mirror of
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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
285 lines
8.7 KiB
C#
285 lines
8.7 KiB
C#
// Accord Statistics Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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namespace Accord.Statistics.Kernels
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{
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using Math.Distances;
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using System;
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using Accord.Compat;
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/// <summary>
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/// Wavelet Kernel.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// In Wavelet analysis theory, one of the common goals is to express or
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/// approximate a signal or function using a family of functions generated
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/// by dilations and translations of a function called the mother wavelet.</para>
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/// <para>
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/// The Wavelet kernel uses a mother wavelet function together with dilation
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/// and translation constants to produce such representations and build a
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/// inner product which can be used by kernel methods. The default wavelet
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/// used by this class is the mother function <c>h(x) = cos(1.75x)*exp(-x²/2)</c>.</para>
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///
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/// <para>
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/// References:
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/// <list type="bullet">
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/// <item><description>
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/// Li Zhang, Weida Zhou, and Licheng Jiao; Wavelet Support Vector Machine. IEEE
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/// Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, Vol. 34,
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/// No. 1, February 2004.</description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <example>
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/// <code source="Unit Tests\Accord.Tests.MachineLearning\VectorMachines\MulticlassSupportVectorLearningTest.cs" region="doc_learn_wavelet" />
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/// </example>
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///
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[Serializable]
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public struct Wavelet : IKernel, ICloneable, IKernel<int[]>, IDistance, IDistance<int[]>
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{
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// Default wavelet mother function : h(x) = cos(1.75x)*exp(-x²/2)
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private Func<double, double> h;
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private double dilation;
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private double translation;
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private bool invariant;
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private static double mother(double x)
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{
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return Math.Cos(1.75 * x) * Math.Exp(-(x * x) / 2.0);
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}
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/// <summary>
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/// Gets or sets the Mother wavelet for this kernel.
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/// </summary>
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///
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public Func<double, double> Mother
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{
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get { return h; }
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set { h = value; }
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}
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/// <summary>
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/// Gets or sets the wavelet dilation for this kernel.
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/// </summary>
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///
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public double Dilation
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{
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get { return dilation; }
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set { dilation = value; }
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}
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/// <summary>
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/// Gets or sets the wavelet translation for this kernel.
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/// </summary>
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///
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public double Translation
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{
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get { return translation; }
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set { translation = value; }
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}
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/// <summary>
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/// Gets or sets whether this is
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/// an invariant Wavelet kernel.
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/// </summary>
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///
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public bool Invariant
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{
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get { return invariant; }
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set { invariant = value; }
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}
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/// <summary>
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/// Constructs a new Wavelet kernel.
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/// </summary>
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///
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public Wavelet(bool invariant)
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{
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this.invariant = invariant;
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this.dilation = 1.0;
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this.translation = 0.0;
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this.h = mother;
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}
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/// <summary>
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/// Constructs a new Wavelet kernel.
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/// </summary>
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///
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public Wavelet(bool invariant, double dilation)
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{
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this.invariant = invariant;
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this.dilation = dilation;
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this.translation = 0.0;
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this.h = mother;
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}
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/// <summary>
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/// Constructs a new Wavelet kernel.
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/// </summary>
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///
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public Wavelet(bool invariant, double dilation, Func<double, double> mother)
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{
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this.invariant = invariant;
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this.dilation = dilation;
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this.translation = 0.0;
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this.h = mother;
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}
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/// <summary>
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/// Constructs a new Wavelet kernel.
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/// </summary>
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///
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public Wavelet(double translation, double dilation)
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{
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this.invariant = false;
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this.dilation = dilation;
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this.translation = translation;
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this.h = mother;
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}
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/// <summary>
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/// Constructs a new Wavelet kernel.
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/// </summary>
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///
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public Wavelet(double translation, double dilation, Func<double, double> mother)
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{
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this.invariant = false;
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this.dilation = dilation;
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this.translation = translation;
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this.h = mother;
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}
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/// <summary>
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/// Wavelet kernel function.
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/// </summary>
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///
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/// <param name="x">Vector <c>x</c> in input space.</param>
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/// <param name="y">Vector <c>y</c> in input space.</param>
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/// <returns>Dot product in feature (kernel) space.</returns>
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///
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public double Function(double[] x, double[] y)
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{
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double prod = 1.0;
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if (invariant)
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{
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for (int i = 0; i < x.Length; i++)
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{
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prod *= (h((x[i] - translation) / dilation)) *
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(h((y[i] - translation) / dilation));
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}
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}
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else
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{
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for (int i = 0; i < x.Length; i++)
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prod *= h((x[i] - y[i]) / dilation);
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}
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return prod;
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}
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/// <summary>
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/// Wavelet kernel function.
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/// </summary>
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///
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/// <param name="x">Vector <c>x</c> in input space.</param>
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/// <param name="y">Vector <c>y</c> in input space.</param>
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/// <returns>Dot product in feature (kernel) space.</returns>
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///
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public double Function(int[] x, int[] y)
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{
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double prod = 1.0;
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if (invariant)
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{
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for (int i = 0; i < x.Length; i++)
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{
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prod *= (h((x[i] - translation) / dilation)) *
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(h((y[i] - translation) / dilation));
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}
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}
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else
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{
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for (int i = 0; i < x.Length; i++)
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prod *= h((x[i] - y[i]) / dilation);
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}
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return prod;
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}
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/// <summary>
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/// Computes the squared distance in feature space
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/// between two points given in input space.
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/// </summary>
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///
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/// <param name="x">Vector <c>x</c> in input space.</param>
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/// <param name="y">Vector <c>y</c> in input space.</param>
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///
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/// <returns>
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/// Squared distance between <c>x</c> and <c>y</c> in feature (kernel) space.
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/// </returns>
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///
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public double Distance(double[] x, double[] y)
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{
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return Function(x, x) + Function(y, y) - 2 * Function(x, y);
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}
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/// <summary>
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/// Computes the squared distance in feature space
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/// between two points given in input space.
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/// </summary>
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///
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/// <param name="x">Vector <c>x</c> in input space.</param>
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/// <param name="y">Vector <c>y</c> in input space.</param>
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///
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/// <returns>
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/// Squared distance between <c>x</c> and <c>y</c> in feature (kernel) space.
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/// </returns>
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///
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public double Distance(int[] x, int[] y)
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{
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return Function(x, x) + Function(y, y) - 2 * Function(x, y);
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}
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/// <summary>
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/// Creates a new object that is a copy of the current instance.
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/// </summary>
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///
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/// <returns>
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/// A new object that is a copy of this instance.
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/// </returns>
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///
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public object Clone()
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{
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return MemberwiseClone();
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}
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}
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}
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