1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using HeuristicLab.Common;
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24 | using HeuristicLab.Core;
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25 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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26 |
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27 | namespace HeuristicLab.Algorithms.DataAnalysis {
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28 | [StorableClass]
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29 | // conditionally positive definite. (need to add polynomials) see http://num.math.uni-goettingen.de/schaback/teaching/sc.pdf
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30 | [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.")]
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31 | public class MultiquadraticKernel : KernelBase {
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32 |
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33 | private const double C = 1.0;
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34 |
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35 | [StorableConstructor]
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36 | protected MultiquadraticKernel(bool deserializing) : base(deserializing) { }
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37 |
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38 | protected MultiquadraticKernel(MultiquadraticKernel original, Cloner cloner) : base(original, cloner) { }
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39 |
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40 | public MultiquadraticKernel() { }
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41 |
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42 | public override IDeepCloneable Clone(Cloner cloner) {
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43 | return new MultiquadraticKernel(this, cloner);
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44 | }
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45 |
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46 | protected override double Get(double norm) {
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47 | if (Beta == null) throw new InvalidOperationException("Can not calculate kernel distance while Beta is null");
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48 | var beta = Beta.Value;
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49 | if (Math.Abs(beta) < double.Epsilon) return double.NaN;
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50 | var d = norm / beta;
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51 | return Math.Sqrt(C + d * d);
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52 | }
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53 |
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54 | //-n²/(d³*sqrt(C+n²/d²))
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55 | protected override double GetGradient(double norm) {
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56 | if (Beta == null) throw new InvalidOperationException("Can not calculate kernel distance gradient while Beta is null");
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57 | var beta = Beta.Value;
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58 | if (Math.Abs(beta) < double.Epsilon) return double.NaN;
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59 | var d = norm / beta;
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60 | return -d * d / (beta * Math.Sqrt(C + d * d));
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61 | }
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62 | }
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63 | }
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