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

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

@@ -22 +22 @@
 using System;
 using HeuristicLab.Common;
-using HeuristicLab.Core;     
+using HeuristicLab.Core;
 using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
 
 namespace HeuristicLab.Algorithms.DataAnalysis.KernelRidgeRegression {
   [StorableClass]
-  [Item("InverseMultiquadraticKernel", "A kernel function that uses the inverse multi-quadratic function  1 / sqrt(1+||x-c||^2/beta). Positive definite: beta > 0")]
+  [Item("InverseMultiquadraticKernel", "A kernel function that uses the inverse multi-quadratic function  1 / 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 InverseMultiquadraticKernel : KernelBase {
+
+    private const double C = 1.0;
     #region HLConstructors & Boilerplate
     [StorableConstructor]
@@ -35 +37 @@
     private void AfterDeserialization() { }
     protected InverseMultiquadraticKernel(InverseMultiquadraticKernel original, Cloner cloner) : base(original, cloner) { }
-    public InverseMultiquadraticKernel() {
-    }
+    public InverseMultiquadraticKernel() { }
     public override IDeepCloneable Clone(Cloner cloner) {
       return new InverseMultiquadraticKernel(this, cloner);
@@ -45 +46 @@
       var beta = Beta.Value;
       if (Math.Abs(beta) < double.Epsilon) return double.NaN;
-      return 1 / Math.Sqrt(1 + norm * norm / beta);
+      var d = norm / beta;
+      return 1 / Math.Sqrt(C + d * d);
     }
 
+    //n²/(b³(n²/b² + C)^1.5)
     protected override double GetGradient(double norm) {
       var beta = Beta.Value;
       if (Math.Abs(beta) < double.Epsilon) return double.NaN;
-      return norm * norm / (2 * beta * beta * Math.Pow((norm * norm + beta) / beta, 1.5));
+      var d = norm / beta;
+      return d * d / (beta * Math.Pow(d * d + C, 1.5));
     }
   }