/// <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>
/// Laplacian 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 * Math.Sqrt(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);
}
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));
}
/// <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)
{
double sum = SparseLinear.Product(x, y);
return(System.Math.Tanh(Gamma * sum + Constant));
}