/// <summary>
/// Computes the squared distance in feature space
/// between two points given in input space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
///
/// <returns>Squared distance between <c>x</c> and <c>y</c> in feature (kernel) space.</returns>
///
public double Distance(Sparse <double> x, Sparse <double> y)
{
if (x == y)
{
return(0.0);
}
double sumx = constant + x.Dot(x);
double sumy = constant + y.Dot(y);
double sum = constant + x.Dot(y);
int d = degree;
return(Math.Pow(sumx, d) + Math.Pow(sumy, d) - 2 * Math.Pow(sum, d));
}
/// <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 double Function(Sparse <double> x, Sparse <double> y)
{
double sum = x.Dot(y);
double value = Math.Tanh(alpha * sum + constant);
return(value);
}
/// <summary>
/// The 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 double Function(double[] y, Sparse <double> x)
{
return(x.Dot(y) + constant);
}
/// <summary>
/// The 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 double Function(Sparse <double> x, Sparse <double> y)
{
return(x.Dot(y) + constant);
}
/// <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 double Function(Sparse <double> x, Sparse <double> y)
{
double sum = x.Dot(y) + constant;
return(Math.Pow(sum, degree));
}