SupportVectorReduction Class

public class SupportVectorReduction : SupportVectorReductionBase<SupportVectorMachine<IKernel<double[]>, double[]>, IKernel<double[]>, double[]>

Public Class SupportVectorReduction
	Inherits SupportVectorReductionBase(Of SupportVectorMachine(Of IKernel(Of Double()), Double()), IKernel(Of Double()), Double())

// 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
};

// Instantiate a new learning algorithm for SVMs
var smo = new SequentialMinimalOptimization<Linear>()
{

    // Set up the learning algorithm
    Complexity = 100.0
};

// Run
var svm = smo.Learn(inputs, labels);

int numberBefore = svm.SupportVectors.Length; // should be

double errorBefore = new ZeroOneLoss(labels).Loss(svm.Decide(inputs)); // should be 0


// At this point we have the weighted support vectors
//     w        sv        b
//   (+4)  *  (1,1)      -3
//   (-2)  *  (1,0)
//   (-2)  *  (0,1)
// 
// However, it can be seen that the last SV can be written
// as a linear combination of the two first vectors:
// 
//   (0,1) = (1,1) - (1,0)
// 
// Since we have a linear space (we are using a linear kernel)
// this vector could be removed from the support vector set.
// 
// f(x) = sum(alpha_i * x * x_i) + b
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(0,1)*x             - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*((1,1) - (1,0))*x   - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(1,1)*x + 2*(1,0)*x - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(1,1)*x + 2*(1,0)*x - 3
//      = 2*(1,1)*x - 3
//      = 2*x1 + 2*x2 - 3
// 

// Clone the original machine so we don't change it
var clone = (SupportVectorMachine<Linear>)svm.Clone();

// Create a support vector reduction algorithm
var svr = new SupportVectorReduction<Linear>(clone);

// Reduce the number of support vectors
var svm2 = svr.Learn();

int numberAfter = svm2.SupportVectors.Length; // should be 1

// Compute the new error
double errorAfter = new ZeroOneLoss(labels).Loss(svm2.Decide(inputs)); // should still be 0