private static void Main()
{
// Here we declare that our samples will be 2 dimensional column vectors.
// (Note that if you don't know the dimensionality of your vectors at compile time
// you can change the 2 to a 0 and then set the size at runtime)
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
using (var rbk = new RadialBasisKernel <double, Matrix <double> >(0.1d, 2, 1))
{
// Here we declare an instance of the kcentroid object. The kcentroid has 3 parameters
// you need to set. The first argument to the constructor is the kernel we wish to
// use. The second is a parameter that determines the numerical accuracy with which
// the object will perform the centroid estimation. Generally, smaller values
// give better results but cause the algorithm to attempt to use more dictionary vectors
// (and thus run slower and use more memory). The third argument, however, is the
// maximum number of dictionary vectors a kcentroid is allowed to use. So you can use
// it to control the runtime complexity.
using (var test = new KCentroid <double, RadialBasisKernel <double, Matrix <double> > >(rbk, 0.01, 15))
{
// now we train our object on a few samples of the sinc function.
using (var m = Matrix <double> .CreateTemplateParameterizeMatrix(2, 1))
{
for (double x = -15; x <= 8; x += 1)
{
m[0] = x;
m[1] = Sinc(x);
test.Train(m);
}
using (var rs = new RunningStats <double>())
{
// Now let's output the distance from the centroid to some points that are from the sinc function.
// These numbers should all be similar. We will also calculate the statistics of these numbers
// by accumulating them into the running_stats object called rs. This will let us easily
// find the mean and standard deviation of the distances for use below.
Console.WriteLine("Points that are on the sinc function:");
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -4.1; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
Console.WriteLine();
// Let's output the distance from the centroid to some points that are NOT from the sinc function.
// These numbers should all be significantly bigger than previous set of numbers. We will also
// use the rs.scale() function to find out how many standard deviations they are away from the
// mean of the test points from the sinc function. So in this case our criterion for "significantly bigger"
// is > 3 or 4 standard deviations away from the above points that actually are on the sinc function.
Console.WriteLine("Points that are NOT on the sinc function:");
m[0] = -1.5; m[1] = Sinc(m[0]) + 4; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -1.5; m[1] = Sinc(m[0]) + 3; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0; m[1] = -Sinc(m[0]); Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0.5; m[1] = -Sinc(m[0]); Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -4.1; m[1] = Sinc(m[0]) + 2; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -1.5; m[1] = Sinc(m[0]) + 0.9; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0.5; m[1] = Sinc(m[0]) + 1; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
// And finally print out the mean and standard deviation of points that are actually from sinc().
Console.WriteLine($"\nmean: {rs.Mean}");
Console.WriteLine($"standard deviation: {rs.StdDev}");
// The output is as follows:
/*
* Points that are on the sinc function:
* 0.869913
* 0.869913
* 0.873408
* 0.872807
* 0.870432
* 0.869913
* 0.872807
*
* Points that are NOT on the sinc function:
* 1.06366 is 119.65 standard deviations from sinc.
* 1.02212 is 93.8106 standard deviations from sinc.
* 0.921382 is 31.1458 standard deviations from sinc.
* 0.918439 is 29.3147 standard deviations from sinc.
* 0.931428 is 37.3949 standard deviations from sinc.
* 0.898018 is 16.6121 standard deviations from sinc.
* 0.914425 is 26.8183 standard deviations from sinc.
*
* mean: 0.871313
* standard deviation: 0.00160756
*/
// So we can see that in this example the kcentroid object correctly indicates that
// the non-sinc points are definitely not points from the sinc function.
}
}
}
}
}
