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.
267 lines
8.7 KiB
C#
267 lines
8.7 KiB
C#
// Accord Neural Net 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.Neuro.ActivationFunctions
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{
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using System;
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using AForge;
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using Accord.Neuro.Neurons;
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using Accord.Neuro.Networks;
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using Accord.Neuro.Learning;
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using Accord.Statistics.Distributions.Univariate;
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using Accord.Math.Random;
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using Accord.Math;
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using Accord.Compat;
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/// <summary>
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/// Gaussian stochastic activation function.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// The Gaussian activation function can be used to create <see cref="StochasticNeuron">
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/// Stochastic Neurons</see>, which can in turn be used to create <see cref="DeepBeliefNetwork">
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/// Deep Belief Networks</see> and <see cref="RestrictedBoltzmannMachine">Restricted Boltzmann
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/// Machines</see>. In contrast to the <see cref="BernoulliFunction"/>, the Gaussian can be used
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/// to model continuous inputs in Deep Belief Networks. If, however, the inputs of the problem
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/// being learned are discrete in nature, the use of a Bernoulli function would be more indicated.</para>
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///
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/// <para>
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/// The Gaussian activation function is modeled after a <see cref="NormalDistribution">
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/// Gaussian (Normal) probability distribution</see>.
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/// </para>
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///
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/// <para>
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/// This function assumes output variables have been
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/// normalized to have zero mean and unit variance.</para>
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a Gaussian function with slope alpha = 4.2
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/// GaussianFunction function = new GaussianFunction(4.2);
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///
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/// // Computes the function output (linear, y = alpha * x)
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/// double y = function.Function(x: 0.2); // 4.2 * 2 = 0.48
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///
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/// // Draws a sample from a Gaussian distribution with
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/// // mean given by the function output y (previously 0.48)
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/// double z = function.Generate(x: 0.4); // (random, between 0 and 1)
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///
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/// // Please note that the above is completely equivalent
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/// // to computing the line below (remember, 0.48 == y)
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/// double w = function.Generate2(y: 0.48); // (random, between 0 and 1)
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///
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///
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/// // We can also compute the derivative of the sigmoid function
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/// double d = function.Derivative(x: 0.2); // 4.2 (the slope)
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///
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/// // Or compute the derivative given the functions' output y
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/// double e = function.Derivative2(y: 0.2); // 4.2 (the slope)
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/// </code>
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/// </example>
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///
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/// <seealso cref="BernoulliFunction"/>
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/// <seealso cref="NormalDistribution"/>
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/// <seealso cref="DeepBeliefNetwork"/>
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///
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[Serializable]
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public class GaussianFunction : IStochasticFunction
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{
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// linear slope value
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private double alpha = 1;
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// function output range
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private DoubleRange range = new DoubleRange(-1, +1);
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/// <summary>
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/// Linear slope value.
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/// </summary>
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///
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/// <remarks>
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/// <para>Default value is set to <b>1</b>.</para>
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/// </remarks>
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///
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public double Alpha
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{
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get { return alpha; }
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set { alpha = value; }
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}
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/// <summary>
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/// Function output range.
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/// </summary>
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///
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/// <remarks>
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/// <para>Default value is set to [-1;+1]</para>
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/// </remarks>
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///
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public DoubleRange Range
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{
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get { return range; }
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set { range = value; }
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}
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/// <summary>
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/// Creates a new <see cref="GaussianFunction"/>.
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/// </summary>
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///
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/// <param name="alpha">The linear slope value. Default is 1.</param>
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///
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public GaussianFunction(double alpha)
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{
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this.alpha = alpha;
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}
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/// <summary>
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/// Creates a new <see cref="GaussianFunction"/>.
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/// </summary>
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///
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public GaussianFunction()
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: this(1.0) { }
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/// <summary>
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/// Initializes a new instance of the <see cref="GaussianFunction"/> class.
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/// </summary>
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///
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public GaussianFunction(double alpha, DoubleRange range)
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{
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this.Alpha = alpha;
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this.Range = range;
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}
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/// <summary>
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/// Calculates function value.
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/// </summary>
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///
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/// <param name="x">Function input value.</param>
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///
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/// <returns>Function output value, <i>f(x)</i>.</returns>
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///
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/// <remarks>The method calculates function value at point <paramref name="x"/>.</remarks>
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///
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public double Function(double x)
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{
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double y = alpha * x;
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if (y > range.Max)
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return range.Max;
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else if (y < range.Min)
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return range.Min;
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return y;
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}
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/// <summary>
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/// Samples a value from the function given a input value.
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/// </summary>
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///
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/// <param name="x">Function input value.</param>
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///
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/// <returns>
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/// Draws a random value from the function.
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/// </returns>
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///
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public double Generate(double x)
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{
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// assume zero-mean noise
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double y = alpha * x + NormalDistribution.Random();
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if (y > range.Max)
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y = range.Max;
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else if (y < range.Min)
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y = range.Min;
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return y;
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}
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/// <summary>
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/// Samples a value from the function given a function output value.
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/// </summary>
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///
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/// <param name="y">Function output value - the value, which was obtained
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/// with the help of <see cref="Function"/> method.</param>
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///
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/// <returns>
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/// Draws a random value from the function.
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/// </returns>
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///
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public double Generate2(double y)
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{
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y = y + NormalDistribution.Random();
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if (y > range.Max)
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y = range.Max;
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else if (y < range.Min)
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y = range.Min;
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return y;
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}
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/// <summary>
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/// Calculates function derivative.
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/// </summary>
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///
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/// <param name="x">Function input value.</param>
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///
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/// <returns>Function derivative, <i>f'(x)</i>.</returns>
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///
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/// <remarks>The method calculates function derivative at point <paramref name="x"/>.</remarks>
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///
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public double Derivative(double x)
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{
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double y = alpha * x;
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if (y <= range.Min || y >= range.Max)
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return 0;
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return alpha;
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}
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/// <summary>
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/// Calculates function derivative.
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/// </summary>
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///
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/// <param name="y">Function output value - the value, which was obtained
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/// with the help of <see cref="Function"/> method.</param>
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///
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/// <returns>Function derivative, <i>f'(x)</i>.</returns>
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///
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/// <remarks><para>The method calculates the same derivative value as the
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/// <see cref="Derivative"/> method, but it takes not the input <b>x</b> value
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/// itself, but the function value, which was calculated previously with
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/// the help of <see cref="Function"/> method.</para>
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///
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/// <para><note>Some applications require as function value, as derivative value,
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/// so they can save the amount of calculations using this method to calculate derivative.</note></para>
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/// </remarks>
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///
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public double Derivative2(double y)
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{
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if (y <= range.Min || y >= range.Max)
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return 0;
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return alpha;
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}
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}
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}
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