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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.
190 lines
6.2 KiB
C#
190 lines
6.2 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.Distributions.DensityKernels
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{
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using System;
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using Accord.Math;
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using Accord.Compat;
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using Accord.Statistics.Distributions.Multivariate;
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/// <summary>
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/// Epanechnikov density kernel.
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/// </summary>
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///
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/// <remarks>
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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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/// Comaniciu, Dorin, and Peter Meer. "Mean shift: A robust approach toward
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/// feature space analysis." Pattern Analysis and Machine Intelligence, IEEE
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/// Transactions on 24.5 (2002): 603-619. Available at:
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/// http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1000236 </description></item>
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/// <item><description>
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/// Dan Styer, Oberlin College Department of Physics and Astronomy; Volume of a d-dimensional
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/// sphere. Last updated 30 August 2007. Available at:
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/// http://www.oberlin.edu/physics/dstyer/StatMech/VolumeDSphere.pdf </description></item>
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/// <item><description>
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/// David W. Scott, Multivariate Density Estimation: Theory, Practice, and
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/// Visualization, Wiley, Aug 31, 1992</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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/// <para>
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/// The following example shows how to fit a <see cref="MultivariateEmpiricalDistribution"/>
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/// using <see cref="EpanechnikovKernel">Epanechnikov kernels</see>.</para>
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/// <code source="Unit Tests\Accord.Tests.Statistics\Distributions\Multivariate\Continuous\MultivariateEmpiricalDistributionTest.cs" region="doc_fit_epanechnikov" />
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/// </example>
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///
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/// <seealso cref="Accord.Statistics.Distributions.Univariate.EmpiricalDistribution"/>
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///
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/// <seealso cref="GaussianKernel"/>
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/// <seealso cref="UniformKernel"/>
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///
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[Serializable]
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public class EpanechnikovKernel : IRadiallySymmetricKernel
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{
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private double constant;
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/// <summary>
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/// Gets or sets the kernel's normalization constant.
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/// </summary>
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///
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public double Constant
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{
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get { return constant; }
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set { constant = value; }
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="EpanechnikovKernel"/> class.
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/// </summary>
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///
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public EpanechnikovKernel()
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: this(1)
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{
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="EpanechnikovKernel"/> class.
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/// </summary>
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///
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/// <param name="constant">The constant by which the kernel formula
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/// is multiplied at the end. Default is to consider the area
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/// of a unit-sphere of dimension 1.</param>
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///
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public EpanechnikovKernel(double constant)
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{
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this.constant = constant;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="EpanechnikovKernel"/> class.
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/// </summary>
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///
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/// <param name="dimension">The desired dimension <c>d</c>.</param>
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///
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public EpanechnikovKernel(int dimension)
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{
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// compute the area of the d-dimensional unit hypersphere
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// http://www.oberlin.edu/physics/dstyer/StatMech/VolumeDSphere.pdf
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double num = Math.Pow(Math.PI, dimension / 2.0);
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double den = Gamma.Function(dimension / 2.0 + 1);
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double area = num / den;
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this.constant = (1.0 / (2.0 * area)) * (dimension + 2);
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}
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/// <summary>
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/// Computes the kernel density function.
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/// </summary>
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///
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/// <param name="x">The input point.</param>
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///
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/// <returns>
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/// A density estimate around <paramref name="x"/>.
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/// </returns>
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///
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public double Function(params double[] x)
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{
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double sum = 0.0;
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for (int i = 0; i < x.Length; i++)
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sum += x[i] * x[i];
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if (sum < 1)
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return constant * (1.0 - sum);
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return 0;
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}
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/// <summary>
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/// Computes the kernel profile function.
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/// </summary>
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///
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/// <param name="x">The point estimate <c>x</c>.</param>
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///
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/// <returns>
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/// The value of the profile function at point <paramref name="x"/>.
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/// </returns>
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///
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public double Profile(double x)
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{
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#if DEBUG
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if (x < 0)
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throw new Exception();
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#endif
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// Equation 7 in (Comaniciu & Meer)
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// https://courses.csail.mit.edu/6.869/handouts/PAMIMeanshift.pdf
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if (x <= 1)
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return 1 - x;
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return 0;
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}
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/// <summary>
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/// Computes the derivative of the kernel profile function.
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/// </summary>
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///
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/// <param name="x">The point estimate <c>x</c>.</param>
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///
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/// <returns>
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/// The value of the derivative profile function at point <paramref name="x"/>.
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/// </returns>
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///
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public double Derivative(double x)
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{
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#if DEBUG
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if (x < 0)
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throw new Exception();
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#endif
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return -1;
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}
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}
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}
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