public void sparse_zero_vector_test()
{
// Create a linear-SVM learning method
var teacher = new LinearNewtonMethod <Linear, Sparse <double> >()
{
Tolerance = 1e-10,
Complexity = 1e+10, // learn a hard-margin model
};
// Now suppose you have some points
Sparse <double>[] inputs = Sparse.FromDense(new[]
{
new double[] { 1, 1, 2 },
new double[] { 0, 1, 6 },
new double[] { 1, 0, 8 },
new double[] { 0, 0, 0 },
});
int[] outputs = { 1, -1, 1, -1 };
// Learn the support vector machine
var svm = teacher.Learn(inputs, outputs);
// Compute the predicted points
bool[] predicted = svm.Decide(inputs);
// And the squared error loss using
double error = new ZeroOneLoss(outputs).Loss(predicted);
Assert.AreEqual(3, svm.NumberOfInputs);
Assert.AreEqual(1, svm.NumberOfOutputs);
Assert.AreEqual(2, svm.NumberOfClasses);
Assert.AreEqual(1, svm.Weights.Length);
Assert.AreEqual(1, svm.SupportVectors.Length);
Assert.AreEqual(1.0, svm.Weights[0], 1e-6);
Assert.AreEqual(2.0056922148257597, svm.SupportVectors[0][0], 1e-6);
Assert.AreEqual(-0.0085361347231909836, svm.SupportVectors[0][1], 1e-6);
Assert.AreEqual(0.0014225721169379331, svm.SupportVectors[0][2], 1e-6);
Assert.AreEqual(0.0, error);
}
public void linear_regression_test()
{
#region doc_linreg
// Declare some training data. This is exactly the same
// data used in the MultipleLinearRegression documentation page
// We will try to model a plane as an equation in the form
// "ax + by + c = z". We have two input variables (x and y)
// and we will be trying to find two parameters a and b and
// an intercept term c.
// Create a linear-SVM learning method
var teacher = new LinearNewtonMethod()
{
Tolerance = 1e-10,
Complexity = 1e+10, // learn a hard-margin model
};
// Now suppose you have some points
double[][] inputs =
{
new double[] { 1, 1 },
new double[] { 0, 1 },
new double[] { 1, 0 },
new double[] { 0, 0 },
};
// located in the same Z (z = 1)
double[] outputs = { 1, 1, 1, 1 };
// Learn the support vector machine
var svm = teacher.Learn(inputs, outputs);
// Convert the svm to logistic regression
var regression = (MultipleLinearRegression)svm;
// As result, we will be given the following:
double a = regression.Weights[0]; // a = 0
double b = regression.Weights[1]; // b = 0
double c = regression.Intercept; // c = 1
// This is the plane described by the equation
// ax + by + c = z => 0x + 0y + 1 = z => 1 = z.
// We can compute the predicted points using
double[] predicted = regression.Transform(inputs);
// And the squared error loss using
double error = new SquareLoss(outputs).Loss(predicted);
#endregion
Assert.AreEqual(2, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(0.0, a, 1e-6);
Assert.AreEqual(0.0, b, 1e-6);
Assert.AreEqual(1.0, c, 1e-6);
Assert.AreEqual(0.0, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
double r = regression.CoefficientOfDetermination(inputs, outputs);
Assert.AreEqual(1.0, r);
}
public void learn_linear_sparse()
{
#region doc_xor_sparse
// As an example, we will try to learn a linear machine that can
// replicate the "exclusive-or" logical function. However, since we
// will be using a linear SVM, we will not be able to solve this
// problem perfectly as the XOR is a non-linear classification problem:
Sparse <double>[] inputs =
{
Sparse.FromDense(new double[] { 0, 0 }), // the XOR function takes two booleans
Sparse.FromDense(new double[] { 0, 1 }), // and computes their exclusive or: the
Sparse.FromDense(new double[] { 1, 0 }), // output is true only if the two booleans
Sparse.FromDense(new double[] { 1, 1 }) // are different
};
int[] xor = // this is the output of the xor function
{
0, // 0 xor 0 = 0 (inputs are equal)
1, // 0 xor 1 = 1 (inputs are different)
1, // 1 xor 0 = 1 (inputs are different)
0, // 1 xor 1 = 0 (inputs are equal)
};
// Now, we can create the sequential minimal optimization teacher
var learn = new LinearNewtonMethod <Linear, Sparse <double> >()
{
UseComplexityHeuristic = true,
UseKernelEstimation = false
};
// And then we can obtain a trained SVM by calling its Learn method
var svm = learn.Learn(inputs, xor);
// Finally, we can obtain the decisions predicted by the machine:
bool[] prediction = svm.Decide(inputs);
#endregion
Assert.AreEqual(prediction[0], false);
Assert.AreEqual(prediction[1], false);
Assert.AreEqual(prediction[2], false);
Assert.AreEqual(prediction[3], false);
int[] or = // this is the output of the xor function
{
0, // 0 or 0 = 0 (inputs are equal)
1, // 0 or 1 = 1 (inputs are different)
1, // 1 or 0 = 1 (inputs are different)
1, // 1 or 1 = 1 (inputs are equal)
};
learn = new LinearNewtonMethod <Linear, Sparse <double> >()
{
Complexity = 1e+8,
UseKernelEstimation = false
};
svm = learn.Learn(inputs, or);
prediction = svm.Decide(inputs);
Assert.AreEqual(0, inputs[0].Indices.Length);
Assert.AreEqual(1, inputs[1].Indices.Length);
Assert.AreEqual(1, inputs[2].Indices.Length);
Assert.AreEqual(2, inputs[3].Indices.Length);
Assert.AreEqual(prediction[0], false);
Assert.AreEqual(prediction[1], true);
Assert.AreEqual(prediction[2], true);
Assert.AreEqual(prediction[3], true);
}