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

Timestamp:

04/26/17 11:06:51 (8 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/CicularKernel.cs (modified) (2 diffs)

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

@@ -27 +27 @@
 namespace HeuristicLab.Algorithms.DataAnalysis.KernelRidgeRegression {
   [StorableClass]
-  [Item("CircularKernel", "A circular kernel function 2*pi*(acos(-d)-d*(1-n²)^(0.5)) where n = ||x-c|| and d = n/beta")]
+  [Item("CircularKernel", "A circular kernel function 2*pi*(acos(-d)-d*(1-d²)^(0.5)) where n = ||x-c|| and d = n/beta \n  As described in http://crsouza.com/2010/03/17/kernel-functions-for-machine-learning-applications/")]
   public class CircularKernel : KernelBase {
 
@@ -45 +45 @@
     protected override double Get(double norm) {
       var beta = Beta.Value;
-      if (Math.Abs(beta) < double.Epsilon) return double.NaN;
-      if (norm >= beta) return 0;
+      if (Math.Abs(Beta.Value) < double.Epsilon) return double.NaN;
+      if (norm >= Beta.Value) return 0;
       var d = norm / beta;
-      return Math.Acos(-d) - d * Math.Sqrt(1 - d * d) - Math.PI / 2;
+      return 2 * Math.PI * (Math.Acos(-d) - d * Math.Sqrt(1 - d * d));
     }
 
+    // 4*pi*n^3 / (beta^4 * sqrt(1-n^2/beta^2) 
     protected override double GetGradient(double norm) {
       var beta = Beta.Value;
       if (Math.Abs(beta) < double.Epsilon) return double.NaN;
       if (beta < norm) return 0;
-      return -2 * Math.Pow(norm, 3) / (Math.Pow(beta, 4) * Math.Sqrt(1 - norm * norm / (beta * beta)));
+      var d = norm / beta;
+      return -4 * Math.PI * d * d * d / beta * Math.Sqrt(1 - d * d);
     }
   }