public void RunTest()
{
// Example regression problem. Suppose we are trying
// to model the following equation: f(x, y) = 2x + y
double[][] inputs = // (x, y)
{
new double[] { 0, 1 }, // 2*0 + 1 = 1
new double[] { 4, 3 }, // 2*4 + 3 = 11
new double[] { 8, -8 }, // 2*8 - 8 = 8
new double[] { 2, 2 }, // 2*2 + 2 = 6
new double[] { 6, 1 }, // 2*6 + 1 = 13
new double[] { 5, 4 }, // 2*5 + 4 = 14
new double[] { 9, 1 }, // 2*9 + 1 = 19
new double[] { 1, 6 }, // 2*1 + 6 = 8
};
double[] outputs = // f(x, y)
{
1, 11, 8, 6, 13, 14, 19, 8
};
// Create a new linear Support Vector Machine
var machine = new SupportVectorMachine(inputs: 2);
// Create the linear regression coordinate descent teacher
var learn = new LinearRegressionNewtonMethod(machine, inputs, outputs)
{
Complexity = 100000000,
Epsilon = 1e-15,
Tolerance = 1e-15,
};
// Run the learning algorithm
double error = learn.Run();
Assert.AreEqual(860.0, error);
// Compute the answer for one particular example
double fxy = machine.Compute(inputs[0]); // 1.0003849827673186
// Check for correct answers
double[] answers = new double[inputs.Length];
for (int i = 0; i < answers.Length; i++)
answers[i] = machine.Compute(inputs[i]);
Assert.AreEqual(1.0, fxy, 1e-5);
for (int i = 0; i < outputs.Length; i++)
Assert.AreEqual(outputs[i], answers[i], 1e-5);
}
public void Run()
{
// Example AND problem
double[][] inputs =
{
new double[] { 0, 0 }, // 0 and 0: 0 (label -1)
new double[] { 0, 1 }, // 0 and 1: 0 (label -1)
new double[] { 1, 0 }, // 1 and 0: 0 (label -1)
new double[] { 1, 1 } // 1 and 1: 1 (label +1)
};
// Dichotomy SVM outputs should be given as [-1;+1]
int[] labels =
{
// 0, 0, 0, 1
-1, -1, -1, 1
};
// Create a Support Vector Machine for the given inputs
SupportVectorMachine machine = new SupportVectorMachine(inputs[0].Length);
// Instantiate a new learning algorithm for SVMs
SequentialMinimalOptimization smo = new SequentialMinimalOptimization(machine, inputs, labels);
// Set up the learning algorithm
smo.Complexity = 1.0;
// Run the learning algorithm
double error = smo.Run();
// Compute the decision output for one of the input vectors
int decision = System.Math.Sign(machine.Compute(inputs[0]));
}
private static void and()
{
// Create a simple binary AND
// classification problem:
double[][] problem =
{
// a b a + b
new double[] { 0, 0, 0 },
new double[] { 0, 1, 0 },
new double[] { 1, 0, 0 },
new double[] { 1, 1, 1 },
};
// Get the two first columns as the problem
// inputs and the last column as the output
// input columns
double[][] inputs = problem.GetColumns(0, 1);
// output column
int[] outputs = problem.GetColumn(2).ToInt32();
// Plot the problem on screen
ScatterplotBox.Show("AND", inputs, outputs).Hold();
// However, SVMs expect the output value to be
// either -1 or +1. As such, we have to convert
// it so the vector contains { -1, -1, -1, +1 }:
//
outputs = outputs.Apply(x => x == 0 ? -1 : 1);
// Create a new linear-SVM for two inputs (a and b)
SupportVectorMachine svm = new SupportVectorMachine(inputs: 2);
// Create a L2-regularized L2-loss support vector classification
var teacher = new LinearDualCoordinateDescent(svm, inputs, outputs)
{
Loss = Loss.L2,
Complexity = 1000,
Tolerance = 1e-5
};
// Learn the machine
double error = teacher.Run(computeError: true);
// Compute the machine's answers for the learned inputs
int[] answers = inputs.Apply(x => Math.Sign(svm.Compute(x)));
// Plot the results
ScatterplotBox.Show("SVM's answer", inputs, answers).Hold();
}
public void LearnTest()
{
double[][] inputs =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
int[] xor =
{
-1,
1,
1,
-1
};
var kernel = new Polynomial(2, 0.0);
double[][] augmented = new double[inputs.Length][];
for (int i = 0; i < inputs.Length; i++)
augmented[i] = kernel.Transform(inputs[i]);
SupportVectorMachine machine = new SupportVectorMachine(augmented[0].Length);
// Create the Least Squares Support Vector Machine teacher
var learn = new LinearDualCoordinateDescent(machine, augmented, xor);
// Run the learning algorithm
double error = learn.Run();
Assert.AreEqual(0, error);
int[] output = augmented.Apply(p => Math.Sign(machine.Compute(p)));
for (int i = 0; i < output.Length; i++)
Assert.AreEqual(System.Math.Sign(xor[i]), System.Math.Sign(output[i]));
}
public void ComputeTest5()
{
var dataset = SequentialMinimalOptimizationTest.yinyang;
double[][] inputs = dataset.Submatrix(null, 0, 1).ToArray();
int[] labels = dataset.GetColumn(2).ToInt32();
var kernel = new Polynomial(2, 1);
Accord.Math.Tools.SetupGenerator(0);
var projection = inputs.Apply(kernel.Transform);
var machine = new SupportVectorMachine(projection[0].Length);
var smo = new LinearCoordinateDescent(machine, projection, labels)
{
Complexity = 1000000,
Tolerance = 1e-15
};
double error = smo.Run();
Assert.AreEqual(1000000.0, smo.Complexity, 1e-15);
int[] actual = new int[labels.Length];
for (int i = 0; i < actual.Length; i++)
actual[i] = Math.Sign(machine.Compute(projection[i]));
ConfusionMatrix matrix = new ConfusionMatrix(actual, labels);
Assert.AreEqual(6, matrix.FalseNegatives);
Assert.AreEqual(7, matrix.FalsePositives);
Assert.AreEqual(44, matrix.TruePositives);
Assert.AreEqual(43, matrix.TrueNegatives);
}
public void LearnTest5()
{
double[][] inputs =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
int[] positives =
{
1,
1,
1,
1
};
// Create Kernel Support Vector Machine with a Polynomial Kernel of 2nd degree
SupportVectorMachine machine = new SupportVectorMachine(inputs[0].Length);
// Create the sequential minimal optimization teacher
SequentialMinimalOptimization learn = new SequentialMinimalOptimization(machine, inputs, positives);
learn.Complexity = 1;
// Run the learning algorithm
double error = learn.Run();
Assert.AreEqual(0, error);
int[] output = inputs.Apply(p => (int)machine.Compute(p));
for (int i = 0; i < output.Length; i++)
{
bool sor = positives[i] >= 0;
bool sou = output[i] >= 0;
Assert.AreEqual(sor, sou);
}
}
public void TrainTest2()
{
double[][] inputs =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
int[] or =
{
-1,
-1,
-1,
+1
};
// Create Kernel Support Vector Machine with a Polynomial Kernel of 2nd degree
SupportVectorMachine machine = new SupportVectorMachine(inputs[0].Length);
// Create the sequential minimal optimization teacher
SequentialMinimalOptimization learn = new SequentialMinimalOptimization(machine, inputs, or);
learn.Complexity = 1;
// Run the learning algorithm
learn.Run();
double[] output = machine.Compute(inputs);
for (int i = 0; i < output.Length; i++)
{
bool sor = or[i] >= 0;
bool sou = output[i] >= 0;
Assert.AreEqual(sor, sou);
}
}
public void TransformTest()
{
var inputs = yinyang.Submatrix(null, 0, 1).ToArray();
var labels = yinyang.GetColumn(2).ToInt32();
ConfusionMatrix actual, expected;
SequentialMinimalOptimization a, b;
var kernel = new Polynomial(2, 0);
{
var machine = new KernelSupportVectorMachine(kernel, inputs[0].Length);
a = new SequentialMinimalOptimization(machine, inputs, labels);
a.UseComplexityHeuristic = true;
a.Run();
int[] values = new int[labels.Length];
for (int i = 0; i < values.Length; i++)
values[i] = Math.Sign(machine.Compute(inputs[i]));
expected = new ConfusionMatrix(values, labels);
}
{
var projection = inputs.Apply(kernel.Transform);
var machine = new SupportVectorMachine(projection[0].Length);
b = new SequentialMinimalOptimization(machine, projection, labels);
b.UseComplexityHeuristic = true;
b.Run();
int[] values = new int[labels.Length];
for (int i = 0; i < values.Length; i++)
values[i] = Math.Sign(machine.Compute(projection[i]));
actual = new ConfusionMatrix(values, labels);
}
Assert.AreEqual(a.Complexity, b.Complexity, 1e-15);
Assert.AreEqual(expected.TrueNegatives, actual.TrueNegatives);
Assert.AreEqual(expected.TruePositives, actual.TruePositives);
Assert.AreEqual(expected.FalseNegatives, actual.FalseNegatives);
Assert.AreEqual(expected.FalsePositives, actual.FalsePositives);
}
public void ComputeTest5()
{
var dataset = SequentialMinimalOptimizationTest.yinyang;
var inputs = dataset.Submatrix(null, 0, 1).ToArray();
var labels = dataset.GetColumn(2).ToInt32();
var kernel = new Polynomial(2, 0);
{
var machine = new KernelSupportVectorMachine(kernel, inputs[0].Length);
var smo = new SequentialMinimalOptimization(machine, inputs, labels);
smo.UseComplexityHeuristic = true;
double error = smo.Run();
Assert.AreEqual(0.2, error);
Assert.AreEqual(0.11714451552090824, smo.Complexity);
int[] actual = new int[labels.Length];
for (int i = 0; i < actual.Length; i++)
actual[i] = Math.Sign(machine.Compute(inputs[i]));
ConfusionMatrix matrix = new ConfusionMatrix(actual, labels);
Assert.AreEqual(20, matrix.FalseNegatives);
Assert.AreEqual(0, matrix.FalsePositives);
Assert.AreEqual(30, matrix.TruePositives);
Assert.AreEqual(50, matrix.TrueNegatives);
}
{
Accord.Math.Tools.SetupGenerator(0);
var projection = inputs.Apply(kernel.Transform);
var machine = new SupportVectorMachine(projection[0].Length);
var smo = new LinearNewtonMethod(machine, projection, labels);
smo.UseComplexityHeuristic = true;
double error = smo.Run();
Assert.AreEqual(0.18, error);
Assert.AreEqual(0.11714451552090821, smo.Complexity, 1e-15);
int[] actual = new int[labels.Length];
for (int i = 0; i < actual.Length; i++)
actual[i] = Math.Sign(machine.Compute(projection[i]));
ConfusionMatrix matrix = new ConfusionMatrix(actual, labels);
Assert.AreEqual(17, matrix.FalseNegatives);
Assert.AreEqual(1, matrix.FalsePositives);
Assert.AreEqual(33, matrix.TruePositives);
Assert.AreEqual(49, matrix.TrueNegatives);
}
}
public void ReceiverOperatingCharacteristicConstructorTest3()
{
// This example shows how to measure the accuracy of a
// binary classifier using a ROC curve. For this example,
// we will be creating a Support Vector Machine trained
// on the following instances:
double[][] inputs =
{
// Those are from class -1
new double[] { 2, 4, 0 },
new double[] { 5, 5, 1 },
new double[] { 4, 5, 0 },
new double[] { 2, 5, 5 },
new double[] { 4, 5, 1 },
new double[] { 4, 5, 0 },
new double[] { 6, 2, 0 },
new double[] { 4, 1, 0 },
// Those are from class +1
new double[] { 1, 4, 5 },
new double[] { 7, 5, 1 },
new double[] { 2, 6, 0 },
new double[] { 7, 4, 7 },
new double[] { 4, 5, 0 },
new double[] { 6, 2, 9 },
new double[] { 4, 1, 6 },
new double[] { 7, 2, 9 },
};
int[] outputs =
{
-1, -1, -1, -1, -1, -1, -1, -1, // fist eight from class -1
+1, +1, +1, +1, +1, +1, +1, +1 // last eight from class +1
};
// Create a linear Support Vector Machine with 4 inputs
SupportVectorMachine machine = new SupportVectorMachine(inputs: 3);
// Create the sequential minimal optimization teacher
SequentialMinimalOptimization learn = new SequentialMinimalOptimization(machine, inputs, outputs);
// Run the learning algorithm
double error = learn.Run();
// Extract the input labels predicted by the machine
double[] predicted = new double[inputs.Length];
for (int i = 0; i < predicted.Length; i++)
predicted[i] = machine.Compute(inputs[i]);
// Create a new ROC curve to assess the performance of the model
var roc = new ReceiverOperatingCharacteristic(outputs, predicted);
roc.Compute(100); // Compute a ROC curve with 100 points
/*
// Generate a connected scatter plot for the ROC curve and show it on-screen
ScatterplotBox.Show(roc.GetScatterplot(includeRandom: true), nonBlocking: true)
.SetSymbolSize(0) // do not display data points
.SetLinesVisible(true) // show lines connecting points
.SetScaleTight(true) // tighten the scale to points
.WaitForClose();
*/
Assert.AreEqual(0.7890625, roc.Area);
// Assert.AreEqual(0.1174774, roc.StandardError, 1e-6); HanleyMcNeil
Assert.AreEqual(0.11958120746409709, roc.StandardError, 1e-6);
}
private static void xor()
{
// Create a simple binary XOR
// classification problem:
double[][] problem =
{
// a b a XOR b
new double[] { 0, 0, 0 },
new double[] { 0, 1, 1 },
new double[] { 1, 0, 1 },
new double[] { 1, 1, 0 },
};
// Get the two first columns as the problem
// inputs and the last column as the output
// input columns
double[][] inputs = problem.GetColumns(0, 1);
// output column
int[] outputs = problem.GetColumn(2).ToInt32();
// Plot the problem on screen
ScatterplotBox.Show("XOR", inputs, outputs).Hold();
// However, SVMs expect the output value to be
// either -1 or +1. As such, we have to convert
// it so the vector contains { -1, -1, -1, +1 }:
//
outputs = outputs.Apply(x => x == 0 ? -1 : 1);
// Create a new linear-SVM for two inputs (a and b)
SupportVectorMachine svm = new SupportVectorMachine(inputs: 2);
// Create a L2-regularized L2-loss support vector classification
var teacher = new LinearDualCoordinateDescent(svm, inputs, outputs)
{
Loss = Loss.L2,
Complexity = 1000,
Tolerance = 1e-5
};
// Learn the machine
double error = teacher.Run(computeError: true);
// Compute the machine's answers for the learned inputs
int[] answers = inputs.Apply(x => Math.Sign(svm.Compute(x)));
// Plot the results
ScatterplotBox.Show("SVM's answer", inputs, answers).Hold();
// Use an explicit kernel expansion to transform the
// non-linear classification problem into a linear one
//
// Create a quadratic kernel
Quadratic quadratic = new Quadratic(constant: 1);
// Project the inptus into a higher dimensionality space
double[][] expansion = inputs.Apply(quadratic.Transform);
// Create a new linear-SVM for the transformed input space
svm = new SupportVectorMachine(inputs: expansion[0].Length);
// Create the same learning algorithm in the expanded input space
teacher = new LinearDualCoordinateDescent(svm, expansion, outputs)
{
Loss = Loss.L2,
Complexity = 1000,
Tolerance = 1e-5
};
// Learn the machine
error = teacher.Run(computeError: true);
// Compute the machine's answers for the learned inputs
answers = expansion.Apply(x => Math.Sign(svm.Compute(x)));
// Plot the results
ScatterplotBox.Show("SVM's answer", inputs, answers).Hold();
}
private static void cancer()
{
// Create a new LibSVM sparse format data reader
// to read the Wisconsin's Breast Cancer dataset
//
var reader = new SparseReader("examples-sparse.txt");
int[] outputs; // Read the classification problem into dense memory
double[][] inputs = reader.ReadToEnd(sparse: false, labels: out outputs);
// The dataset has output labels as 4 and 2. We have to convert them
// into negative and positive labels so they can be properly processed.
//
outputs = outputs.Apply(x => x == 2 ? -1 : +1);
// Create a new linear-SVM for the problem dimensions
var svm = new SupportVectorMachine(inputs: reader.Dimensions);
// Create a learning algorithm for the problem's dimensions
var teacher = new LinearDualCoordinateDescent(svm, inputs, outputs)
{
Loss = Loss.L2,
Complexity = 1000,
Tolerance = 1e-5
};
// Learn the classification
double error = teacher.Run();
// Compute the machine's answers for the learned inputs
int[] answers = inputs.Apply(x => Math.Sign(svm.Compute(x)));
// Create a confusion matrix to show the machine's performance
var m = new ConfusionMatrix(predicted: answers, expected: outputs);
// Show it onscreen
DataGridBox.Show(new ConfusionMatrixView(m));
}