Changeset 14891 for branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/KernelRidgeRegression/KernelFunctions/ThinPlatePolysplineKernel.cs

Timestamp:

04/26/17 11:06:51 (7 years ago)

Author:

bwerth

Message:

#2699 reworked kenel functions (beta is always a scaling factor now), added LU-Decomposition as a fall-back if Cholesky-decomposition fails

File:

• branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/KernelRidgeRegression/KernelFunctions/ThinPlatePolysplineKernel.cs (modified) (4 diffs)

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/KernelRidgeRegression/KernelFunctions/ThinPlatePolysplineKernel.cs

@@ -23 +23 @@
 using HeuristicLab.Common;
 using HeuristicLab.Core;
+using HeuristicLab.Data;
+using HeuristicLab.Parameters;
 using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
 
@@ -28 +30 @@
   [StorableClass]
   // conditionally positive definite. (need to add polynomials) see http://num.math.uni-goettingen.de/schaback/teaching/sc.pdf 
-  [Item("ThinPlatePolysplineKernel", "A kernel function that uses the ThinPlatePolyspline function ||x-c||^(2*Beta)*log(||x-c||^Beta)")]
+  [Item("ThinPlatePolysplineKernel", "A kernel function that uses the ThinPlatePolyspline function (||x-c||/Beta)^(Degree)*log(||x-c||/Beta) as described in \"Thin-Plate Spline Radial Basis Function Scheme for Advection-Diffusion Problems\" with beta as a scaling parameter.")]
   public class ThinPlatePolysplineKernel : KernelBase {
+
+    #region Parameternames
+    private const string DegreeParameterName = "Degree";
+    #endregion
+    #region Parameterproperties
+    public IFixedValueParameter<DoubleValue> DegreeParameter
+    {
+      get { return Parameters[DegreeParameterName] as IFixedValueParameter<DoubleValue>; }
+    }
+    #endregion
+    #region Properties
+    public DoubleValue Degree
+    {
+      get { return DegreeParameter.Value; }
+    }
+    #endregion
+
     #region HLConstructors & Boilerplate
     [StorableConstructor]
@@ -37 +56 @@
     protected ThinPlatePolysplineKernel(ThinPlatePolysplineKernel original, Cloner cloner) : base(original, cloner) { }
     public ThinPlatePolysplineKernel() {
+      Parameters.Add(new FixedValueParameter<DoubleValue>(DegreeParameterName, "The degree of the kernel. Needs to be greater than zero.", new DoubleValue(2.0)));
     }
     public override IDeepCloneable Clone(Cloner cloner) {
@@ -45 +65 @@
     protected override double Get(double norm) {
       var beta = Beta.Value;
-      if (Math.Pow(norm, beta) < 0) return double.NaN;
-      return Math.Pow(norm, 2 * beta) * Math.Log(1 + Math.Pow(norm, beta));
+      if (Math.Abs(beta) < double.Epsilon) return double.NaN;
+      var d = norm / beta;
+      if (Math.Abs(d) < double.Epsilon) return 0;
+      return Math.Pow(d, Degree.Value) * Math.Log(d);
     }
 
+    // (Degree/beta) * (norm/beta)^Degree * log(norm/beta) 
     protected override double GetGradient(double norm) {
       var beta = Beta.Value;
-      if (Math.Pow(norm, beta) <= 0) return double.NaN;
-      return 2 * Math.Log(norm) * Math.Pow(norm, 2 * beta) * Math.Log(1 + Math.Pow(norm, beta)) + Math.Pow(norm, 3 * beta) * Math.Log(norm) / (Math.Pow(norm, beta) + 1);
+      if (Math.Abs(beta) < double.Epsilon) return double.NaN;
+      var d = norm / beta;
+      if (Math.Abs(d) < double.Epsilon) return 0;
+      return Degree.Value / beta * Math.Pow(d, Degree.Value) * Math.Log(d);
     }
   }