public void FunctionTest()
{
Linear dense = new Linear(1);
SparseLinear target = new SparseLinear(1);
double[] sx = { 1, -0.555556, 2, +0.250000, 3, -0.864407, 4, -0.916667 };
double[] sy = { 1, -0.666667, 2, -0.166667, 3, -0.864407, 4, -0.916667 };
double[] sz = { 1, -0.944444, 3, -0.898305, 4, -0.916667 };
double[] dx = { -0.555556, +0.250000, -0.864407, -0.916667 };
double[] dy = { -0.666667, -0.166667, -0.864407, -0.916667 };
double[] dz = { -0.944444, +0.000000, -0.898305, -0.916667 };
double expected, actual;
expected = dense.Function(dx, dy);
actual = target.Function(sx, sy);
Assert.AreEqual(expected, actual, 1e-10);
expected = dense.Function(dx, dz);
actual = target.Function(sx, sz);
Assert.AreEqual(expected, actual, 1e-10);
expected = dense.Function(dy, dz);
actual = target.Function(sy, sz);
Assert.AreEqual(expected, actual, 1e-10);
}
/// <summary>
/// Polynomial kernel function.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>Dot product in feature (kernel) space.</returns>
///
public override double Function(double[] x, double[] y)
{
#pragma warning disable 0618
double sum = SparseLinear.Product(x, y) + constant;
return(Math.Pow(sum, Degree));
}
/// <summary>
/// Sigmoid kernel function.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>Dot product in feature (kernel) space.</returns>
///
public override double Function(double[] x, double[] y)
{
#pragma warning disable 0618
double sum = SparseLinear.Product(x, y);
return(System.Math.Tanh(Gamma * sum + Constant));
}
/// <summary>
/// Computes the distance in input space
/// between two points given in feature space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
///
/// <returns>Distance between <c>x</c> and <c>y</c> in input space.</returns>
///
public override double Distance(double[] x, double[] y)
{
if (x == y)
{
return(0.0);
}
double norm = SparseLinear.SquaredEuclidean(x, y);
return(2 - 2 * Math.Exp(-gamma * Math.Sqrt(norm)));
}
/// <summary>
/// Computes the squared distance in input space
/// between two points given in feature space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
///
/// <returns>
/// Squared distance between <c>x</c> and <c>y</c> in input space.
/// </returns>
///
public double ReverseDistance(double[] x, double[] y)
{
if (x == y)
{
return(0.0);
}
double norm = SparseLinear.SquaredEuclidean(x, y);
return(-(1.0 / gamma) * Math.Log(1.0 - 0.5 * norm));
}
/// <summary>
/// Gaussian Kernel function.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>Dot product in feature (kernel) space.</returns>
///
public override double Function(double[] x, double[] y)
{
// Optimization in case x and y are
// exactly the same object reference.
if (x == y)
{
return(1.0);
}
double norm = SparseLinear.SquaredEuclidean(x, y);
return(Math.Exp(-gamma * norm));
}
/// <summary>
/// Cauchy Kernel Function
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
///
/// <returns>Dot product in feature (kernel) space.</returns>
///
public override double Function(double[] x, double[] y)
{
// Optimization in case x and y are
// exactly the same object reference.
if (x == y)
{
return(1.0);
}
#pragma warning disable 0618
double norm = SparseLinear.SquaredEuclidean(x, y);
return(1.0 / (1.0 + norm / Sigma));
}
/// <summary>
/// Polynomial kernel function.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>Dot product in feature (kernel) space.</returns>
///
public override double Function(double[] x, double[] y)
{
double sum = SparseLinear.Product(x, y) + constant;
return(Math.Pow(sum, Degree));
}