Changeset 14891 for branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/KernelRidgeRegression/KernelFunctions/MultiquadraticKernel.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/MultiquadraticKernel.cs (modified) (3 diffs)

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

@@ -22 +22 @@
 using System;
 using HeuristicLab.Common;
-using HeuristicLab.Core;            
+using HeuristicLab.Core;
 using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
 
@@ -28 +28 @@
   [StorableClass]
   // conditionally positive definite. (need to add polynomials) see http://num.math.uni-goettingen.de/schaback/teaching/sc.pdf 
-  [Item("MultiquadraticKernel", "A kernel function that uses the multi-quadratic function (sqrt(1+||x-c||²/β).")]
+  [Item("MultiquadraticKernel", "A kernel function that uses the multi-quadratic function sqrt(1+||x-c||²/beta²). Similar to http://crsouza.com/2010/03/17/kernel-functions-for-machine-learning-applications/ with beta as a scaling factor.")]
   public class MultiquadraticKernel : KernelBase {
 
+    private const double C = 1.0;
     #region HLConstructors & Boilerplate
     [StorableConstructor]
@@ -48 +49 @@
       var beta = Beta.Value;
       if (Math.Abs(beta) < double.Epsilon) return double.NaN;
-      return Math.Sqrt(1 + norm * norm / beta);
+      var d = norm / beta;
+      return Math.Sqrt(C + d * d);
     }
 
+    //-n²/(d³*sqrt(C+n²/d²))
     protected override double GetGradient(double norm) {
       var beta = Beta.Value;
       if (Math.Abs(beta) < double.Epsilon) return double.NaN;
-      var dividend = 2 * beta * beta * Math.Sqrt((beta + norm * norm) / beta);
-      return -norm * norm / dividend;
+      var d = norm / beta;
+      return -d * d / (beta * Math.Sqrt(C + d * d));
     }
   }