[14414] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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| 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 |
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| 21 | //Code is based on an implementation from Laurens van der Maaten
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| 22 |
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| 23 | /*
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| 24 | *
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| 25 | * Copyright (c) 2014, Laurens van der Maaten (Delft University of Technology)
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| 26 | * All rights reserved.
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| 27 | *
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| 28 | * Redistribution and use in source and binary forms, with or without
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| 29 | * modification, are permitted provided that the following conditions are met:
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| 30 | * 1. Redistributions of source code must retain the above copyright
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| 31 | * notice, this list of conditions and the following disclaimer.
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| 32 | * 2. Redistributions in binary form must reproduce the above copyright
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| 33 | * notice, this list of conditions and the following disclaimer in the
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| 34 | * documentation and/or other materials provided with the distribution.
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| 35 | * 3. All advertising materials mentioning features or use of this software
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| 36 | * must display the following acknowledgement:
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| 37 | * This product includes software developed by the Delft University of Technology.
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| 38 | * 4. Neither the name of the Delft University of Technology nor the names of
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| 39 | * its contributors may be used to endorse or promote products derived from
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| 40 | * this software without specific prior written permission.
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| 41 | *
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| 42 | * THIS SOFTWARE IS PROVIDED BY LAURENS VAN DER MAATEN ''AS IS'' AND ANY EXPRESS
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| 43 | * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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| 44 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
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| 45 | * EVENT SHALL LAURENS VAN DER MAATEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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| 46 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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| 47 | * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
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| 48 | * BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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| 49 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
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| 50 | * IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
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| 51 | * OF SUCH DAMAGE.
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| 52 | *
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| 53 | */
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| 54 | #endregion
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| 55 |
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| 56 | using System;
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| 57 | using System.Collections.Generic;
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| 58 | using System.Linq;
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[14785] | 59 | using HeuristicLab.Collections;
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[14414] | 60 | using HeuristicLab.Common;
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| 61 | using HeuristicLab.Core;
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| 62 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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| 63 | using HeuristicLab.Random;
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| 64 |
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| 65 | namespace HeuristicLab.Algorithms.DataAnalysis {
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| 66 | [StorableClass]
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[14788] | 67 | public class TSNE<T> {
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[14414] | 68 |
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[14788] | 69 | [StorableClass]
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| 70 | public sealed class TSNEState : DeepCloneable {
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| 71 | // initialized once
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| 72 | public IDistance<T> distance;
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| 73 | public IRandom random;
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| 74 | public double perplexity;
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| 75 | public bool exact;
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| 76 | public int noDatapoints;
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| 77 | public double finalMomentum;
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| 78 | public int momSwitchIter;
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| 79 | public int stopLyingIter;
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| 80 | public double theta;
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| 81 | public double eta;
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| 82 | public int newDimensions;
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[14414] | 83 |
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[14788] | 84 | // for approximate version: sparse representation of similarity/distance matrix
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| 85 | public double[] valP; // similarity/distance
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| 86 | public int[] rowP; // row index
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| 87 | public int[] colP; // col index
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[14414] | 88 |
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[14788] | 89 | // for exact version: dense representation of distance/similarity matrix
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| 90 | public double[,] p;
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[14512] | 91 |
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[14788] | 92 | // mapped data
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| 93 | public double[,] newData;
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[14414] | 94 |
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[14788] | 95 | public int iter;
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| 96 | public double currentMomentum;
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[14414] | 97 |
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[14788] | 98 | // helper variables (updated in each iteration)
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| 99 | public double[,] gains;
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| 100 | public double[,] uY;
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| 101 | public double[,] dY;
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[14512] | 102 |
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[14788] | 103 | private TSNEState(TSNEState original, Cloner cloner) : base(original, cloner) {
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| 104 | }
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| 105 | public override IDeepCloneable Clone(Cloner cloner) {
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| 106 | return new TSNEState(this, cloner);
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| 107 | }
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[14414] | 108 |
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[14788] | 109 | public TSNEState(T[] data, IDistance<T> distance, IRandom random, int newDimensions, double perplexity, double theta, int stopLyingIter, int momSwitchIter, double momentum, double finalMomentum, double eta) {
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| 110 | this.distance = distance;
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| 111 | this.random = random;
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| 112 | this.newDimensions = newDimensions;
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| 113 | this.perplexity = perplexity;
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| 114 | this.theta = theta;
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| 115 | this.stopLyingIter = stopLyingIter;
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| 116 | this.momSwitchIter = momSwitchIter;
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| 117 | this.currentMomentum = momentum;
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| 118 | this.finalMomentum = finalMomentum;
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| 119 | this.eta = eta;
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[14414] | 120 |
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| 121 |
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[14788] | 122 | // initialize
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| 123 | noDatapoints = data.Length;
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| 124 | if (noDatapoints - 1 < 3 * perplexity) throw new ArgumentException("Perplexity too large for the number of data points!");
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| 125 |
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| 126 | exact = Math.Abs(theta) < double.Epsilon;
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| 127 | newData = new double[noDatapoints, newDimensions];
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| 128 | dY = new double[noDatapoints, newDimensions];
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| 129 | uY = new double[noDatapoints, newDimensions];
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| 130 | gains = new double[noDatapoints, newDimensions];
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| 131 | for (var i = 0; i < noDatapoints; i++)
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| 132 | for (var j = 0; j < newDimensions; j++)
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| 133 | gains[i, j] = 1.0;
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| 134 |
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| 135 | p = null;
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| 136 | rowP = null;
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| 137 | colP = null;
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| 138 | valP = null;
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| 139 |
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| 140 | //Calculate Similarities
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| 141 | if (exact) p = CalculateExactSimilarites(data, distance, perplexity);
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| 142 | else CalculateApproximateSimilarities(data, distance, perplexity, out rowP, out colP, out valP);
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| 143 |
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| 144 | // Lie about the P-values
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| 145 | if (exact) for (var i = 0; i < noDatapoints; i++) for (var j = 0; j < noDatapoints; j++) p[i, j] *= 12.0;
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| 146 | else for (var i = 0; i < rowP[noDatapoints]; i++) valP[i] *= 12.0;
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| 147 |
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| 148 | // Initialize solution (randomly)
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| 149 | var rand = new NormalDistributedRandom(random, 0, 1);
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| 150 | for (var i = 0; i < noDatapoints; i++)
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| 151 | for (var j = 0; j < newDimensions; j++)
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| 152 | newData[i, j] = rand.NextDouble() * .0001; // TODO const
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[14414] | 153 | }
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| 154 |
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[14788] | 155 | public double EvaluateError() {
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| 156 | return exact ? EvaluateErrorExact(p, newData, noDatapoints, newDimensions) : EvaluateErrorApproximate(rowP, colP, valP, newData, theta);
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| 157 | }
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[14512] | 158 |
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[14788] | 159 | private static void CalculateApproximateSimilarities(T[] data, IDistance<T> distance, double perplexity, out int[] rowP, out int[] colP, out double[] valP) {
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| 160 | // Compute asymmetric pairwise input similarities
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| 161 | ComputeGaussianPerplexity(data, distance, out rowP, out colP, out valP, perplexity, (int)(3 * perplexity)); // TODO: why 3?
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| 162 | // Symmetrize input similarities
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| 163 | int[] sRowP, symColP;
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| 164 | double[] sValP;
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| 165 | SymmetrizeMatrix(rowP, colP, valP, out sRowP, out symColP, out sValP);
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| 166 | rowP = sRowP;
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| 167 | colP = symColP;
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| 168 | valP = sValP;
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| 169 | var sumP = .0;
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| 170 | for (var i = 0; i < rowP[data.Length]; i++) sumP += valP[i];
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| 171 | for (var i = 0; i < rowP[data.Length]; i++) valP[i] /= sumP;
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| 172 | }
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| 173 | private static double[,] CalculateExactSimilarites(T[] data, IDistance<T> distance, double perplexity) {
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| 174 | // Compute similarities
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| 175 | var p = new double[data.Length, data.Length];
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| 176 | ComputeGaussianPerplexity(data, distance, p, perplexity);
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| 177 | // Symmetrize input similarities
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| 178 | for (var n = 0; n < data.Length; n++) {
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| 179 | for (var m = n + 1; m < data.Length; m++) {
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| 180 | p[n, m] += p[m, n];
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| 181 | p[m, n] = p[n, m];
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| 182 | }
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| 183 | }
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| 184 | var sumP = .0;
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| 185 | for (var i = 0; i < data.Length; i++) for (var j = 0; j < data.Length; j++) sumP += p[i, j];
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| 186 | for (var i = 0; i < data.Length; i++) for (var j = 0; j < data.Length; j++) p[i, j] /= sumP;
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| 187 | return p;
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| 188 | }
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[14742] | 189 |
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[14788] | 190 | private static void ComputeGaussianPerplexity(IReadOnlyList<T> x, IDistance<T> distance, out int[] rowP, out int[] colP, out double[] valP, double perplexity, int k) {
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| 191 | if (perplexity > k) throw new ArgumentException("Perplexity should be lower than k!");
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[14512] | 192 |
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[14788] | 193 | int n = x.Count;
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| 194 | // Allocate the memory we need
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| 195 | rowP = new int[n + 1];
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| 196 | colP = new int[n * k];
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| 197 | valP = new double[n * k];
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| 198 | var curP = new double[n - 1];
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| 199 | rowP[0] = 0;
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| 200 | for (var i = 0; i < n; i++) rowP[i + 1] = rowP[i] + k;
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[14512] | 201 |
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[14788] | 202 | var objX = new List<IndexedItem<T>>();
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| 203 | for (var i = 0; i < n; i++) objX.Add(new IndexedItem<T>(i, x[i]));
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[14512] | 204 |
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[14788] | 205 | // Build ball tree on data set
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| 206 | var tree = new VantagePointTree<IndexedItem<T>>(new IndexedItemDistance<T>(distance), objX); // do we really want to re-create the tree on each call?
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[14742] | 207 |
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[14788] | 208 | // Loop over all points to find nearest neighbors
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| 209 | for (var i = 0; i < n; i++) {
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| 210 | IList<IndexedItem<T>> indices;
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| 211 | IList<double> distances;
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[14742] | 212 |
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[14788] | 213 | // Find nearest neighbors
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| 214 | tree.Search(objX[i], k + 1, out indices, out distances);
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[14512] | 215 |
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[14788] | 216 | // Initialize some variables for binary search
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| 217 | var found = false;
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| 218 | var beta = 1.0;
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| 219 | var minBeta = double.MinValue;
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| 220 | var maxBeta = double.MaxValue;
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| 221 | const double tol = 1e-5; // TODO: why 1e-5?
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[14512] | 222 |
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[14788] | 223 | // Iterate until we found a good perplexity
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| 224 | var iter = 0; double sumP = 0;
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| 225 | while (!found && iter < 200) {
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[14512] | 226 |
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[14788] | 227 | // Compute Gaussian kernel row
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| 228 | for (var m = 0; m < k; m++) curP[m] = Math.Exp(-beta * distances[m + 1]);
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[14512] | 229 |
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[14788] | 230 | // Compute entropy of current row
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| 231 | sumP = double.Epsilon;
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| 232 | for (var m = 0; m < k; m++) sumP += curP[m];
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| 233 | var h = .0;
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| 234 | for (var m = 0; m < k; m++) h += beta * (distances[m + 1] * curP[m]);
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| 235 | h = h / sumP + Math.Log(sumP);
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| 236 |
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| 237 | // Evaluate whether the entropy is within the tolerance level
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| 238 | var hdiff = h - Math.Log(perplexity);
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| 239 | if (hdiff < tol && -hdiff < tol) {
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| 240 | found = true;
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| 241 | } else {
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| 242 | if (hdiff > 0) {
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| 243 | minBeta = beta;
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| 244 | if (maxBeta.IsAlmost(double.MaxValue) || maxBeta.IsAlmost(double.MinValue))
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| 245 | beta *= 2.0;
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| 246 | else
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| 247 | beta = (beta + maxBeta) / 2.0;
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| 248 | } else {
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| 249 | maxBeta = beta;
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| 250 | if (minBeta.IsAlmost(double.MinValue) || minBeta.IsAlmost(double.MaxValue))
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| 251 | beta /= 2.0;
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| 252 | else
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| 253 | beta = (beta + minBeta) / 2.0;
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| 254 | }
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| 255 | }
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| 256 |
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| 257 | // Update iteration counter
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| 258 | iter++;
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| 259 | }
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| 260 |
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| 261 | // Row-normalize current row of P and store in matrix
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| 262 | for (var m = 0; m < k; m++) curP[m] /= sumP;
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| 263 | for (var m = 0; m < k; m++) {
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| 264 | colP[rowP[i] + m] = indices[m + 1].Index;
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| 265 | valP[rowP[i] + m] = curP[m];
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| 266 | }
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[14512] | 267 | }
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| 268 | }
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[14788] | 269 | private static void ComputeGaussianPerplexity(T[] x, IDistance<T> distance, double[,] p, double perplexity) {
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| 270 | // Compute the distance matrix
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| 271 | var dd = ComputeDistances(x, distance);
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| 272 |
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| 273 | int n = x.Length;
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| 274 | // Compute the Gaussian kernel row by row
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| 275 | for (var i = 0; i < n; i++) {
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| 276 | // Initialize some variables
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| 277 | var found = false;
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| 278 | var beta = 1.0;
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| 279 | var minBeta = -double.MaxValue;
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| 280 | var maxBeta = double.MaxValue;
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| 281 | const double tol = 1e-5;
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| 282 | double sumP = 0;
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| 283 |
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| 284 | // Iterate until we found a good perplexity
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| 285 | var iter = 0;
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| 286 | while (!found && iter < 200) { // TODO constant
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| 287 |
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| 288 | // Compute Gaussian kernel row
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| 289 | for (var m = 0; m < n; m++) p[i, m] = Math.Exp(-beta * dd[i][m]);
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| 290 | p[i, i] = double.Epsilon;
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| 291 |
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| 292 | // Compute entropy of current row
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| 293 | sumP = double.Epsilon;
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| 294 | for (var m = 0; m < n; m++) sumP += p[i, m];
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| 295 | var h = 0.0;
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| 296 | for (var m = 0; m < n; m++) h += beta * (dd[i][m] * p[i, m]);
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| 297 | h = h / sumP + Math.Log(sumP);
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| 298 |
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| 299 | // Evaluate whether the entropy is within the tolerance level
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| 300 | var hdiff = h - Math.Log(perplexity);
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| 301 | if (hdiff < tol && -hdiff < tol) {
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| 302 | found = true;
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| 303 | } else {
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| 304 | if (hdiff > 0) {
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| 305 | minBeta = beta;
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| 306 | if (maxBeta.IsAlmost(double.MaxValue) || maxBeta.IsAlmost(double.MinValue))
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| 307 | beta *= 2.0;
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| 308 | else
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| 309 | beta = (beta + maxBeta) / 2.0;
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| 310 | } else {
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| 311 | maxBeta = beta;
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| 312 | if (minBeta.IsAlmost(double.MinValue) || minBeta.IsAlmost(double.MaxValue))
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| 313 | beta /= 2.0;
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| 314 | else
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| 315 | beta = (beta + minBeta) / 2.0;
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| 316 | }
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| 317 | }
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| 318 |
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| 319 | // Update iteration counter
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| 320 | iter++;
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| 321 | }
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| 322 |
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| 323 | // Row normalize P
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| 324 | for (var m = 0; m < n; m++) p[i, m] /= sumP;
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[14512] | 325 | }
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| 326 | }
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| 327 |
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[14788] | 328 | private static double[][] ComputeDistances(T[] x, IDistance<T> distance) {
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| 329 | return x.Select(m => x.Select(n => distance.Get(m, n)).ToArray()).ToArray();
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| 330 | }
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[14414] | 331 |
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| 332 |
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[14785] | 333 |
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[14788] | 334 | private static double EvaluateErrorExact(double[,] p, double[,] y, int n, int d) {
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| 335 | // Compute the squared Euclidean distance matrix
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| 336 | var dd = new double[n, n];
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| 337 | var q = new double[n, n];
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| 338 | ComputeSquaredEuclideanDistance(y, n, d, dd);
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[14414] | 339 |
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[14788] | 340 | // Compute Q-matrix and normalization sum
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| 341 | var sumQ = double.Epsilon;
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| 342 | for (var n1 = 0; n1 < n; n1++) {
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| 343 | for (var m = 0; m < n; m++) {
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| 344 | if (n1 != m) {
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| 345 | q[n1, m] = 1 / (1 + dd[n1, m]);
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| 346 | sumQ += q[n1, m];
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| 347 | } else q[n1, m] = double.Epsilon;
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| 348 | }
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| 349 | }
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| 350 | for (var i = 0; i < n; i++) for (var j = 0; j < n; j++) q[i, j] /= sumQ;
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[14414] | 351 |
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[14788] | 352 | // Sum t-SNE error
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| 353 | var c = .0;
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| 354 | for (var i = 0; i < n; i++)
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| 355 | for (var j = 0; j < n; j++) {
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| 356 | c += p[i, j] * Math.Log((p[i, j] + float.Epsilon) / (q[i, j] + float.Epsilon));
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| 357 | }
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| 358 | return c;
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| 359 | }
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| 360 | private static double EvaluateErrorApproximate(IReadOnlyList<int> rowP, IReadOnlyList<int> colP, IReadOnlyList<double> valP, double[,] y, double theta) {
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| 361 | // Get estimate of normalization term
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| 362 | var n = y.GetLength(0);
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| 363 | var d = y.GetLength(1);
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| 364 | var tree = new SpacePartitioningTree(y);
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| 365 | var buff = new double[d];
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| 366 | double sumQ = 0.0;
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| 367 | for (var i = 0; i < n; i++) tree.ComputeNonEdgeForces(i, theta, buff, ref sumQ);
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[14414] | 368 |
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[14788] | 369 | // Loop over all edges to compute t-SNE error
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| 370 | var c = .0;
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| 371 | for (var k = 0; k < n; k++) {
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| 372 | for (var i = rowP[k]; i < rowP[k + 1]; i++) {
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| 373 | var q = .0;
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| 374 | for (var j = 0; j < d; j++) buff[j] = y[k, j];
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| 375 | for (var j = 0; j < d; j++) buff[j] -= y[colP[i], j];
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| 376 | for (var j = 0; j < d; j++) q += buff[j] * buff[j];
|
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| 377 | q = 1.0 / (1.0 + q) / sumQ;
|
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| 378 | c += valP[i] * Math.Log((valP[i] + float.Epsilon) / (q + float.Epsilon));
|
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| 379 | }
|
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| 380 | }
|
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| 381 | return c;
|
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| 382 | }
|
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| 383 | private static void SymmetrizeMatrix(IReadOnlyList<int> rowP, IReadOnlyList<int> colP, IReadOnlyList<double> valP, out int[] symRowP, out int[] symColP, out double[] symValP) {
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[14414] | 384 |
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[14788] | 385 | // Count number of elements and row counts of symmetric matrix
|
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| 386 | var n = rowP.Count - 1;
|
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| 387 | var rowCounts = new int[n];
|
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| 388 | for (var j = 0; j < n; j++) {
|
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| 389 | for (var i = rowP[j]; i < rowP[j + 1]; i++) {
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[14414] | 390 |
|
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[14788] | 391 | // Check whether element (col_P[i], n) is present
|
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| 392 | var present = false;
|
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| 393 | for (var m = rowP[colP[i]]; m < rowP[colP[i] + 1]; m++) {
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| 394 | if (colP[m] == j) present = true;
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| 395 | }
|
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| 396 | if (present) rowCounts[j]++;
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| 397 | else {
|
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| 398 | rowCounts[j]++;
|
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| 399 | rowCounts[colP[i]]++;
|
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| 400 | }
|
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| 401 | }
|
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| 402 | }
|
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| 403 | var noElem = 0;
|
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| 404 | for (var i = 0; i < n; i++) noElem += rowCounts[i];
|
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[14414] | 405 |
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[14788] | 406 | // Allocate memory for symmetrized matrix
|
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| 407 | symRowP = new int[n + 1];
|
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| 408 | symColP = new int[noElem];
|
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| 409 | symValP = new double[noElem];
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[14414] | 410 |
|
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[14788] | 411 | // Construct new row indices for symmetric matrix
|
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| 412 | symRowP[0] = 0;
|
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| 413 | for (var i = 0; i < n; i++) symRowP[i + 1] = symRowP[i] + rowCounts[i];
|
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| 414 |
|
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| 415 | // Fill the result matrix
|
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| 416 | var offset = new int[n];
|
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| 417 | for (var j = 0; j < n; j++) {
|
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| 418 | for (var i = rowP[j]; i < rowP[j + 1]; i++) { // considering element(n, colP[i])
|
---|
| 419 |
|
---|
| 420 | // Check whether element (col_P[i], n) is present
|
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| 421 | var present = false;
|
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| 422 | for (var m = rowP[colP[i]]; m < rowP[colP[i] + 1]; m++) {
|
---|
| 423 | if (colP[m] != j) continue;
|
---|
| 424 | present = true;
|
---|
| 425 | if (j > colP[i]) continue; // make sure we do not add elements twice
|
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| 426 | symColP[symRowP[j] + offset[j]] = colP[i];
|
---|
| 427 | symColP[symRowP[colP[i]] + offset[colP[i]]] = j;
|
---|
| 428 | symValP[symRowP[j] + offset[j]] = valP[i] + valP[m];
|
---|
| 429 | symValP[symRowP[colP[i]] + offset[colP[i]]] = valP[i] + valP[m];
|
---|
[14414] | 430 | }
|
---|
[14788] | 431 |
|
---|
| 432 | // If (colP[i], n) is not present, there is no addition involved
|
---|
| 433 | if (!present) {
|
---|
| 434 | symColP[symRowP[j] + offset[j]] = colP[i];
|
---|
| 435 | symColP[symRowP[colP[i]] + offset[colP[i]]] = j;
|
---|
| 436 | symValP[symRowP[j] + offset[j]] = valP[i];
|
---|
| 437 | symValP[symRowP[colP[i]] + offset[colP[i]]] = valP[i];
|
---|
| 438 | }
|
---|
| 439 |
|
---|
| 440 | // Update offsets
|
---|
| 441 | if (present && (j > colP[i])) continue;
|
---|
| 442 | offset[j]++;
|
---|
| 443 | if (colP[i] != j) offset[colP[i]]++;
|
---|
[14414] | 444 | }
|
---|
| 445 | }
|
---|
| 446 |
|
---|
[14788] | 447 | // Divide the result by two
|
---|
| 448 | for (var i = 0; i < noElem; i++) symValP[i] /= 2.0;
|
---|
[14414] | 449 | }
|
---|
[14788] | 450 |
|
---|
[14414] | 451 | }
|
---|
[14785] | 452 |
|
---|
[14788] | 453 | public static TSNEState CreateState(T[] data, IDistance<T> distance, IRandom random, int newDimensions = 2, double perplexity = 25, double theta = 0,
|
---|
| 454 | int stopLyingIter = 250, int momSwitchIter = 250, double momentum = .5, double finalMomentum = .8, double eta = 200.0
|
---|
| 455 | ) {
|
---|
| 456 | return new TSNEState(data, distance, random, newDimensions, perplexity, theta, stopLyingIter, momSwitchIter, momentum, finalMomentum, eta);
|
---|
| 457 | }
|
---|
[14414] | 458 |
|
---|
| 459 |
|
---|
[14788] | 460 | public static double[,] Iterate(TSNEState state) {
|
---|
| 461 | if (state.exact)
|
---|
| 462 | ComputeExactGradient(state.p, state.newData, state.noDatapoints, state.newDimensions, state.dY);
|
---|
| 463 | else
|
---|
| 464 | ComputeApproximateGradient(state.rowP, state.colP, state.valP, state.newData, state.noDatapoints, state.newDimensions, state.dY, state.theta);
|
---|
[14414] | 465 |
|
---|
[14788] | 466 | // Update gains
|
---|
| 467 | for (var i = 0; i < state.noDatapoints; i++) {
|
---|
| 468 | for (var j = 0; j < state.newDimensions; j++) {
|
---|
| 469 | state.gains[i, j] = Math.Sign(state.dY[i, j]) != Math.Sign(state.uY[i, j])
|
---|
| 470 | ? state.gains[i, j] + .2
|
---|
| 471 | : state.gains[i, j] * .8; // 20% up or 20% down // TODO: +0.2?!
|
---|
[14414] | 472 |
|
---|
[14788] | 473 | if (state.gains[i, j] < .01) state.gains[i, j] = .01;
|
---|
[14414] | 474 | }
|
---|
[14788] | 475 | }
|
---|
[14414] | 476 |
|
---|
[14788] | 477 |
|
---|
| 478 | // Perform gradient update (with momentum and gains)
|
---|
| 479 | for (var i = 0; i < state.noDatapoints; i++)
|
---|
| 480 | for (var j = 0; j < state.newDimensions; j++)
|
---|
| 481 | state.uY[i, j] = state.currentMomentum * state.uY[i, j] - state.eta * state.gains[i, j] * state.dY[i, j];
|
---|
| 482 |
|
---|
| 483 | for (var i = 0; i < state.noDatapoints; i++)
|
---|
| 484 | for (var j = 0; j < state.newDimensions; j++)
|
---|
| 485 | state.newData[i, j] = state.newData[i, j] + state.uY[i, j];
|
---|
| 486 |
|
---|
| 487 | // Make solution zero-mean
|
---|
| 488 | ZeroMean(state.newData);
|
---|
| 489 | // Stop lying about the P-values after a while, and switch momentum
|
---|
| 490 |
|
---|
| 491 | if (state.iter == state.stopLyingIter) {
|
---|
| 492 | if (state.exact)
|
---|
| 493 | for (var i = 0; i < state.noDatapoints; i++) for (var j = 0; j < state.noDatapoints; j++) state.p[i, j] /= 12.0; //XXX why 12?
|
---|
| 494 | else
|
---|
| 495 | for (var i = 0; i < state.rowP[state.noDatapoints]; i++) state.valP[i] /= 12.0; // XXX are we not scaling all values?
|
---|
[14414] | 496 | }
|
---|
[14788] | 497 |
|
---|
| 498 | if (state.iter == state.momSwitchIter)
|
---|
| 499 | state.currentMomentum = state.finalMomentum;
|
---|
| 500 |
|
---|
| 501 | state.iter++;
|
---|
| 502 | return state.newData;
|
---|
[14414] | 503 | }
|
---|
[14785] | 504 |
|
---|
[14788] | 505 |
|
---|
| 506 | private static void ComputeApproximateGradient(int[] rowP, int[] colP, double[] valP, double[,] y, int n, int d, double[,] dC, double theta) {
|
---|
| 507 | var tree = new SpacePartitioningTree(y);
|
---|
| 508 | double sumQ = 0.0;
|
---|
| 509 | var posF = new double[n, d];
|
---|
| 510 | var negF = new double[n, d];
|
---|
| 511 | tree.ComputeEdgeForces(rowP, colP, valP, n, posF);
|
---|
| 512 | var row = new double[d];
|
---|
| 513 | for (var n1 = 0; n1 < n; n1++) {
|
---|
| 514 | Buffer.BlockCopy(negF, (sizeof(double) * n1 * d), row, 0, d);
|
---|
| 515 | tree.ComputeNonEdgeForces(n1, theta, row, ref sumQ);
|
---|
| 516 | }
|
---|
| 517 |
|
---|
| 518 | // Compute final t-SNE gradient
|
---|
| 519 | for (var i = 0; i < n; i++)
|
---|
| 520 | for (var j = 0; j < d; j++) {
|
---|
| 521 | dC[i, j] = posF[i, j] - negF[i, j] / sumQ;
|
---|
| 522 | }
|
---|
[14414] | 523 | }
|
---|
[14785] | 524 |
|
---|
[14414] | 525 | private static void ComputeExactGradient(double[,] p, double[,] y, int n, int d, double[,] dC) {
|
---|
| 526 |
|
---|
| 527 | // Make sure the current gradient contains zeros
|
---|
| 528 | for (var i = 0; i < n; i++) for (var j = 0; j < d; j++) dC[i, j] = 0.0;
|
---|
| 529 |
|
---|
| 530 | // Compute the squared Euclidean distance matrix
|
---|
| 531 | var dd = new double[n, n];
|
---|
| 532 | ComputeSquaredEuclideanDistance(y, n, d, dd);
|
---|
| 533 |
|
---|
| 534 | // Compute Q-matrix and normalization sum
|
---|
| 535 | var q = new double[n, n];
|
---|
| 536 | var sumQ = .0;
|
---|
| 537 | for (var n1 = 0; n1 < n; n1++) {
|
---|
| 538 | for (var m = 0; m < n; m++) {
|
---|
| 539 | if (n1 == m) continue;
|
---|
| 540 | q[n1, m] = 1 / (1 + dd[n1, m]);
|
---|
| 541 | sumQ += q[n1, m];
|
---|
| 542 | }
|
---|
| 543 | }
|
---|
| 544 |
|
---|
| 545 | // Perform the computation of the gradient
|
---|
| 546 | for (var n1 = 0; n1 < n; n1++) {
|
---|
| 547 | for (var m = 0; m < n; m++) {
|
---|
| 548 | if (n1 == m) continue;
|
---|
| 549 | var mult = (p[n1, m] - q[n1, m] / sumQ) * q[n1, m];
|
---|
| 550 | for (var d1 = 0; d1 < d; d1++) {
|
---|
| 551 | dC[n1, d1] += (y[n1, d1] - y[m, d1]) * mult;
|
---|
| 552 | }
|
---|
| 553 | }
|
---|
| 554 | }
|
---|
| 555 | }
|
---|
[14788] | 556 |
|
---|
[14414] | 557 | private static void ComputeSquaredEuclideanDistance(double[,] x, int n, int d, double[,] dd) {
|
---|
| 558 | var dataSums = new double[n];
|
---|
| 559 | for (var i = 0; i < n; i++) {
|
---|
| 560 | for (var j = 0; j < d; j++) {
|
---|
| 561 | dataSums[i] += x[i, j] * x[i, j];
|
---|
| 562 | }
|
---|
| 563 | }
|
---|
| 564 | for (var i = 0; i < n; i++) {
|
---|
| 565 | for (var m = 0; m < n; m++) {
|
---|
| 566 | dd[i, m] = dataSums[i] + dataSums[m];
|
---|
| 567 | }
|
---|
| 568 | }
|
---|
| 569 | for (var i = 0; i < n; i++) {
|
---|
| 570 | dd[i, i] = 0.0;
|
---|
| 571 | for (var m = i + 1; m < n; m++) {
|
---|
| 572 | dd[i, m] = 0.0;
|
---|
| 573 | for (var j = 0; j < d; j++) {
|
---|
| 574 | dd[i, m] += (x[i, j] - x[m, j]) * (x[i, j] - x[m, j]);
|
---|
| 575 | }
|
---|
| 576 | dd[m, i] = dd[i, m];
|
---|
| 577 | }
|
---|
| 578 | }
|
---|
| 579 | }
|
---|
| 580 |
|
---|
| 581 | private static void ZeroMean(double[,] x) {
|
---|
| 582 | // Compute data mean
|
---|
| 583 | var n = x.GetLength(0);
|
---|
| 584 | var d = x.GetLength(1);
|
---|
| 585 | var mean = new double[d];
|
---|
| 586 | for (var i = 0; i < n; i++) {
|
---|
| 587 | for (var j = 0; j < d; j++) {
|
---|
| 588 | mean[j] += x[i, j];
|
---|
| 589 | }
|
---|
| 590 | }
|
---|
| 591 | for (var i = 0; i < d; i++) {
|
---|
| 592 | mean[i] /= n;
|
---|
| 593 | }
|
---|
| 594 | // Subtract data mean
|
---|
| 595 | for (var i = 0; i < n; i++) {
|
---|
| 596 | for (var j = 0; j < d; j++) {
|
---|
| 597 | x[i, j] -= mean[j];
|
---|
| 598 | }
|
---|
| 599 | }
|
---|
| 600 | }
|
---|
| 601 | }
|
---|
| 602 | }
|
---|