Changeset 14883 for branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions

Timestamp:

04/24/17 13:17:43 (8 years ago)

Author:

bwerth

Message:

#2699 checked and reformulated gradient functions for kernels

Location:

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions

Files:

• CicularKernel.cs (modified) (2 diffs)
• GaussianKernel.cs (modified) (1 diff)
• InverseMultiquadraticKernel.cs (modified) (2 diffs)
• LaplacianKernel.cs (modified) (1 diff)
• MultiquadraticKernel.cs (modified) (1 diff)
• PolysplineKernel.cs (modified) (1 diff)
• ThinPlatePolysplineKernel.cs (modified) (1 diff)

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/CicularKernel.cs

@@ -47 +47 @@
 
     protected override double Get(double norm) {
-      if (norm >= Beta || Math.Abs(Beta) < double.Epsilon) return 0;
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
+      if (norm >= Beta) return 0;
       var d = norm / Beta;
       return Math.Acos(-d) - d * Math.Sqrt(1 - d * d) - Math.PI / 2;
@@ -53 +54 @@
 
     protected override double GetGradient(double norm) {
-      if (Beta <= 0) return double.NaN;
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
       if (Beta < norm) return 0;
-      return 2 * norm * Math.Sqrt(Beta * Beta - norm * norm) / (Beta * Beta * Beta);
+      return -2*Math.Pow(norm,3)/(Math.Pow(Beta,4)*Math.Sqrt(1-norm*norm/(Beta*Beta)));
     }
   }

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/GaussianKernel.cs

@@ -47 +47 @@
 
     protected override double Get(double norm) {
-      if (Math.Abs(Beta) < double.Epsilon) return 0;
-      return Math.Abs(norm) < double.Epsilon ? 1 : Math.Exp(-norm * norm / (Beta * Beta));
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
+      return Math.Exp(-norm * norm / (Beta * Beta));
     }
 
     protected override double GetGradient(double norm) {
       if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
-      norm *= norm;
-      return 2 * norm * Math.Exp(-norm / (Beta * Beta)) / (Beta * Beta * Beta);
+      return 2 * norm * norm / Math.Pow(Beta, 3) * Math.Exp(-norm * norm / (Beta * Beta));
     }
   }

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/InverseMultiquadraticKernel.cs

@@ -46 +46 @@
 
     protected override double Get(double norm) {
-      if (Math.Abs(Beta) < double.Epsilon) return 0;
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
       return 1 / Math.Sqrt(1 + norm * norm / Beta);
     }
@@ -52 +52 @@
     protected override double GetGradient(double norm) {
       if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
-      norm *= norm;
-      return norm / (2 * Beta * Beta * Math.Pow((norm + Beta) / Beta, 1.5));
+      return norm * norm / (2 * Beta * Beta * Math.Pow((norm * norm + Beta) / Beta, 1.5));
     }
   }

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/LaplacianKernel.cs

@@ -44 +44 @@
 
     protected override double Get(double norm) {
-      return Math.Abs(Beta) < double.Epsilon ? 0 : Math.Exp(-norm / Beta);
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
+      return Math.Exp(-norm / Beta);
     }
 

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/MultiquadraticKernel.cs

@@ -48 +48 @@
     #endregion
     protected override double Get(double norm) {
-      return Math.Abs(Beta) < double.Epsilon ? 0 : Math.Sqrt(1 + norm * norm / Beta);
+      if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
+      return Math.Sqrt(1 + norm * norm / Beta);
     }
 
     protected override double GetGradient(double norm) {
       if (Math.Abs(Beta) < double.Epsilon) return double.NaN;
-      norm *= norm;
-      return -norm / (2 * Beta * Beta * Math.Sqrt((norm + Beta) / Beta));
+      var dividend = 2 * Beta * Beta * Math.Sqrt((Beta + norm * norm) / Beta);
+      return -norm * norm / dividend;
     }
   }

branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/RadialBasisFunctions/KernelFunctions/PolysplineKernel.cs

@@ -52 +52 @@
 
     protected override double GetGradient(double norm) {
-      return Math.Pow(norm, Beta) * Math.Log(Beta);
+      return Math.Pow(norm, Beta) * Math.Log(norm);
     }
   }

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

@@ -46 +46 @@
 
     protected override double Get(double norm) {
-      if (Math.Pow(norm, Beta) <= 0) return 0;
-      return Math.Pow(norm, Beta * 2) * Math.Log(1 + Math.Pow(norm, Beta));
+      if (Math.Pow(norm, Beta) <= 0) return double.NaN;
+      return Math.Pow(norm, 2 * Beta) * Math.Log(1 + Math.Pow(norm, Beta));
     }
 
     protected override double GetGradient(double norm) {
       if (Math.Pow(norm, Beta) <= 0) return double.NaN;
-      var ax = Math.Pow(norm, Beta);
-      var a2x = ax * ax;
-      var a3x = a2x * ax;
-      var loga = Math.Log(norm);
-      return 2 * a2x * loga * Math.Log(ax + 1) + a3x * loga / (ax + 1);
+      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);
     }
   }