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.
327 lines
11 KiB
C#
327 lines
11 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 System;
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using Accord.Math;
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using Accord.Math.Distances;
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using Accord.Compat;
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/// <summary>
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/// Taylor approximation for the explicit Gaussian 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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/// Lin, Keng-Pei, and Ming-Syan Chen. "Efficient kernel approximation for large-scale support
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/// vector machine classification." Proceedings of the Eleventh SIAM International Conference on
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/// Data Mining. 2011. Available on: http://epubs.siam.org/doi/pdf/10.1137/1.9781611972818.19
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/// </description></item>
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/// </list></para>
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/// </remarks>
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///
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[Serializable]
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public struct TaylorGaussian : ITransform, ILinear, IReverseDistance, IDistance
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{
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Gaussian gaussian;
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Linear linear;
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double[] coefficients;
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/// <summary>
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/// Gets or sets the approximation degree
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/// for this kernel. Default is 1024.
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/// </summary>
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///
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public int Degree
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{
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get { return coefficients.Length; }
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set
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{
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if (value <= 0)
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throw new ArgumentOutOfRangeException("value", "Value must be higher than zero.");
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createCoefficients(value);
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}
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}
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/// <summary>
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/// Gets or sets the Gaussian kernel being
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/// approximated by this Taylor expansion.
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/// </summary>
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///
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public Gaussian Gaussian
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{
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get { return gaussian; }
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set { gaussian = value; }
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}
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/// <summary>
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/// Constructs a new <see cref="TaylorGaussian"/> kernel with the given sigma.
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/// </summary>
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///
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/// <param name="sigma">The kernel's sigma parameter.</param>
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/// <param name="degree">The Gaussian approximation degree. Default is 1024.</param>
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///
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public TaylorGaussian(double sigma, int degree = 1024)
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: this(new Gaussian(sigma), degree)
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{
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}
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/// <summary>
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/// Constructs a new <see cref="TaylorGaussian"/> kernel with the given sigma.
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/// </summary>
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///
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/// <param name="gaussian">The original Gaussian kernel to be approximated.</param>
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/// <param name="degree">The Gaussian approximation degree. Default is 1024.</param>
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///
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public TaylorGaussian(Gaussian gaussian, int degree = 1024)
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{
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this.gaussian = gaussian;
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this.coefficients = new double[degree];
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this.linear = new Linear();
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this.createCoefficients(degree);
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}
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/// <summary>
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/// Gaussian 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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///
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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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return linear.Function(x, Transform(y));
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}
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/// <summary>
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/// Projects an input point into feature space.
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/// </summary>
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///
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/// <param name="input">The input point to be projected into feature space.</param>
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///
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/// <returns>
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/// The feature space representation of the given <paramref name="input"/> point.
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/// </returns>
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///
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public double[] Transform(double[] input)
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{
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// http://epubs.siam.org/doi/pdf/10.1137/1.9781611972818.19
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double[] features = new double[coefficients.Length];
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features[0] = 1;
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for (int index = 1, k = 0; index < coefficients.Length; k++)
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{
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double alpha = coefficients[k];
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foreach (int[] s in Combinatorics.Sequences(input.Length, k + 1))
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{
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double prod = 1.0;
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for (int i = 0; i < s.Length; i++)
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prod *= input[s[i]];
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features[index++] = alpha * prod;
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if (index >= coefficients.Length)
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break;
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}
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}
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double norm = Norm.SquareEuclidean(input);
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double constant = Math.Exp(-gaussian.Gamma * norm);
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for (int i = 0; i < features.Length; i++)
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features[i] *= constant;
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return features;
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}
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/// <summary>
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/// Projects a set of input points into feature space.
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/// </summary>
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///
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/// <param name="inputs">The input points to be projected into feature space.</param>
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///
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/// <returns>
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/// The feature space representation of the given <paramref name="inputs"/> points.
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/// </returns>
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///
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public double[][] Transform(double[][] inputs)
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{
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double[][] r = new double[inputs.Length][];
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for (int i = 0; i < inputs.Length; i++)
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r[i] = Transform(inputs[i]);
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return r;
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}
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private void createCoefficients(int degree)
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{
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coefficients = new double[degree];
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for (int i = 0; i < coefficients.Length; i++)
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coefficients[i] = Math.Sqrt(Math.Pow(2 * gaussian.Gamma, i + 1) / Special.Factorial(i + 1));
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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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/// <returns>
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/// A new object that is a copy of this instance.
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/// </returns>
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public object Clone()
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{
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return new TaylorGaussian(gaussian, Degree);
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}
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/// <summary>
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/// Elementwise multiplication of scalar a and vector b, storing in result.
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/// </summary>
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///
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/// <param name="a">The scalar to be multiplied.</param>
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/// <param name="b">The vector to be multiplied.</param>
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/// <param name="result">An array to store the result.</param>
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///
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public void Product(double a, double[] b, double[] result)
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{
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linear.Product(a, Transform(b), result);
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}
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/// <summary>
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/// Compress a set of support vectors and weights into a single
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/// parameter vector.
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/// </summary>
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///
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/// <param name="weights">The weights associated with each support vector.</param>
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/// <param name="supportVectors">The support vectors.</param>
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/// <param name="c">The constant (bias) value.</param>
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///
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/// <returns>A single parameter vector.</returns>
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///
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public double[] Compress(double[] weights, double[][] supportVectors, out double c)
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{
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return linear.Compress(weights, supportVectors.Apply(Transform), out c);
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}
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/// <summary>
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/// Computes the squared distance in input space
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/// between two points given in feature space.
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/// </summary>
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/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
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/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
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/// <returns>
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/// Squared distance between <c>x</c> and <c>y</c> in input space.
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/// </returns>
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public double ReverseDistance(double[] x, double[] y)
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{
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return gaussian.ReverseDistance(x, y);
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}
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/// <summary>
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/// Computes the distance <c>d(x,y)</c> between points
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/// <paramref name="x" /> and <paramref name="y" />.
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/// </summary>
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/// <param name="x">The first point <c>x</c>.</param>
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/// <param name="y">The second point <c>y</c>.</param>
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/// <returns>
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/// A double-precision value representing the distance <c>d(x,y)</c>
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/// between <paramref name="x" /> and <paramref name="y" /> according
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/// to the distance function implemented by this class.
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/// </returns>
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public double Distance(double[] x, double[] y)
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{
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return linear.Distance(Transform(x), Transform(y));
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}
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/// <summary>
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/// Elementwise addition of a and b, storing in result.
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/// </summary>
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///
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/// <param name="a">The first vector to add.</param>
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/// <param name="b">The second vector to add.</param>
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/// <param name="result">An array to store the result.</param>
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/// <returns>The same vector passed as result.</returns>
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///
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public void Add(double[] a, double[] b, double[] result)
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{
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linear.Add(Transform(a), Transform(b), result);
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}
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/// <summary>
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/// Gets the number of parameters in the input vectors.
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/// </summary>
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///
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public int GetLength(double[][] inputs)
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{
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return coefficients.Length;
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}
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/// <summary>
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/// Creates an input vector from the given double values.
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/// </summary>
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///
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public double[] CreateVector(double[] values)
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{
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return Vector.Create(values);
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}
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///// <summary>
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///// Creates an input vector with the given dimensions.
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///// </summary>
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/////
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//public double[] CreateVector(int dimensions)
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//{
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// return new double[dimensions];
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//}
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/// <summary>
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/// Elementwise multiplication of vector a and vector b, accumulating in result.
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/// </summary>
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///
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/// <param name="a">The vector to be multiplied.</param>
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/// <param name="b">The vector to be multiplied.</param>
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/// <param name="accumulate">An array to store the result.</param>
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///
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public void Product(double[] a, double[] b, double[] accumulate)
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{
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for (int i = 0; i < a.Length; i++)
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accumulate[i] += a[i] * b[i];
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}
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/// <summary>
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/// Converts the input vectors to a double-precision representation.
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/// </summary>
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///
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public double[][] ToDouble(double[][] input)
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{
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return input;
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}
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}
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}
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