Non-linear Support Vector Regression with C# and "Accord.NET"

Accord.NET provides a Support Vector Machine learning algorithm for regression problems in the SequentialMinimalOptimizationRegression class. There is an example application for this topic in the sample application's wiki page.

Here is an example on how to use it:

// 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, 20, 8
};

// Create the sequential minimal optimization teacher
var learn = new SequentialMinimalOptimizationRegression<Polynomial>()
{
    Kernel = new Polynomial(degree: 2)
}

// Use the teacher to learn a new machine
var svm = teacher.Learn(inputs, outputs);

// Compute the answer for one particular example
double fxy = machine.Transform(inputs[0]); // 1.0003849827673186

// Compute the answer for all examples 
double[] fxys = machine.Transform(inputs);