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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.
208 lines
7.1 KiB
C#
208 lines
7.1 KiB
C#
// Accord Math 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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// Copyright © Antonino Porcino, 2010
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// nino.porcino at yahoo.it
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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.Math.Decompositions
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{
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using System;
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/// <summary>
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/// Nonnegative Matrix Factorization.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// Non-negative matrix factorization (NMF) is a group of algorithms in multivariate
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/// analysis and linear algebra where a matrix <c>X</c> is factorized into (usually)
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/// two matrices, <c>W</c> and <c>H</c>. The non-negative factorization enforces the
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/// constraint that the factors <c>W</c> and <c>H</c> must be non-negative, i.e., all
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/// elements must be equal to or greater than zero. The factorization is not unique.</para>
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///
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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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/// <a href="http://en.wikipedia.org/wiki/Non-negative_matrix_factorization">
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/// http://en.wikipedia.org/wiki/Non-negative_matrix_factorization </a>
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/// </description></item>
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/// <item><description>
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/// Lee, D., Seung, H., 1999. Learning the Parts of Objects by Non-Negative
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/// Matrix Factorization. Nature 401, 788–791. </description></item>
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/// <item><description>
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/// Michael W. Berry, et al. (June 2006). Algorithms and Applications for
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/// Approximate Nonnegative Matrix Factorization. </description></item>
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/// </list>
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/// </para>
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/// </remarks>
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///
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public class NonnegativeMatrixFactorization
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{
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private double[,] X; // X is m x n (input data, must be positive)
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private double[,] W; // W is m x r (weights)
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private double[,] H; // H is r x n (transformed data) (transposed)
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private int n; // number of input data vectors
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private int m; // dimension of input vector
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private int r; // dimension of output vector (reduced dimension)
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/// <summary>
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/// Gets the nonnegative factor matrix W.
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/// </summary>
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///
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public double[,] LeftNonnegativeFactors
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{
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get { return W; }
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}
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/// <summary>
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/// Gets the nonnegative factor matrix H.
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/// </summary>
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///
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public double[,] RightNonnegativeFactors
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{
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get { return H; }
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}
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/// <summary>
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/// Initializes a new instance of the NMF algorithm
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/// </summary>
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///
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/// <param name="value">The input data matrix (must be positive).</param>
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/// <param name="r">The reduced dimension.</param>
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///
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public NonnegativeMatrixFactorization(double[,] value, int r)
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: this(value, r, 100) { }
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/// <summary>
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/// Initializes a new instance of the NMF algorithm
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/// </summary>
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///
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/// <param name="value">The input data matrix (must be positive).</param>
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/// <param name="r">The reduced dimension.</param>
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/// <param name="maxiter">The number of iterations to perform.</param>
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///
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public NonnegativeMatrixFactorization(double[,] value, int r, int maxiter)
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{
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this.X = value;
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this.n = value.GetLength(0);
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this.m = value.GetLength(1);
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this.r = r;
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compute(maxiter);
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}
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/// <summary>
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/// Performs NMF using the multiplicative method
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/// </summary>
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///
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/// <param name="maxiter">The maximum number of iterations</param>
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///
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/// <remarks>
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/// At the end of the computation H contains the projected data
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/// and W contains the weights. The multiplicative method is the
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/// simplest factorization method.
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/// </remarks>
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///
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private void compute(int maxiter)
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{
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// chose W and H randomly, W with unit norm
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W = Accord.Math.Matrix.Random(m, r);
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H = Accord.Math.Matrix.Random(r, n);
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var Z = new double[r, r];
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// a small epsilon is added to the
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// denominator to avoid overflow.
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double eps = 10e-9;
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for (int t = 0; t < maxiter; t++)
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{
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var newW = new double[m, r];
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var newH = new double[r, n];
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// Update H using the multiplicative
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// H = H .* (W'*A) ./ (W'*W*H + eps)
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for (int i = 0; i < r; i++)
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{
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for (int j = i; j < r; j++)
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{
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double s = 0.0;
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for (int l = 0; l < m; l++)
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s += W[l, i] * W[l, j];
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Z[i, j] = Z[j, i] = s;
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}
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for (int j = 0; j < n; j++)
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{
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double d = 0.0;
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for (int l = 0; l < r; l++)
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d += Z[i, l] * H[l, j];
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double s = 0.0;
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for (int l = 0; l < m; l++)
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s += W[l, i] * X[j, l];
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newH[i, j] = H[i, j] * s / (d + eps);
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}
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}
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// Update W using the multiplicative
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// W = W .* (A*H') ./ (W*H*H' + eps)
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for (int j = 0; j < r; j++)
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{
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for (int i = j; i < r; i++)
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{
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double s = 0.0;
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for (int l = 0; l < n; l++)
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s += newH[i, l] * newH[j, l];
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Z[i, j] = Z[j, i] = s;
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}
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for (int i = 0; i < m; i++)
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{
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double d = 0.0;
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for (int l = 0; l < r; l++)
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d += W[i, l] * Z[j, l];
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double s = 0.0;
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for (int l = 0; l < n; l++)
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s += X[l, i] * newH[j, l];
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newW[i, j] = W[i, j] * s / (d + eps);
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}
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}
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W = newW;
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H = newH;
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}
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}
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}
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}
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