mirror of
https://github.com/hanzoai/jube-fork.git
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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.
278 lines
8.8 KiB
C#
278 lines
8.8 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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/// Sigmoid Kernel.
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/// </summary>
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///
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/// <remarks>
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/// Sigmoid kernel of the form k(x,z) = tanh(a * x'z + c). Sigmoid kernels are only
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/// conditionally positive definite for some values of a and c, and therefore may not
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/// induce a reproducing kernel Hilbert space. However, they have been successfully
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/// used in practice (Schölkopf and Smola, 2002).
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/// </remarks>
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///
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[Serializable]
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public sealed class Sigmoid : KernelBase, IKernel, ICloneable, IEstimable,
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IKernel<Sparse<double>>, IDistance<Sparse<double>>
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{
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private double alpha;
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private double constant;
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/// <summary>
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/// Estimates suitable values for the sigmoid kernel
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/// by exploring the response area of the tanh function.
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/// </summary>
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///
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/// <param name="inputs">An input data set.</param>
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///
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/// <returns>A Sigmoid kernel initialized with appropriate values.</returns>
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///
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public static Sigmoid Estimate(double[][] inputs)
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{
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double[] norm = new double[inputs.Length];
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for (int i = 0; i < inputs.Length; i++)
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norm[i] = Norm.SquareEuclidean(inputs[i]);
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double max = Matrix.Max(norm);
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double r = -Math.E;
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double a = -r / max;
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return new Sigmoid(a, r);
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}
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/// <summary>
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/// Estimates suitable values for the sigmoid kernel
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/// by exploring the response area of the tanh function.
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/// </summary>
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///
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/// <param name="inputs">An input data set.</param>
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/// <param name="samples">The size of the subset to use in the estimation.</param>
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/// <param name="range">The interquartile range for the data.</param>
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///
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/// <returns>A Sigmoid kernel initialized with appropriate values.</returns>
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///
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public static Sigmoid Estimate(double[][] inputs, int samples, out DoubleRange range)
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{
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if (samples > inputs.Length)
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throw new ArgumentOutOfRangeException("samples");
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double[] distances = Products(inputs, samples);
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double q1 = Math.Sqrt(distances[(int)Math.Ceiling(0.15 * distances.Length)] / 2.0);
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double q9 = Math.Sqrt(distances[(int)Math.Ceiling(0.85 * distances.Length)] / 2.0);
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double qm = Math.Sqrt(distances.Median(alreadySorted: true) / 2.0);
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range = new DoubleRange(q1, q9);
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double max = qm;
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double r = -Math.E;
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double a = -r / max;
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return new Sigmoid(a, r);
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}
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/// <summary>
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/// Computes the set of all distances between
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/// all points in a random subset of the data.
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/// </summary>
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///
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/// <param name="inputs">The inputs points.</param>
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/// <param name="samples">The number of samples.</param>
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///
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public static double[] Products(double[][] inputs, int samples)
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{
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int[] idx = Vector.Sample(inputs.Length, samples);
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int[] idy = Vector.Sample(inputs.Length, samples);
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double[] products = new double[samples * samples];
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for (int i = 0; i < idx.Length; i++)
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{
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double[] x = inputs[idx[i]];
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for (int j = 0; j < idy.Length; j++)
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{
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double[] y = inputs[idy[j]];
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double sum = 0;
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for (int k = 0; k < x.Length; k++)
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sum = x[k] * y[k];
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products[i * samples + j] = sum;
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}
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}
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Array.Sort(products);
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return products;
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}
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/// <summary>
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/// Constructs a Sigmoid kernel.
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/// </summary>
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///
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public Sigmoid()
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: this(0.01, -Math.E) { }
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/// <summary>
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/// Constructs a Sigmoid kernel.
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/// </summary>
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///
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/// <param name="alpha">
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/// Alpha parameter. Typically should be set to
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/// a small positive value. Default is 0.01.</param>
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/// <param name="constant">
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/// Constant parameter. Typically should be set to
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/// a negative value. Default is -e (Euler's constant).</param>
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///
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public Sigmoid(double alpha, double constant)
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{
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this.alpha = alpha;
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this.constant = constant;
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}
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/// <summary>
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/// Gets or sets the kernel's alpha parameter.
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/// </summary>
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///
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/// <remarks>
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/// In a sigmoid kernel, alpha is a inner product
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/// coefficient for the hyperbolic tangent function.
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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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/// Gets or sets the kernel's constant term.
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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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/// Sigmoid 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 override double Function(double[] x, double[] y)
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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] * y[i];
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double value = Math.Tanh(alpha * sum + constant);
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return value;
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}
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/// <summary>
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/// Sigmoid 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(Sparse<double> x, Sparse<double> y)
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{
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double sum = x.Dot(y);
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double value = Math.Tanh(alpha * sum + constant);
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return value;
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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(Sparse<double> x, Sparse<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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/// Sigmoid kernel function.
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/// </summary>
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///
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/// <param name="z">Distance <c>z</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 z)
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{
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return Math.Tanh(alpha * z + constant);
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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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void IEstimable<double[]>.Estimate(double[][] inputs)
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{
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var s = Estimate(inputs);
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this.Alpha = s.Alpha;
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this.Constant = s.Constant;
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}
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}
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}
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