source: branches/RBFRegression/HeuristicLab.Algorithms.DataAnalysis/3.4/KernelRidgeRegression/KernelFunctions/MultiquadraticKernel.cs @ 14888

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using HeuristicLab.Common;
using HeuristicLab.Core;            
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;

namespace HeuristicLab.Algorithms.DataAnalysis.KernelRidgeRegression {
  [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).")]
  public class MultiquadraticKernel : KernelBase {

    #region HLConstructors & Boilerplate
    [StorableConstructor]
    protected MultiquadraticKernel(bool deserializing) : base(deserializing) { }
    [StorableHook(HookType.AfterDeserialization)]
    private void AfterDeserialization() { }
    protected MultiquadraticKernel(MultiquadraticKernel original, Cloner cloner)
                : base(original, cloner) { }

    public MultiquadraticKernel() {
    }
    public override IDeepCloneable Clone(Cloner cloner) {
      return new MultiquadraticKernel(this, cloner);
    }
    #endregion
    protected override double Get(double norm) {
      var beta = Beta.Value;
      if (Math.Abs(beta) < double.Epsilon) return double.NaN;
      return Math.Sqrt(1 + norm * norm / beta);
    }

    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;
    }
  }
}