert.IsTrue(hessian1.IsUpperTriangular());
Assert.IsTrue(hessian2.IsUpperTriangular());
var gradient1 = teacher1.Gradient;
var gradient2 = teacher2.Gradient;
for (int i = 0; i < gradient1.Length; i++)
{
double j1 = gradient1[i];
double j2 = gradient2[i];
Assert.AreEqual(j1, j2, 1e-5);
Assert.IsFalse(Double.IsNaN(j1));
Assert.IsFalse(Double.IsNaN(j2));
}
}
// Worker thread
void SearchSolution()
{
// number of learning samples
int samples = data.GetLength(0);
// prepare learning data
DoubleRange unit = new DoubleRange(-1, 1);
double[][] input = data.GetColumn(0).Scale(fromRange: xRange, toRange: unit).ToArray();
double[][] output = data.GetColumn(1).Scale(fromRange: yRange, toRange: unit).ToArray();
// create multi-layer neural network
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(sigmoidAlphaValue),
1, neuronsInFirstLayer, 1);
if (useNguyenWidrow)
{
new NguyenWidrow(network).Randomize();
}
// create teacher
var teacher = new ParallelResilientBackpropagationLearning(network);
// iterations
int iteration = 1;
// solution array
double[,] solution = new double[samples, 2];
// loop
while (!needToStop)
{
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output) / samples;
// calculate solution
for (int j = 0; j < samples; j++)
{
double x = input[j][0];
double y = network.Compute(new[] { x })[0];
solution[j, 0] = x.Scale(fromRange: unit, toRange: xRange);
solution[j, 1] = y.Scale(fromRange: unit, toRange: yRange);
}
chart.UpdateDataSeries("solution", solution);
// calculate error
double learningError = 0.0;
for (int j = 0; j < samples; j++)
{
double x = input[j][0];
double expected = data[j, 1];
double actual = network.Compute(new[] { x })[0];
learningError += Math.Abs(expected - actual);
}
// set current iteration's info
SetText(currentIterationBox, iteration.ToString());
SetText(currentErrorBox, learningError.ToString("F3"));
// increase current iteration
iteration++;
// check if we need to stop
if ((iterations != 0) && (iteration > iterations))
break;
}
// enable settings controls
EnableControls(true);
}
public void JacobianByChainRuleTest_MultipleOutput()
{
// Network with no hidden layers: 3-4
int numberOfInputs = 3;
int numberOfClasses = 4;
double[][] input =
{
new double[] { -1, -1, -1 }, // 0
new double[] { -1, 1, -1 }, // 1
new double[] { 1, -1, -1 }, // 1
new double[] { 1, 1, -1 }, // 0
new double[] { -1, -1, 1 }, // 2
new double[] { -1, 1, 1 }, // 3
new double[] { 1, -1, 1 }, // 3
new double[] { 1, 1, 1 } // 2
};
int[] labels =
{
0,
1,
1,
0,
2,
3,
3,
2,
};
double[][] output = Accord.Statistics.Tools
.Expand(labels, numberOfClasses, -1, 1);
// Neuron.RandGenerator = new ThreadSafeRandom(0);
Accord.Math.Random.Generator.Seed = 0;
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), numberOfInputs, numberOfClasses);
var teacher1 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByFiniteDifferences);
var teacher2 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByBackpropagation);
// Set lambda to lambda max so no iterations are performed
teacher1.LearningRate = 1e30f;
teacher2.LearningRate = 1e30f;
teacher1.RunEpoch(input, output);
teacher2.RunEpoch(input, output);
var jacobian1 = teacher1.Jacobian;
var jacobian2 = teacher2.Jacobian;
for (int i = 0; i < jacobian1.Length; i++)
{
for (int j = 0; j < jacobian1[i].Length; j++)
{
double j1 = jacobian1[i][j];
double j2 = jacobian2[i][j];
Assert.AreEqual(j1, j2, 1e-3);
Assert.IsFalse(Double.IsNaN(j1));
Assert.IsFalse(Double.IsNaN(j2));
}
}
}
public void JacobianByChainRuleTest4()
{
// Network with no hidden layers: 3-1
double[][] input =
{
new double[] {-1, -1 },
new double[] {-1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
double[][] output =
{
new double[] {-1 },
new double[] { 1 },
new double[] { 1 },
new double[] {-1 }
};
// Neuron.RandGenerator = new ThreadSafeRandom(0);
Accord.Math.Random.Generator.Seed = 0;
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 1);
var teacher1 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByFiniteDifferences);
var teacher2 = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByBackpropagation);
// Set lambda to lambda max so no iterations are performed
teacher1.LearningRate = 1e30f;
teacher2.LearningRate = 1e30f;
teacher1.RunEpoch(input, output);
teacher2.RunEpoch(input, output);
var jacobian1 = teacher1.Jacobian;
var jacobian2 = teacher2.Jacobian;
for (int i = 0; i < jacobian1.Length; i++)
{
for (int j = 0; j < jacobian1[i].Length; j++)
{
double j1 = jacobian1[i][j];
double j2 = jacobian2[i][j];
Assert.AreEqual(j1, j2, 1e-5);
Assert.IsFalse(Double.IsNaN(j1));
Assert.IsFalse(Double.IsNaN(j2));
}
}
}
public void RunEpochTest3()
{
double[,] dataset = yinyang;
double[][] input = dataset.GetColumns(new[] { 0, 1 }).ToJagged();
double[][] output = dataset.GetColumn(2).ToJagged();
// Neuron.RandGenerator = new ThreadSafeRandom(0);
Accord.Math.Random.Generator.Seed = 0;
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 5, 1);
var teacher = new LevenbergMarquardtLearning(network,
true, JacobianMethod.ByBackpropagation);
Assert.IsTrue(teacher.UseRegularization);
double error = 1.0;
for (int i = 0; i < 500; i++)
error = teacher.RunEpoch(input, output);
double[][] actual = new double[output.Length][];
for (int i = 0; i < input.Length; i++)
actual[i] = network.Compute(input[i]);
for (int i = 0; i < input.Length; i++)
Assert.AreEqual(Math.Sign(output[i][0]), Math.Sign(actual[i][0]));
}
public void ConstructorTest()
{
// Four training samples of the xor function
// two inputs (x and y)
double[][] input =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
// one output (z = x ^ y)
double[][] output =
{
new double[] { -1 },
new double[] { 1 },
new double[] { 1 },
new double[] { -1 }
};
// create multi-layer neural network
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), // use a bipolar sigmoid activation function
2, // two inputs
3, // three hidden neurons
1 // one output neuron
);
// create teacher
LevenbergMarquardtLearning teacher = new LevenbergMarquardtLearning(
network, // the neural network
false, // whether or not to use Bayesian regularization
JacobianMethod.ByBackpropagation // Jacobian calculation method
);
// set learning rate and momentum
teacher.LearningRate = 0.1f;
// start the supervisioned learning
for (int i = 0; i < 1000; i++)
{
double error = teacher.RunEpoch(input, output);
}
// If we reached here, the constructor test has passed.
}
public void RunEpochTest4()
{
Accord.Math.Tools.SetupGenerator(0);
double[][] input =
{
new double[] { 0, 0 },
};
double[][] output =
{
new double[] { 0 },
};
// Neuron.RandGenerator = new ThreadSafeRandom(0);
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 1);
var teacher = new LevenbergMarquardtLearning(network,
true, JacobianMethod.ByBackpropagation);
double error = 1.0;
for (int i = 0; i < 1000; i++)
error = teacher.RunEpoch(input, output);
for (int i = 0; i < input.Length; i++)
Assert.AreEqual(network.Compute(input[i])[0], output[i][0], 0.1);
}
public void RunEpochTest1()
{
Accord.Math.Tools.SetupGenerator(0);
double[][] input =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
double[][] output =
{
new double[] { -1 },
new double[] { 1 },
new double[] { 1 },
new double[] { -1 }
};
// Neuron.RandGenerator = new ThreadSafeRandom(0);
ActivationNetwork network = new ActivationNetwork(
new BipolarSigmoidFunction(2), 2, 2, 1);
var teacher = new LevenbergMarquardtLearning(network,
false, JacobianMethod.ByFiniteDifferences);
double error = 1.0;
while (error > 1e-5)
error = teacher.RunEpoch(input, output);
for (int i = 0; i < input.Length; i++)
Assert.AreEqual(network.Compute(input[i])[0], output[i][0], 0.1);
}
// Worker thread
void SearchSolution()
{
// initialize input and output values
double[][] input = null;
double[][] output = null;
if (sigmoidType == 0)
{
// unipolar data
input = new double[4][] {
new double[] {0, 0},
new double[] {0, 1},
new double[] {1, 0},
new double[] {1, 1}
};
output = new double[4][] {
new double[] {0},
new double[] {1},
new double[] {1},
new double[] {0}
};
}
else
{
// bipolar data
input = new double[4][] {
new double[] {-1, -1},
new double[] {-1, 1},
new double[] { 1, -1},
new double[] { 1, 1}
};
output = new double[4][] {
new double[] {-1},
new double[] { 1},
new double[] { 1},
new double[] {-1}
};
}
// create neural network
ActivationNetwork network = new ActivationNetwork(
(sigmoidType == 0) ?
(IActivationFunction)new SigmoidFunction(sigmoidAlphaValue) :
(IActivationFunction)new BipolarSigmoidFunction(sigmoidAlphaValue),
2, 2, 1);
// create teacher
LevenbergMarquardtLearning teacher = new LevenbergMarquardtLearning(network);
// set learning rate
teacher.LearningRate = learningRate;
// iterations
int iteration = 0;
// statistic files
StreamWriter errorsFile = null;
try
{
// check if we need to save statistics to files
if (saveStatisticsToFiles)
{
// open files
errorsFile = File.CreateText("errors.csv");
}
// erros list
ArrayList errorsList = new ArrayList();
// loop
while (!needToStop)
{
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output);
errorsList.Add(error);
// save current error
if (errorsFile != null)
{
errorsFile.WriteLine(error);
}
// show current iteration & error
SetText(currentIterationBox, iteration.ToString());
SetText(currentErrorBox, error.ToString());
iteration++;
// check if we need to stop
if (error <= learningErrorLimit)
break;
}
// show error's dynamics
double[,] errors = new double[errorsList.Count, 2];
for (int i = 0, n = errorsList.Count; i < n; i++)
{
errors[i, 0] = i;
errors[i, 1] = (double)errorsList[i];
}
errorChart.RangeX = new Range(0, errorsList.Count - 1);
errorChart.UpdateDataSeries("error", errors);
}
catch (IOException)
{
MessageBox.Show("Failed writing file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
finally
{
// close files
if (errorsFile != null)
errorsFile.Close();
}
// enable settings controls
EnableControls(true);
}
public void MulticlassTest1()
{
Accord.Math.Tools.SetupGenerator(0);
// Suppose we would like to teach a network to recognize
// the following input vectors into 3 possible classes:
//
double[][] inputs =
{
new double[] { 0, 1, 1, 0 }, // 0
new double[] { 0, 1, 0, 0 }, // 0
new double[] { 0, 0, 1, 0 }, // 0
new double[] { 0, 1, 1, 0 }, // 0
new double[] { 0, 1, 0, 0 }, // 0
new double[] { 1, 0, 0, 0 }, // 1
new double[] { 1, 0, 0, 0 }, // 1
new double[] { 1, 0, 0, 1 }, // 1
new double[] { 0, 0, 0, 1 }, // 1
new double[] { 0, 0, 0, 1 }, // 1
new double[] { 1, 1, 1, 1 }, // 2
new double[] { 1, 0, 1, 1 }, // 2
new double[] { 1, 1, 0, 1 }, // 2
new double[] { 0, 1, 1, 1 }, // 2
new double[] { 1, 1, 1, 1 }, // 2
};
int[] classes =
{
0, 0, 0, 0, 0,
1, 1, 1, 1, 1,
2, 2, 2, 2, 2,
};
// First we have to convert this problem into a way that the neural
// network can handle. The first step is to expand the classes into
// indicator vectors, where a 1 into a position signifies that this
// position indicates the class the sample belongs to.
//
double[][] outputs = Statistics.Tools.Expand(classes, -1, +1);
// Create an activation function for the net
var function = new BipolarSigmoidFunction();
// Create an activation network with the function and
// 4 inputs, 5 hidden neurons and 3 possible outputs:
var network = new ActivationNetwork(function, 4, 5, 3);
// Randomly initialize the network
new NguyenWidrow(network).Randomize();
// Teach the network using parallel Rprop:
var teacher = new ParallelResilientBackpropagationLearning(network);
double error = 1.0;
while (error > 1e-5)
error = teacher.RunEpoch(inputs, outputs);
// Checks if the network has learned
for (int i = 0; i < inputs.Length; i++)
{
double[] answer = network.Compute(inputs[i]);
int expected = classes[i];
int actual; answer.Max(out actual);
Assert.AreEqual(expected, actual, 0.01);
}
}
// Worker thread
void SearchSolution()
{
bool reducedNetwork = ((classesCount == 2) && (useOneNeuronForTwoClasses));
// prepare learning data
double[][] input = new double[samples][];
double[][] output = new double[samples][];
for (int i = 0; i < samples; i++)
{
input[i] = new double[variables];
output[i] = new double[neuronsCount];
// set input
for (int j = 0; j < variables; j++)
input[i][j] = data[i, j];
// set output
if (reducedNetwork)
{
output[i][0] = classes[i];
}
else
{
output[i][classes[i]] = 1;
}
}
// create perceptron
ActivationNetwork network = new ActivationNetwork(
new SigmoidFunction(sigmoidAlphaValue), variables, neuronsCount);
ActivationLayer layer = network.Layers[0] as ActivationLayer;
// create teacher
DeltaRuleLearning teacher = new DeltaRuleLearning(network);
// set learning rate
teacher.LearningRate = learningRate;
// iterations
int iteration = 1;
// statistic files
StreamWriter errorsFile = null;
StreamWriter weightsFile = null;
try
{
// check if we need to save statistics to files
if (saveStatisticsToFiles)
{
// open files
errorsFile = File.CreateText("errors.csv");
weightsFile = File.CreateText("weights.csv");
}
// erros list
ArrayList errorsList = new ArrayList();
// loop
while (!needToStop)
{
// save current weights
if (weightsFile != null)
{
for (int i = 0; i < neuronsCount; i++)
{
weightsFile.Write("neuron" + i + ",");
for (int j = 0; j < variables; j++)
weightsFile.Write(layer.Neurons[i].Weights[j] + ",");
weightsFile.WriteLine(((ActivationNeuron)layer.Neurons[i]).Threshold);
}
}
// run epoch of learning procedure
double error = teacher.RunEpoch(input, output) / samples;
errorsList.Add(error);
// save current error
if (errorsFile != null)
{
errorsFile.WriteLine(error);
}
// show current iteration & error
SetText(currentIterationBox, iteration.ToString());
SetText(currentErrorBox, error.ToString());
iteration++;
// check if we need to stop
if ((useErrorLimit) && (error <= learningErrorLimit))
break;
if ((!useErrorLimit) && (iterationLimit != 0) && (iteration > iterationLimit))
break;
}
// show perceptron's weights
ClearList(weightsList);
for (int i = 0; i < neuronsCount; i++)
{
string neuronName = string.Format("Neuron {0}", i + 1);
ListViewItem item = null;
// add all weights
for (int j = 0; j < variables; j++)
{
item = AddListItem(weightsList, neuronName);
AddListSubitem(item, string.Format("Weight {0}", j + 1));
AddListSubitem(item, layer.Neurons[i].Weights[0].ToString("F6"));
}
// threshold
item = AddListItem(weightsList, neuronName);
AddListSubitem(item, "Threshold");
AddListSubitem(item, ((ActivationNeuron)layer.Neurons[i]).Threshold.ToString("F6"));
}
// show error's dynamics
double[,] errors = new double[errorsList.Count, 2];
for (int i = 0, n = errorsList.Count; i < n; i++)
{
errors[i, 0] = i;
errors[i, 1] = (double)errorsList[i];
}
errorChart.RangeX = new Range(0, errorsList.Count - 1);
errorChart.UpdateDataSeries("error", errors);
}
catch (IOException)
{
MessageBox.Show("Failed writing file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
finally
{
// close files
if (errorsFile != null)
errorsFile.Close();
if (weightsFile != null)
weightsFile.Close();
}
// enable settings controls
EnableControls(true);
}