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.
441 lines
17 KiB
C#
441 lines
17 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 Accord.Math;
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using Accord.Math.Distances;
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using System;
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using Accord.Compat;
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using System.Threading.Tasks;
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/// <summary>
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/// Extension methods for <see cref="IKernel">kernel functions</see>.
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/// </summary>
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///
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public static class Kernel
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{
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/// <summary>
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/// Creates the Gram matrix from the given vectors.
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/// </summary>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="x">The vectors.</param>
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///
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/// <param name="result">An optional matrix where the result should be stored in.</param>
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///
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/// <returns>A symmetric matrix containing the dot-products in
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/// feature (kernel) space between all vectors in <paramref name="x"/>.</returns>
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///
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public static double[,] ToMatrix<TKernel, TInput>(this TKernel kernel, TInput[] x, double[,] result = null)
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where TKernel : IKernel<TInput>
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{
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if (result == null)
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result = new double[x.Length, x.Length];
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for (int i = 0; i < x.Length; i++)
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for (int j = i; j < x.Length; j++)
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result[j, i] = result[i, j] = kernel.Function(x[i], x[j]);
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return result;
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}
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/// <summary>
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/// Creates the Gram matrix containing all dot products in feature
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/// (kernel) space between each vector in <paramref name="x">x</paramref>
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/// and the ones in <paramref name="y">y</paramref>.
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/// </summary>
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///
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/// <param name="x">The first vectors.</param>
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/// <param name="y">The second vectors.</param>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="result">An optional matrix where the result should be stored in.</param>
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///
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/// <returns>A symmetric matrix containing the dot-products in
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/// feature (kernel) space between each vector in <paramref name="x"/>
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/// and the ones in <paramref name="y"/>.</returns>
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///
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public static double[,] ToMatrix2<TKernel, TInput>(this TKernel kernel, TInput[] x, TInput[] y, double[,] result = null)
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where TKernel : IKernel<TInput>
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{
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if (result == null)
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result = new double[x.Length, y.Length];
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for (int i = 0; i < x.Length; i++)
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for (int j = 0; j < y.Length; j++)
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result[i, j] = kernel.Function(x[i], y[j]);
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return result;
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}
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/// <summary>
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/// Creates the Gram matrix from the given vectors.
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/// </summary>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="x">The vectors.</param>
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///
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/// <param name="result">An optional matrix where the result should be stored in.</param>
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///
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/// <returns>A symmetric matrix containing the dot-products in
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/// feature (kernel) space between all vectors in <paramref name="x"/>.</returns>
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///
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public static double[][] ToJagged<TKernel, TInput>(this TKernel kernel, TInput[] x, double[][] result = null)
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where TKernel : IKernel<TInput>
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{
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if (result == null)
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result = Jagged.Create<double>(x.Length, x.Length);
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for (int i = 0; i < x.Length; i++)
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for (int j = i; j < x.Length; j++)
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result[j][i] = result[i][j] = kernel.Function(x[i], x[j]);
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return result;
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}
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/// <summary>
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/// Creates the Gram matrix containing all dot products in feature
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/// (kernel) space between each vector in <paramref name="x">x</paramref>
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/// and the ones in <paramref name="y">y</paramref>.
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/// </summary>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="x">The first vectors.</param>
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/// <param name="y">The second vectors.</param>
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///
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/// <param name="result">An optional matrix where the result should be stored in.</param>
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///
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/// <returns>A symmetric matrix containing the dot-products in
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/// feature (kernel) space between each vector in <paramref name="x"/>
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/// and the ones in <paramref name="y"/>.</returns>
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///
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public static double[][] ToJagged2<TKernel, TInput>(this TKernel kernel, TInput[] x, TInput[] y, double[][] result = null)
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where TKernel : IKernel<TInput>
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{
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if (result == null)
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result = Jagged.Create<double>(x.Length, y.Length);
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for (int i = 0; i < x.Length; i++)
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for (int j = 0; j < y.Length; j++)
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result[i][j] = kernel.Function(x[i], y[j]);
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return result;
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}
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/// <summary>
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/// Estimates the complexity parameter C, present in many SVM algorithms,
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/// for a given kernel and a given data set by summing every element
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/// on the diagonal of the kernel matrix and using an heuristic based
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/// on it.
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/// </summary>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="inputs">The input samples.</param>
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///
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/// <returns>A suitable value for C.</returns>
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///
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public static double EstimateComplexity<TKernel, TInput>(this TKernel kernel, TInput[] inputs)
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where TKernel : IKernel<TInput>
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{
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// Compute initial value for C as the number of examples
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// divided by the trace of the input sample kernel matrix.
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double sum = 0.0;
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for (int i = 0; i < inputs.Length; i++)
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{
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sum += kernel.Function(inputs[i], inputs[i]);
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if (Double.IsNaN(sum))
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throw new OverflowException();
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}
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return inputs.Length / sum;
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}
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/// <summary>
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/// Estimates the complexity parameter C, present in many SVM algorithms,
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/// for a given kernel and an unbalanced data set by summing every element
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/// on the diagonal of the kernel matrix and using an heuristic based on it.
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/// </summary>
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///
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/// <param name="kernel">The kernel function.</param>
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/// <param name="inputs">The input samples.</param>
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/// <param name="outputs">The output samples.</param>
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///
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/// <returns>A suitable value for positive C and negative C, respectively.</returns>
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///
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public static Tuple<double, double> EstimateComplexity<TKernel, TInput>(this TKernel kernel, TInput[] inputs, int[] outputs)
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where TKernel : IKernel<TInput>
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{
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// Compute initial value for C as the number of examples
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// divided by the trace of the input sample kernel matrix.
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double negativeSum = 0.0;
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double positiveSum = 0.0;
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int negativeCount = 0;
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int positiveCount = 0;
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for (int i = 0; i < inputs.Length; i++)
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{
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if (outputs[i] == -1)
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{
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negativeSum += kernel.Function(inputs[i], inputs[i]);
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negativeCount++;
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}
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else // outputs[i] == +1
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{
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positiveSum += kernel.Function(inputs[i], inputs[i]);
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positiveCount++;
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}
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if (Double.IsNaN(positiveSum) || Double.IsNaN(negativeSum))
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throw new OverflowException();
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}
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return Tuple.Create
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(
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positiveCount / positiveSum,
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negativeCount / negativeSum
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);
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}
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/// <summary>
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/// Estimates the complexity parameter C, present in many SVM algorithms,
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/// for a given kernel and a given data set by summing every element
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/// on the diagonal of the kernel matrix and using an heuristic based
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/// on it.
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/// </summary>
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///
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/// <param name="inputs">The input samples.</param>
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///
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/// <returns>A suitable value for C.</returns>
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///
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public static double EstimateComplexity(double[][] inputs)
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{
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return EstimateComplexity(new Linear(), inputs);
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}
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/// <summary>
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/// Estimates the complexity parameter C, present in many SVM algorithms,
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/// for a given kernel and an unbalanced data set by summing every element
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/// on the diagonal of the kernel matrix and using an heuristic based on it.
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/// </summary>
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///
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/// <param name="inputs">The input samples.</param>
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/// <param name="outputs">The output samples.</param>
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///
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/// <returns>A suitable value for positive C and negative C, respectively.</returns>
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///
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public static Tuple<double, double> EstimateComplexity(double[][] inputs, int[] outputs)
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{
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return EstimateComplexity(new Linear(), inputs, outputs);
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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="kernel">The inner kernel.</param>
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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[] Distances<T>(this T kernel, double[][] inputs, int samples)
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where T : IDistance<double[]>, ICloneable
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{
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int[] idx = Vector.Sample(samples, inputs.Length);
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int[] idy = Vector.Sample(samples, inputs.Length);
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double[] distances = 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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distances[i * samples + j] = kernel.Distance(x, y);
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}
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}
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Array.Sort(distances);
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return distances;
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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="kernel">The inner kernel.</param>
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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[] Distances<TKernel, TData>(this TKernel kernel, TData[] inputs, int samples)
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where TKernel : IDistance<TData>, ICloneable
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{
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int[] idx = Vector.Sample(samples, inputs.Length);
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int[] idy = Vector.Sample(samples, inputs.Length);
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double[] distances = new double[samples * samples];
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for (int i = 0; i < idx.Length; i++)
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{
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TData x = inputs[idx[i]];
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for (int j = 0; j < idy.Length; j++)
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{
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TData y = inputs[idy[j]];
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distances[i * samples + j] = kernel.Distance(x, y);
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}
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}
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Array.Sort(distances);
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return distances;
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}
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/// <summary>
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/// Centers the given kernel matrix K.
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/// </summary>
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///
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/// <param name="kernelMatrix">The kernel matrix to be centered.</param>
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/// <param name="result">The array where to store results.</param>
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///
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public static double[,] Center(double[,] kernelMatrix, double[,] result = null)
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{
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if (result == null)
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result = Matrix.CreateAs(kernelMatrix);
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double[] rowMean = kernelMatrix.Mean(dimension: 1);
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#if DEBUG
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// row mean and column means should be equal on a symmetric matrix
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double[] colMean = kernelMatrix.Mean(dimension: 0);
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for (int i = 0; i < colMean.Length; i++)
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Accord.Diagnostics.Debug.Assert(colMean[i] == rowMean[i]);
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#endif
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double mean = kernelMatrix.Mean();
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for (int i = 0; i < rowMean.Length; i++)
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for (int j = i; j < rowMean.Length; j++)
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result[i, j] = result[j, i] = kernelMatrix[i, j] - rowMean[i] - rowMean[j] + mean;
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return result;
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}
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/// <summary>
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/// Centers the given kernel matrix K.
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/// </summary>
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///
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/// <param name="kernelMatrix">The kernel matrix to be centered.</param>
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/// <param name="rowMean">The row-wise mean vector.</param>
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/// <param name="mean">The total mean (across all values in the matrix).</param>
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/// <param name="result">The array where to store results.</param>
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///
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public static double[][] Center(double[][] kernelMatrix, out double[] rowMean, out double mean, double[][] result = null)
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{
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if (result == null)
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result = Jagged.CreateAs(kernelMatrix);
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rowMean = kernelMatrix.Mean(dimension: 1);
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#if DEBUG
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// row mean and column means should be equal on a symmetric matrix
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double[] colMean = kernelMatrix.Mean(dimension: 0);
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for (int i = 0; i < colMean.Length; i++)
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Accord.Diagnostics.Debug.Assert(colMean[i] == rowMean[i]);
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#endif
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mean = kernelMatrix.Mean(); // TODO: This should become simply mean = K.Mean()
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for (int i = 0; i < rowMean.Length; i++)
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for (int j = i; j < rowMean.Length; j++)
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result[i][j] = result[j][i] = kernelMatrix[i][j] - rowMean[i] - rowMean[j] + mean;
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return result;
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}
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/// <summary>
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/// Centers the given kernel matrix K.
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/// </summary>
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///
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/// <param name="kernelMatrix">The kernel matrix to be centered.</param>
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/// <param name="rowMean">The row-wise mean vector.</param>
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/// <param name="mean">The total mean (across all values in the matrix).</param>
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/// <param name="result">The array where to store results.</param>
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///
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public static double[,] Center(double[,] kernelMatrix, double[] rowMean, double mean, double[,] result = null)
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{
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if (result == null)
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result = Matrix.CreateAs(kernelMatrix);
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int rows = kernelMatrix.Rows();
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int cols = kernelMatrix.Columns();
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double[] rowMean1 = kernelMatrix.Mean(1);
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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result[i, j] = kernelMatrix[i, j] - rowMean1[i] - rowMean[j] + mean;
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return result;
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}
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/// <summary>
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/// Centers the given kernel matrix K.
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/// </summary>
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///
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/// <param name="kernelMatrix">The kernel matrix to be centered.</param>
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/// <param name="rowMean">The row-wise mean vector.</param>
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/// <param name="mean">The total mean (across all values in the matrix).</param>
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/// <param name="result">The array where to store results.</param>
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///
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public static double[][] Center(double[][] kernelMatrix, double[] rowMean, double mean, double[][] result = null)
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{
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if (result == null)
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result = Jagged.CreateAs(kernelMatrix);
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#if DEBUG
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double[,] r = Center(kernelMatrix.ToMatrix(), rowMean, mean);
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#endif
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//int cols = kernelMatrix.Columns();
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double[] rowMean1 = kernelMatrix.Mean(1);
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for (int i = 0; i < result.Length; i++)
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for (int j = 0; j < kernelMatrix[i].Length; j++)
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result[i][j] = kernelMatrix[i][j] - rowMean1[i] - rowMean[j] + mean;
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#if DEBUG
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if (!r.IsEqual(result, 1e-8))
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throw new Exception();
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#endif
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return result;
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}
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}
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}
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