public void FunctionTest()
{
Quadratic target = new Quadratic(0);
double[] x = new double[] { 1, 1 };
double[] y = new double[] { 1, 1 };
double expected = System.Math.Pow(x.InnerProduct(y), 2);
double actual = target.Function(x, y);
Assert.AreEqual(expected, actual);
x = new double[] { 0.5, 2.0 };
y = new double[] { 1.3, -0.2 };
expected = 0.0625;
actual = target.Function(x, y);
Assert.AreEqual(expected, actual);
target = new Quadratic(4.2);
x = new double[] { 9.4, 22.1 };
y = new double[] { -6.21, 4 };
expected = System.Math.Pow(x.InnerProduct(y) + 4.2, 2);
actual = target.Function(x, y);
Assert.AreEqual(expected, actual, 0.0001);
}
public void DistanceTest()
{
Quadratic target = new Quadratic(1);
double[] x = new double[] { 1, 1 };
double[] y = new double[] { 1, 1 };
double expected = 0;
double actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
x = new double[] { 0.5, 2.0 };
y = new double[] { 1.3, -0.2 };
expected = 31.8904;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
target = new Quadratic(3);
x = new double[] { 9.4, 22.1 };
y = new double[] { -6.21, 4 };
expected = 337265.44515681011;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
}
/// <summary>
/// Projects an input point into feature space.
/// </summary>
///
/// <param name="input">The input point to be projected into feature space.</param>
///
/// <returns>
/// The feature space representation of the given <paramref name="input"/> point.
/// </returns>
///
public double[] Transform(double[] input)
{
switch (degree)
{
case 1:
return(Linear.Transform(input, constant));
case 2:
return(Quadratic.Transform(input, constant));
default:
return(Transform(input, degree, constant));
}
}
public void TransformTest_Quadratic()
{
double[][] data =
{
new double[] { 5.1, 3.5, 1.4, 0.2 },
new double[] { 5.0, 3.6, 1.4, 0.2 },
new double[] { 4.9, 3.0, 1.4, 0.2 },
new double[] { 5.8, 4.0, 1.2, 0.2 },
new double[] { 4.7, 3.2, 1.3, 0.2 },
};
var target = new Polynomial(2);
var quadratic = new Quadratic();
double[][] expected = data.Apply(quadratic.Transform);
double[][] actual = data.Apply(target.Transform);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
}
public void ExpandReverseDistanceWithConstantTest()
{
Quadratic kernel = new Quadratic(4.2);
var x = new double[] { 0.5, 2.0 };
var y = new double[] { 1.3, -0.2 };
var phi_x = kernel.Transform(x);
var phi_y = kernel.Transform(y);
double d = Distance.SquareEuclidean(x, y);
double phi_d = kernel.ReverseDistance(phi_x, phi_y);
Assert.AreEqual(5.48, phi_d, 1e-10);
Assert.AreEqual(5.48, d);
Assert.IsFalse(double.IsNaN(phi_d));
Assert.IsFalse(double.IsNaN(d));
}
public void ExpandDistanceWithConstantTest()
{
Quadratic kernel = new Quadratic(4.2);
var x = new double[] { 0.5, 2.0 };
var y = new double[] { 1.3, -0.2 };
var phi_x = kernel.Transform(x);
var phi_y = kernel.Transform(y);
double d1 = Distance.SquareEuclidean(phi_x, phi_y);
double d2 = kernel.Distance(x, y);
double d3 = Accord.Statistics.Tools.Distance(kernel, x, y);
Assert.AreEqual(66.9624, d1);
Assert.AreEqual(66.9624, d2, 1e-10);
Assert.AreEqual(66.9624, d3, 1e-10);
Assert.IsFalse(double.IsNaN(d1));
Assert.IsFalse(double.IsNaN(d2));
Assert.IsFalse(double.IsNaN(d3));
}
public void ExpandReverseDistanceTest()
{
Quadratic kernel = new Quadratic(0);
var x = new double[] { 0.5, 2.0 };
var y = new double[] { 1.3, -0.2 };
var phi_x = kernel.Transform(x);
var phi_y = kernel.Transform(y);
double d = Distance.SquareEuclidean(x, y);
double phi_d = kernel.ReverseDistance(phi_x, phi_y);
Assert.AreEqual(phi_d, d);
}
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();
}