| 1 | /*
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| 2 | * SVM.NET Library
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| 3 | * Copyright (C) 2008 Matthew Johnson
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| 4 | *
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| 5 | * This program is free software: you can redistribute it and/or modify
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| 6 | * it under the terms of the GNU General Public License as published by
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| 7 | * the Free Software Foundation, either version 3 of the License, or
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| 8 | * (at your option) any later version.
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| 9 | *
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| 10 | * This program is distributed in the hope that it will be useful,
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| 11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 13 | * GNU General Public License for more details.
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| 14 | *
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| 15 | * You should have received a copy of the GNU General Public License
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| 16 | * along with this program. If not, see <http://www.gnu.org/licenses/>.
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| 17 | */
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| 18 |
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| 19 |
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| 20 | using System;
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| 21 | using System.Linq;
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| 22 | using System.Collections.Generic;
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| 23 | using System.Diagnostics;
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| 24 | using System.IO;
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| 25 |
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| 26 | namespace SVM
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| 27 | {
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| 28 |
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| 29 | // An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
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| 30 | // Solves:
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| 31 | //
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| 32 | // Min 0.5(\alpha^T Q \alpha) + p^T \alpha
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| 33 | //
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| 34 | // y^T \alpha = \delta
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| 35 | // y_i = +1 or -1
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| 36 | // 0 <= alpha_i <= Cp for y_i = 1
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| 37 | // 0 <= alpha_i <= Cn for y_i = -1
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| 38 | //
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| 39 | // Given:
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| 40 | //
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| 41 | // Q, p, y, Cp, Cn, and an initial feasible point \alpha
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| 42 | // l is the size of vectors and matrices
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| 43 | // eps is the stopping tolerance
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| 44 | //
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| 45 | // solution will be put in \alpha, objective value will be put in obj
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| 46 | //
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| 47 | internal class Solver
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| 48 | {
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| 49 | protected int active_size;
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| 50 | protected sbyte[] y;
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| 51 | protected double[] G; // gradient of objective function
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| 52 | private const byte LOWER_BOUND = 0;
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| 53 | private const byte UPPER_BOUND = 1;
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| 54 | private const byte FREE = 2;
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| 55 | private byte[] alpha_status; // LOWER_BOUND, UPPER_BOUND, FREE
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| 56 | private double[] alpha;
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| 57 | protected IQMatrix Q;
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| 58 | protected float[] QD;
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| 59 | protected double EPS;
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| 60 | private double Cp, Cn;
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| 61 | private double[] p;
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| 62 | private int[] active_set;
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| 63 | private double[] G_bar; // gradient, if we treat free variables as 0
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| 64 | protected int l;
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| 65 | protected bool unshrink; // XXX
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| 66 |
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| 67 | protected const double INF = double.PositiveInfinity;
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| 68 |
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| 69 | private double get_C(int i)
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| 70 | {
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| 71 | return (y[i] > 0) ? Cp : Cn;
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| 72 | }
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| 73 |
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| 74 | private void update_alpha_status(int i)
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| 75 | {
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| 76 | if (alpha[i] >= get_C(i))
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| 77 | alpha_status[i] = UPPER_BOUND;
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| 78 | else if (alpha[i] <= 0)
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| 79 | alpha_status[i] = LOWER_BOUND;
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| 80 | else alpha_status[i] = FREE;
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| 81 | }
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| 82 |
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| 83 | protected bool is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
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| 84 | protected bool is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }
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| 85 |
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| 86 | private bool is_free(int i) { return alpha_status[i] == FREE; }
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| 87 |
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| 88 | public class SolutionInfo
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| 89 | {
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| 90 | public double obj;
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| 91 | public double rho;
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| 92 | public double upper_bound_p;
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| 93 | public double upper_bound_n;
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| 94 | public double r; // for Solver_NU
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| 95 | }
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| 96 |
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| 97 | protected void swap_index(int i, int j)
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| 98 | {
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| 99 | Q.SwapIndex(i, j);
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| 100 | y.SwapIndex(i, j);
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| 101 | G.SwapIndex(i, j);
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| 102 | alpha_status.SwapIndex(i, j);
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| 103 | alpha.SwapIndex(i, j);
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| 104 | p.SwapIndex(i, j);
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| 105 | active_set.SwapIndex(i, j);
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| 106 | G_bar.SwapIndex(i, j);
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| 107 | }
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| 108 |
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| 109 | protected void reconstruct_gradient()
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| 110 | {
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| 111 | // reconstruct inactive elements of G from G_bar and free variables
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| 112 |
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| 113 | if (active_size == l) return;
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| 114 |
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| 115 | int i, j;
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| 116 | int nr_free = 0;
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| 117 |
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| 118 | for (j = active_size; j < l; j++)
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| 119 | G[j] = G_bar[j] + p[j];
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| 120 |
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| 121 | for (j = 0; j < active_size; j++)
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| 122 | if (is_free(j))
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| 123 | nr_free++;
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| 124 |
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| 125 | if (2 * nr_free < active_size)
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| 126 | Procedures.info("\nWarning: using -h 0 may be faster\n");
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| 127 |
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| 128 | if (nr_free * l > 2 * active_size * (l - active_size))
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| 129 | {
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| 130 | for (i = active_size; i < l; i++)
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| 131 | {
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| 132 | float[] Q_i = Q.GetQ(i, active_size);
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| 133 | for (j = 0; j < active_size; j++)
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| 134 | if (is_free(j))
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| 135 | G[i] += alpha[j] * Q_i[j];
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| 136 | }
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| 137 | }
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| 138 | else
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| 139 | {
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| 140 | for (i = 0; i < active_size; i++)
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| 141 | if (is_free(i))
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| 142 | {
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| 143 | float[] Q_i = Q.GetQ(i, l);
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| 144 | double alpha_i = alpha[i];
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| 145 | for (j = active_size; j < l; j++)
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| 146 | G[j] += alpha_i * Q_i[j];
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| 147 | }
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| 148 | }
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| 149 | }
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| 150 |
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| 151 | public virtual void Solve(int l, IQMatrix Q, double[] p_, sbyte[] y_, double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, bool shrinking)
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| 152 | {
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| 153 | this.l = l;
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| 154 | this.Q = Q;
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| 155 | QD = Q.GetQD();
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| 156 | p = (double[])p_.Clone();
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| 157 | y = (sbyte[])y_.Clone();
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| 158 | alpha = (double[])alpha_.Clone();
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| 159 | this.Cp = Cp;
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| 160 | this.Cn = Cn;
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| 161 | this.EPS = eps;
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| 162 | this.unshrink = false;
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| 163 |
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| 164 | // initialize alpha_status
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| 165 | {
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| 166 | alpha_status = new byte[l];
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| 167 | for (int i = 0; i < l; i++)
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| 168 | update_alpha_status(i);
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| 169 | }
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| 170 |
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| 171 | // initialize active set (for shrinking)
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| 172 | {
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| 173 | active_set = new int[l];
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| 174 | for (int i = 0; i < l; i++)
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| 175 | active_set[i] = i;
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| 176 | active_size = l;
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| 177 | }
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| 178 |
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| 179 | // initialize gradient
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| 180 | {
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| 181 | G = new double[l];
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| 182 | G_bar = new double[l];
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| 183 | int i;
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| 184 | for (i = 0; i < l; i++)
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| 185 | {
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| 186 | G[i] = p[i];
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| 187 | G_bar[i] = 0;
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| 188 | }
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| 189 | for (i = 0; i < l; i++)
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| 190 | if (!is_lower_bound(i))
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| 191 | {
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| 192 | float[] Q_i = Q.GetQ(i, l);
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| 193 | double alpha_i = alpha[i];
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| 194 | int j;
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| 195 | for (j = 0; j < l; j++)
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| 196 | G[j] += alpha_i * Q_i[j];
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| 197 | if (is_upper_bound(i))
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| 198 | for (j = 0; j < l; j++)
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| 199 | G_bar[j] += get_C(i) * Q_i[j];
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| 200 | }
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| 201 | }
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| 202 |
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| 203 | // optimization step
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| 204 |
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| 205 | int iter = 0;
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| 206 | int counter = Math.Min(l, 1000) + 1;
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| 207 | int[] working_set = new int[2];
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| 208 |
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| 209 | while (true)
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| 210 | {
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| 211 | // show progress and do shrinking
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| 212 |
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| 213 | if (--counter == 0)
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| 214 | {
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| 215 | counter = Math.Min(l, 1000);
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| 216 | if (shrinking) do_shrinking();
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| 217 | Procedures.info(".");
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| 218 | }
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| 219 |
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| 220 | if (select_working_set(working_set) != 0)
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| 221 | {
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| 222 | // reconstruct the whole gradient
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| 223 | reconstruct_gradient();
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| 224 | // reset active set size and check
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| 225 | active_size = l;
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| 226 | Procedures.info("*");
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| 227 | if (select_working_set(working_set) != 0)
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| 228 | break;
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| 229 | else
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| 230 | counter = 1; // do shrinking next iteration
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| 231 | }
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| 232 |
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| 233 | int i = working_set[0];
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| 234 | int j = working_set[1];
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| 235 |
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| 236 | ++iter;
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| 237 |
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| 238 | // update alpha[i] and alpha[j], handle bounds carefully
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| 239 |
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| 240 | float[] Q_i = Q.GetQ(i, active_size);
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| 241 | float[] Q_j = Q.GetQ(j, active_size);
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| 242 |
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| 243 | double C_i = get_C(i);
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| 244 | double C_j = get_C(j);
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| 245 |
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| 246 | double old_alpha_i = alpha[i];
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| 247 | double old_alpha_j = alpha[j];
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| 248 |
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| 249 | if (y[i] != y[j])
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| 250 | {
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| 251 | double quad_coef = Q_i[i] + Q_j[j] + 2 * Q_i[j];
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| 252 | if (quad_coef <= 0)
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| 253 | quad_coef = 1e-12;
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| 254 | double delta = (-G[i] - G[j]) / quad_coef;
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| 255 | double diff = alpha[i] - alpha[j];
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| 256 | alpha[i] += delta;
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| 257 | alpha[j] += delta;
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| 258 |
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| 259 | if (diff > 0)
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| 260 | {
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| 261 | if (alpha[j] < 0)
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| 262 | {
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| 263 | alpha[j] = 0;
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| 264 | alpha[i] = diff;
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| 265 | }
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| 266 | }
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| 267 | else
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| 268 | {
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| 269 | if (alpha[i] < 0)
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| 270 | {
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| 271 | alpha[i] = 0;
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| 272 | alpha[j] = -diff;
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| 273 | }
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| 274 | }
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| 275 | if (diff > C_i - C_j)
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| 276 | {
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| 277 | if (alpha[i] > C_i)
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| 278 | {
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| 279 | alpha[i] = C_i;
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| 280 | alpha[j] = C_i - diff;
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| 281 | }
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| 282 | }
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| 283 | else
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| 284 | {
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| 285 | if (alpha[j] > C_j)
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| 286 | {
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| 287 | alpha[j] = C_j;
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| 288 | alpha[i] = C_j + diff;
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| 289 | }
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| 290 | }
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| 291 | }
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| 292 | else
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| 293 | {
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| 294 | double quad_coef = Q_i[i] + Q_j[j] - 2 * Q_i[j];
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| 295 | if (quad_coef <= 0)
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| 296 | quad_coef = 1e-12;
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| 297 | double delta = (G[i] - G[j]) / quad_coef;
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| 298 | double sum = alpha[i] + alpha[j];
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| 299 | alpha[i] -= delta;
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| 300 | alpha[j] += delta;
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| 301 |
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| 302 | if (sum > C_i)
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| 303 | {
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| 304 | if (alpha[i] > C_i)
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| 305 | {
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| 306 | alpha[i] = C_i;
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| 307 | alpha[j] = sum - C_i;
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| 308 | }
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| 309 | }
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| 310 | else
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| 311 | {
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| 312 | if (alpha[j] < 0)
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| 313 | {
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| 314 | alpha[j] = 0;
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| 315 | alpha[i] = sum;
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| 316 | }
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| 317 | }
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| 318 | if (sum > C_j)
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| 319 | {
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| 320 | if (alpha[j] > C_j)
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| 321 | {
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| 322 | alpha[j] = C_j;
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| 323 | alpha[i] = sum - C_j;
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| 324 | }
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| 325 | }
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| 326 | else
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| 327 | {
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| 328 | if (alpha[i] < 0)
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| 329 | {
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| 330 | alpha[i] = 0;
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| 331 | alpha[j] = sum;
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| 332 | }
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| 333 | }
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| 334 | }
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| 335 |
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| 336 | // update G
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| 337 |
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| 338 | double delta_alpha_i = alpha[i] - old_alpha_i;
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| 339 | double delta_alpha_j = alpha[j] - old_alpha_j;
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| 340 |
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| 341 | for (int k = 0; k < active_size; k++)
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| 342 | {
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| 343 | G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
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| 344 | }
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| 345 |
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| 346 | // update alpha_status and G_bar
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| 347 |
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| 348 | {
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| 349 | bool ui = is_upper_bound(i);
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| 350 | bool uj = is_upper_bound(j);
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| 351 | update_alpha_status(i);
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| 352 | update_alpha_status(j);
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| 353 | int k;
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| 354 | if (ui != is_upper_bound(i))
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| 355 | {
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| 356 | Q_i = Q.GetQ(i, l);
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| 357 | if (ui)
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| 358 | for (k = 0; k < l; k++)
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| 359 | G_bar[k] -= C_i * Q_i[k];
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| 360 | else
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| 361 | for (k = 0; k < l; k++)
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| 362 | G_bar[k] += C_i * Q_i[k];
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| 363 | }
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| 364 |
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| 365 | if (uj != is_upper_bound(j))
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| 366 | {
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| 367 | Q_j = Q.GetQ(j, l);
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| 368 | if (uj)
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| 369 | for (k = 0; k < l; k++)
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| 370 | G_bar[k] -= C_j * Q_j[k];
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| 371 | else
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| 372 | for (k = 0; k < l; k++)
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| 373 | G_bar[k] += C_j * Q_j[k];
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| 374 | }
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| 375 | }
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| 376 |
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| 377 | }
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| 378 |
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| 379 | // calculate rho
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| 380 |
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| 381 | si.rho = calculate_rho();
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| 382 |
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| 383 | // calculate objective value
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| 384 | {
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| 385 | double v = 0;
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| 386 | int i;
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| 387 | for (i = 0; i < l; i++)
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| 388 | v += alpha[i] * (G[i] + p[i]);
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| 389 |
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| 390 | si.obj = v / 2;
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| 391 | }
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| 392 |
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| 393 | // put back the solution
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| 394 | {
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| 395 | for (int i = 0; i < l; i++)
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| 396 | alpha_[active_set[i]] = alpha[i];
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| 397 | }
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| 398 |
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| 399 | si.upper_bound_p = Cp;
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| 400 | si.upper_bound_n = Cn;
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| 401 |
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| 402 | Procedures.info("\noptimization finished, #iter = " + iter + "\n");
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| 403 | }
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| 404 |
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| 405 | // return 1 if already optimal, return 0 otherwise
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| 406 | protected virtual int select_working_set(int[] working_set)
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| 407 | {
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| 408 | // return i,j such that
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| 409 | // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
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| 410 | // j: mimimizes the decrease of obj value
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| 411 | // (if quadratic coefficeint <= 0, replace it with tau)
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| 412 | // -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
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| 413 |
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| 414 | double GMax = -INF;
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| 415 | double GMax2 = -INF;
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| 416 | int GMax_idx = -1;
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| 417 | int GMin_idx = -1;
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| 418 | double obj_diff_Min = INF;
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| 419 |
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| 420 | for (int t = 0; t < active_size; t++)
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| 421 | if (y[t] == +1)
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| 422 | {
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| 423 | if (!is_upper_bound(t))
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| 424 | if (-G[t] >= GMax)
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| 425 | {
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| 426 | GMax = -G[t];
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| 427 | GMax_idx = t;
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| 428 | }
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| 429 | }
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| 430 | else
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| 431 | {
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| 432 | if (!is_lower_bound(t))
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| 433 | if (G[t] >= GMax)
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| 434 | {
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| 435 | GMax = G[t];
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| 436 | GMax_idx = t;
|
|---|
| 437 | }
|
|---|
| 438 | }
|
|---|
| 439 |
|
|---|
| 440 | int i = GMax_idx;
|
|---|
| 441 | float[] Q_i = null;
|
|---|
| 442 | if (i != -1) // null Q_i not accessed: GMax=-INF if i=-1
|
|---|
| 443 | Q_i = Q.GetQ(i, active_size);
|
|---|
| 444 |
|
|---|
| 445 | for (int j = 0; j < active_size; j++)
|
|---|
| 446 | {
|
|---|
| 447 | if (y[j] == +1)
|
|---|
| 448 | {
|
|---|
| 449 | if (!is_lower_bound(j))
|
|---|
| 450 | {
|
|---|
| 451 | double grad_diff = GMax + G[j];
|
|---|
| 452 | if (G[j] >= GMax2)
|
|---|
| 453 | GMax2 = G[j];
|
|---|
| 454 | if (grad_diff > 0)
|
|---|
| 455 | {
|
|---|
| 456 | double obj_diff;
|
|---|
| 457 | double quad_coef = Q_i[i] + QD[j] - 2.0 * y[i] * Q_i[j];
|
|---|
| 458 | if (quad_coef > 0)
|
|---|
| 459 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
|---|
| 460 | else
|
|---|
| 461 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
|---|
| 462 |
|
|---|
| 463 | if (obj_diff <= obj_diff_Min)
|
|---|
| 464 | {
|
|---|
| 465 | GMin_idx = j;
|
|---|
| 466 | obj_diff_Min = obj_diff;
|
|---|
| 467 | }
|
|---|
| 468 | }
|
|---|
| 469 | }
|
|---|
| 470 | }
|
|---|
| 471 | else
|
|---|
| 472 | {
|
|---|
| 473 | if (!is_upper_bound(j))
|
|---|
| 474 | {
|
|---|
| 475 | double grad_diff = GMax - G[j];
|
|---|
| 476 | if (-G[j] >= GMax2)
|
|---|
| 477 | GMax2 = -G[j];
|
|---|
| 478 | if (grad_diff > 0)
|
|---|
| 479 | {
|
|---|
| 480 | double obj_diff;
|
|---|
| 481 | double quad_coef = Q_i[i] + QD[j] + 2.0 * y[i] * Q_i[j];
|
|---|
| 482 | if (quad_coef > 0)
|
|---|
| 483 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
|---|
| 484 | else
|
|---|
| 485 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
|---|
| 486 |
|
|---|
| 487 | if (obj_diff <= obj_diff_Min)
|
|---|
| 488 | {
|
|---|
| 489 | GMin_idx = j;
|
|---|
| 490 | obj_diff_Min = obj_diff;
|
|---|
| 491 | }
|
|---|
| 492 | }
|
|---|
| 493 | }
|
|---|
| 494 | }
|
|---|
| 495 | }
|
|---|
| 496 |
|
|---|
| 497 | if (GMax + GMax2 < EPS)
|
|---|
| 498 | return 1;
|
|---|
| 499 |
|
|---|
| 500 | working_set[0] = GMax_idx;
|
|---|
| 501 | working_set[1] = GMin_idx;
|
|---|
| 502 | return 0;
|
|---|
| 503 | }
|
|---|
| 504 |
|
|---|
| 505 | private bool be_shrunk(int i, double GMax1, double GMax2)
|
|---|
| 506 | {
|
|---|
| 507 | if (is_upper_bound(i))
|
|---|
| 508 | {
|
|---|
| 509 | if (y[i] == +1)
|
|---|
| 510 | return (-G[i] > GMax1);
|
|---|
| 511 | else
|
|---|
| 512 | return (-G[i] > GMax2);
|
|---|
| 513 | }
|
|---|
| 514 | else if (is_lower_bound(i))
|
|---|
| 515 | {
|
|---|
| 516 | if (y[i] == +1)
|
|---|
| 517 | return (G[i] > GMax2);
|
|---|
| 518 | else
|
|---|
| 519 | return (G[i] > GMax1);
|
|---|
| 520 | }
|
|---|
| 521 | else
|
|---|
| 522 | return (false);
|
|---|
| 523 | }
|
|---|
| 524 |
|
|---|
| 525 | protected virtual void do_shrinking()
|
|---|
| 526 | {
|
|---|
| 527 | int i;
|
|---|
| 528 | double GMax1 = -INF; // Max { -y_i * grad(f)_i | i in I_up(\alpha) }
|
|---|
| 529 | double GMax2 = -INF; // Max { y_i * grad(f)_i | i in I_low(\alpha) }
|
|---|
| 530 |
|
|---|
| 531 | // find Maximal violating pair first
|
|---|
| 532 | for (i = 0; i < active_size; i++)
|
|---|
| 533 | {
|
|---|
| 534 | if (y[i] == +1)
|
|---|
| 535 | {
|
|---|
| 536 | if (!is_upper_bound(i))
|
|---|
| 537 | {
|
|---|
| 538 | if (-G[i] >= GMax1)
|
|---|
| 539 | GMax1 = -G[i];
|
|---|
| 540 | }
|
|---|
| 541 | if (!is_lower_bound(i))
|
|---|
| 542 | {
|
|---|
| 543 | if (G[i] >= GMax2)
|
|---|
| 544 | GMax2 = G[i];
|
|---|
| 545 | }
|
|---|
| 546 | }
|
|---|
| 547 | else
|
|---|
| 548 | {
|
|---|
| 549 | if (!is_upper_bound(i))
|
|---|
| 550 | {
|
|---|
| 551 | if (-G[i] >= GMax2)
|
|---|
| 552 | GMax2 = -G[i];
|
|---|
| 553 | }
|
|---|
| 554 | if (!is_lower_bound(i))
|
|---|
| 555 | {
|
|---|
| 556 | if (G[i] >= GMax1)
|
|---|
| 557 | GMax1 = G[i];
|
|---|
| 558 | }
|
|---|
| 559 | }
|
|---|
| 560 | }
|
|---|
| 561 |
|
|---|
| 562 | if (unshrink == false && GMax1 + GMax2 <= EPS * 10)
|
|---|
| 563 | {
|
|---|
| 564 | unshrink = true;
|
|---|
| 565 | reconstruct_gradient();
|
|---|
| 566 | active_size = l;
|
|---|
| 567 | }
|
|---|
| 568 |
|
|---|
| 569 | for (i = 0; i < active_size; i++)
|
|---|
| 570 | if (be_shrunk(i, GMax1, GMax2))
|
|---|
| 571 | {
|
|---|
| 572 | active_size--;
|
|---|
| 573 | while (active_size > i)
|
|---|
| 574 | {
|
|---|
| 575 | if (!be_shrunk(active_size, GMax1, GMax2))
|
|---|
| 576 | {
|
|---|
| 577 | swap_index(i, active_size);
|
|---|
| 578 | break;
|
|---|
| 579 | }
|
|---|
| 580 | active_size--;
|
|---|
| 581 | }
|
|---|
| 582 | }
|
|---|
| 583 | }
|
|---|
| 584 |
|
|---|
| 585 | protected virtual double calculate_rho()
|
|---|
| 586 | {
|
|---|
| 587 | double r;
|
|---|
| 588 | int nr_free = 0;
|
|---|
| 589 | double ub = INF, lb = -INF, sum_free = 0;
|
|---|
| 590 | for (int i = 0; i < active_size; i++)
|
|---|
| 591 | {
|
|---|
| 592 | double yG = y[i] * G[i];
|
|---|
| 593 |
|
|---|
| 594 | if (is_lower_bound(i))
|
|---|
| 595 | {
|
|---|
| 596 | if (y[i] > 0)
|
|---|
| 597 | ub = Math.Min(ub, yG);
|
|---|
| 598 | else
|
|---|
| 599 | lb = Math.Max(lb, yG);
|
|---|
| 600 | }
|
|---|
| 601 | else if (is_upper_bound(i))
|
|---|
| 602 | {
|
|---|
| 603 | if (y[i] < 0)
|
|---|
| 604 | ub = Math.Min(ub, yG);
|
|---|
| 605 | else
|
|---|
| 606 | lb = Math.Max(lb, yG);
|
|---|
| 607 | }
|
|---|
| 608 | else
|
|---|
| 609 | {
|
|---|
| 610 | ++nr_free;
|
|---|
| 611 | sum_free += yG;
|
|---|
| 612 | }
|
|---|
| 613 | }
|
|---|
| 614 |
|
|---|
| 615 | if (nr_free > 0)
|
|---|
| 616 | r = sum_free / nr_free;
|
|---|
| 617 | else
|
|---|
| 618 | r = (ub + lb) / 2;
|
|---|
| 619 |
|
|---|
| 620 | return r;
|
|---|
| 621 | }
|
|---|
| 622 |
|
|---|
| 623 | }
|
|---|
| 624 |
|
|---|
| 625 | //
|
|---|
| 626 | // Solver for nu-svm classification and regression
|
|---|
| 627 | //
|
|---|
| 628 | // additional constraint: e^T \alpha = constant
|
|---|
| 629 | //
|
|---|
| 630 | class Solver_NU : Solver
|
|---|
| 631 | {
|
|---|
| 632 | private SolutionInfo si;
|
|---|
| 633 |
|
|---|
| 634 | public sealed override void Solve(int l, IQMatrix Q, double[] p, sbyte[] y,
|
|---|
| 635 | double[] alpha, double Cp, double Cn, double eps,
|
|---|
| 636 | SolutionInfo si, bool shrinking)
|
|---|
| 637 | {
|
|---|
| 638 | this.si = si;
|
|---|
| 639 | base.Solve(l, Q, p, y, alpha, Cp, Cn, eps, si, shrinking);
|
|---|
| 640 | }
|
|---|
| 641 |
|
|---|
| 642 | // return 1 if already optimal, return 0 otherwise
|
|---|
| 643 | protected override sealed int select_working_set(int[] working_set)
|
|---|
| 644 | {
|
|---|
| 645 | // return i,j such that y_i = y_j and
|
|---|
| 646 | // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
|
|---|
| 647 | // j: Minimizes the decrease of obj value
|
|---|
| 648 | // (if quadratic coefficeint <= 0, replace it with tau)
|
|---|
| 649 | // -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
|
|---|
| 650 |
|
|---|
| 651 | double GMaxp = -INF;
|
|---|
| 652 | double GMaxp2 = -INF;
|
|---|
| 653 | int GMaxp_idx = -1;
|
|---|
| 654 |
|
|---|
| 655 | double GMaxn = -INF;
|
|---|
| 656 | double GMaxn2 = -INF;
|
|---|
| 657 | int GMaxn_idx = -1;
|
|---|
| 658 |
|
|---|
| 659 | int GMin_idx = -1;
|
|---|
| 660 | double obj_diff_Min = INF;
|
|---|
| 661 |
|
|---|
| 662 | for (int t = 0; t < active_size; t++)
|
|---|
| 663 | if (y[t] == +1)
|
|---|
| 664 | {
|
|---|
| 665 | if (!is_upper_bound(t))
|
|---|
| 666 | if (-G[t] >= GMaxp)
|
|---|
| 667 | {
|
|---|
| 668 | GMaxp = -G[t];
|
|---|
| 669 | GMaxp_idx = t;
|
|---|
| 670 | }
|
|---|
| 671 | }
|
|---|
| 672 | else
|
|---|
| 673 | {
|
|---|
| 674 | if (!is_lower_bound(t))
|
|---|
| 675 | if (G[t] >= GMaxn)
|
|---|
| 676 | {
|
|---|
| 677 | GMaxn = G[t];
|
|---|
| 678 | GMaxn_idx = t;
|
|---|
| 679 | }
|
|---|
| 680 | }
|
|---|
| 681 |
|
|---|
| 682 | int ip = GMaxp_idx;
|
|---|
| 683 | int iN = GMaxn_idx;
|
|---|
| 684 | float[] Q_ip = null;
|
|---|
| 685 | float[] Q_in = null;
|
|---|
| 686 | if (ip != -1) // null Q_ip not accessed: GMaxp=-INF if ip=-1
|
|---|
| 687 | Q_ip = Q.GetQ(ip, active_size);
|
|---|
| 688 | if (iN != -1)
|
|---|
| 689 | Q_in = Q.GetQ(iN, active_size);
|
|---|
| 690 |
|
|---|
| 691 | for (int j = 0; j < active_size; j++)
|
|---|
| 692 | {
|
|---|
| 693 | if (y[j] == +1)
|
|---|
| 694 | {
|
|---|
| 695 | if (!is_lower_bound(j))
|
|---|
| 696 | {
|
|---|
| 697 | double grad_diff = GMaxp + G[j];
|
|---|
| 698 | if (G[j] >= GMaxp2)
|
|---|
| 699 | GMaxp2 = G[j];
|
|---|
| 700 | if (grad_diff > 0)
|
|---|
| 701 | {
|
|---|
| 702 | double obj_diff;
|
|---|
| 703 | double quad_coef = Q_ip[ip] + QD[j] - 2 * Q_ip[j];
|
|---|
| 704 | if (quad_coef > 0)
|
|---|
| 705 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
|---|
| 706 | else
|
|---|
| 707 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
|---|
| 708 |
|
|---|
| 709 | if (obj_diff <= obj_diff_Min)
|
|---|
| 710 | {
|
|---|
| 711 | GMin_idx = j;
|
|---|
| 712 | obj_diff_Min = obj_diff;
|
|---|
| 713 | }
|
|---|
| 714 | }
|
|---|
| 715 | }
|
|---|
| 716 | }
|
|---|
| 717 | else
|
|---|
| 718 | {
|
|---|
| 719 | if (!is_upper_bound(j))
|
|---|
| 720 | {
|
|---|
| 721 | double grad_diff = GMaxn - G[j];
|
|---|
| 722 | if (-G[j] >= GMaxn2)
|
|---|
| 723 | GMaxn2 = -G[j];
|
|---|
| 724 | if (grad_diff > 0)
|
|---|
| 725 | {
|
|---|
| 726 | double obj_diff;
|
|---|
| 727 | double quad_coef = Q_in[iN] + QD[j] - 2 * Q_in[j];
|
|---|
| 728 | if (quad_coef > 0)
|
|---|
| 729 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
|---|
| 730 | else
|
|---|
| 731 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
|---|
| 732 |
|
|---|
| 733 | if (obj_diff <= obj_diff_Min)
|
|---|
| 734 | {
|
|---|
| 735 | GMin_idx = j;
|
|---|
| 736 | obj_diff_Min = obj_diff;
|
|---|
| 737 | }
|
|---|
| 738 | }
|
|---|
| 739 | }
|
|---|
| 740 | }
|
|---|
| 741 | }
|
|---|
| 742 |
|
|---|
| 743 | if (Math.Max(GMaxp + GMaxp2, GMaxn + GMaxn2) < EPS)
|
|---|
| 744 | return 1;
|
|---|
| 745 |
|
|---|
| 746 | if (y[GMin_idx] == +1)
|
|---|
| 747 | working_set[0] = GMaxp_idx;
|
|---|
| 748 | else
|
|---|
| 749 | working_set[0] = GMaxn_idx;
|
|---|
| 750 | working_set[1] = GMin_idx;
|
|---|
| 751 |
|
|---|
| 752 | return 0;
|
|---|
| 753 | }
|
|---|
| 754 |
|
|---|
| 755 | private bool be_shrunk(int i, double GMax1, double GMax2, double GMax3, double GMax4)
|
|---|
| 756 | {
|
|---|
| 757 | if (is_upper_bound(i))
|
|---|
| 758 | {
|
|---|
| 759 | if (y[i] == +1)
|
|---|
| 760 | return (-G[i] > GMax1);
|
|---|
| 761 | else
|
|---|
| 762 | return (-G[i] > GMax4);
|
|---|
| 763 | }
|
|---|
| 764 | else if (is_lower_bound(i))
|
|---|
| 765 | {
|
|---|
| 766 | if (y[i] == +1)
|
|---|
| 767 | return (G[i] > GMax2);
|
|---|
| 768 | else
|
|---|
| 769 | return (G[i] > GMax3);
|
|---|
| 770 | }
|
|---|
| 771 | else
|
|---|
| 772 | return (false);
|
|---|
| 773 | }
|
|---|
| 774 |
|
|---|
| 775 | protected override sealed void do_shrinking()
|
|---|
| 776 | {
|
|---|
| 777 | double GMax1 = -INF; // Max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
|
|---|
| 778 | double GMax2 = -INF; // Max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
|
|---|
| 779 | double GMax3 = -INF; // Max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
|
|---|
| 780 | double GMax4 = -INF; // Max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }
|
|---|
| 781 |
|
|---|
| 782 | // find Maximal violating pair first
|
|---|
| 783 | int i;
|
|---|
| 784 | for (i = 0; i < active_size; i++)
|
|---|
| 785 | {
|
|---|
| 786 | if (!is_upper_bound(i))
|
|---|
| 787 | {
|
|---|
| 788 | if (y[i] == +1)
|
|---|
| 789 | {
|
|---|
| 790 | if (-G[i] > GMax1) GMax1 = -G[i];
|
|---|
| 791 | }
|
|---|
| 792 | else if (-G[i] > GMax4) GMax4 = -G[i];
|
|---|
| 793 | }
|
|---|
| 794 | if (!is_lower_bound(i))
|
|---|
| 795 | {
|
|---|
| 796 | if (y[i] == +1)
|
|---|
| 797 | {
|
|---|
| 798 | if (G[i] > GMax2) GMax2 = G[i];
|
|---|
| 799 | }
|
|---|
| 800 | else if (G[i] > GMax3) GMax3 = G[i];
|
|---|
| 801 | }
|
|---|
| 802 | }
|
|---|
| 803 |
|
|---|
| 804 | if (unshrink == false && Math.Max(GMax1 + GMax2, GMax3 + GMax4) <= EPS * 10)
|
|---|
| 805 | {
|
|---|
| 806 | unshrink = true;
|
|---|
| 807 | reconstruct_gradient();
|
|---|
| 808 | active_size = l;
|
|---|
| 809 | }
|
|---|
| 810 |
|
|---|
| 811 | for (i = 0; i < active_size; i++)
|
|---|
| 812 | if (be_shrunk(i, GMax1, GMax2, GMax3, GMax4))
|
|---|
| 813 | {
|
|---|
| 814 | active_size--;
|
|---|
| 815 | while (active_size > i)
|
|---|
| 816 | {
|
|---|
| 817 | if (!be_shrunk(active_size, GMax1, GMax2, GMax3, GMax4))
|
|---|
| 818 | {
|
|---|
| 819 | swap_index(i, active_size);
|
|---|
| 820 | break;
|
|---|
| 821 | }
|
|---|
| 822 | active_size--;
|
|---|
| 823 | }
|
|---|
| 824 | }
|
|---|
| 825 | }
|
|---|
| 826 |
|
|---|
| 827 | protected override sealed double calculate_rho()
|
|---|
| 828 | {
|
|---|
| 829 | int nr_free1 = 0, nr_free2 = 0;
|
|---|
| 830 | double ub1 = INF, ub2 = INF;
|
|---|
| 831 | double lb1 = -INF, lb2 = -INF;
|
|---|
| 832 | double sum_free1 = 0, sum_free2 = 0;
|
|---|
| 833 |
|
|---|
| 834 | for (int i = 0; i < active_size; i++)
|
|---|
| 835 | {
|
|---|
| 836 | if (y[i] == +1)
|
|---|
| 837 | {
|
|---|
| 838 | if (is_lower_bound(i))
|
|---|
| 839 | ub1 = Math.Min(ub1, G[i]);
|
|---|
| 840 | else if (is_upper_bound(i))
|
|---|
| 841 | lb1 = Math.Max(lb1, G[i]);
|
|---|
| 842 | else
|
|---|
| 843 | {
|
|---|
| 844 | ++nr_free1;
|
|---|
| 845 | sum_free1 += G[i];
|
|---|
| 846 | }
|
|---|
| 847 | }
|
|---|
| 848 | else
|
|---|
| 849 | {
|
|---|
| 850 | if (is_lower_bound(i))
|
|---|
| 851 | ub2 = Math.Min(ub2, G[i]);
|
|---|
| 852 | else if (is_upper_bound(i))
|
|---|
| 853 | lb2 = Math.Max(lb2, G[i]);
|
|---|
| 854 | else
|
|---|
| 855 | {
|
|---|
| 856 | ++nr_free2;
|
|---|
| 857 | sum_free2 += G[i];
|
|---|
| 858 | }
|
|---|
| 859 | }
|
|---|
| 860 | }
|
|---|
| 861 |
|
|---|
| 862 | double r1, r2;
|
|---|
| 863 | if (nr_free1 > 0)
|
|---|
| 864 | r1 = sum_free1 / nr_free1;
|
|---|
| 865 | else
|
|---|
| 866 | r1 = (ub1 + lb1) / 2;
|
|---|
| 867 |
|
|---|
| 868 | if (nr_free2 > 0)
|
|---|
| 869 | r2 = sum_free2 / nr_free2;
|
|---|
| 870 | else
|
|---|
| 871 | r2 = (ub2 + lb2) / 2;
|
|---|
| 872 |
|
|---|
| 873 | si.r = (r1 + r2) / 2;
|
|---|
| 874 | return (r1 - r2) / 2;
|
|---|
| 875 | }
|
|---|
| 876 | }
|
|---|
| 877 |
|
|---|
| 878 | //
|
|---|
| 879 | // Q matrices for various formulations
|
|---|
| 880 | //
|
|---|
| 881 | class SVC_Q : Kernel
|
|---|
| 882 | {
|
|---|
| 883 | private sbyte[] y;
|
|---|
| 884 | private Cache cache;
|
|---|
| 885 | private float[] QD;
|
|---|
| 886 |
|
|---|
| 887 | public SVC_Q(Problem prob, Parameter param, sbyte[] y_) : base(prob.Count, prob.X, param)
|
|---|
| 888 | {
|
|---|
| 889 | y = (sbyte[])y_.Clone();
|
|---|
| 890 | cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
|
|---|
| 891 | QD = new float[prob.Count];
|
|---|
| 892 | for (int i = 0; i < prob.Count; i++)
|
|---|
| 893 | QD[i] = (float)KernelFunction(i, i);
|
|---|
| 894 | }
|
|---|
| 895 |
|
|---|
| 896 | public override sealed float[] GetQ(int i, int len)
|
|---|
| 897 | {
|
|---|
| 898 | float[] data = null;
|
|---|
| 899 | int start, j;
|
|---|
| 900 | if ((start = cache.GetData(i, ref data, len)) < len)
|
|---|
| 901 | {
|
|---|
| 902 | for (j = start; j < len; j++)
|
|---|
| 903 | data[j] = (float)(y[i] * y[j] * KernelFunction(i, j));
|
|---|
| 904 | }
|
|---|
| 905 | return data;
|
|---|
| 906 | }
|
|---|
| 907 |
|
|---|
| 908 | public override sealed float[] GetQD()
|
|---|
| 909 | {
|
|---|
| 910 | return QD;
|
|---|
| 911 | }
|
|---|
| 912 |
|
|---|
| 913 | public override sealed void SwapIndex(int i, int j)
|
|---|
| 914 | {
|
|---|
| 915 | cache.SwapIndex(i, j);
|
|---|
| 916 | base.SwapIndex(i, j);
|
|---|
| 917 | y.SwapIndex(i, j);
|
|---|
| 918 | QD.SwapIndex(i, j);
|
|---|
| 919 | }
|
|---|
| 920 | }
|
|---|
| 921 |
|
|---|
| 922 | class ONE_CLASS_Q : Kernel
|
|---|
| 923 | {
|
|---|
| 924 | private Cache cache;
|
|---|
| 925 | private float[] QD;
|
|---|
| 926 |
|
|---|
| 927 | public ONE_CLASS_Q(Problem prob, Parameter param) : base(prob.Count, prob.X, param)
|
|---|
| 928 | {
|
|---|
| 929 | cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
|
|---|
| 930 | QD = new float[prob.Count];
|
|---|
| 931 | for (int i = 0; i < prob.Count; i++)
|
|---|
| 932 | QD[i] = (float)KernelFunction(i, i);
|
|---|
| 933 | }
|
|---|
| 934 |
|
|---|
| 935 | public override sealed float[] GetQ(int i, int len)
|
|---|
| 936 | {
|
|---|
| 937 | float[] data = null;
|
|---|
| 938 | int start, j;
|
|---|
| 939 | if ((start = cache.GetData(i, ref data, len)) < len)
|
|---|
| 940 | {
|
|---|
| 941 | for (j = start; j < len; j++)
|
|---|
| 942 | data[j] = (float)KernelFunction(i, j);
|
|---|
| 943 | }
|
|---|
| 944 | return data;
|
|---|
| 945 | }
|
|---|
| 946 |
|
|---|
| 947 | public override sealed float[] GetQD()
|
|---|
| 948 | {
|
|---|
| 949 | return QD;
|
|---|
| 950 | }
|
|---|
| 951 |
|
|---|
| 952 | public override sealed void SwapIndex(int i, int j)
|
|---|
| 953 | {
|
|---|
| 954 | cache.SwapIndex(i, j);
|
|---|
| 955 | base.SwapIndex(i, j);
|
|---|
| 956 | QD.SwapIndex(i, j);
|
|---|
| 957 | }
|
|---|
| 958 | }
|
|---|
| 959 |
|
|---|
| 960 | class SVR_Q : Kernel
|
|---|
| 961 | {
|
|---|
| 962 | private int l;
|
|---|
| 963 | private Cache cache;
|
|---|
| 964 | private sbyte[] sign;
|
|---|
| 965 | private int[] index;
|
|---|
| 966 | private int next_buffer;
|
|---|
| 967 | private float[][] buffer;
|
|---|
| 968 | private float[] QD;
|
|---|
| 969 |
|
|---|
| 970 | public SVR_Q(Problem prob, Parameter param) : base(prob.Count, prob.X, param)
|
|---|
| 971 | {
|
|---|
| 972 | l = prob.Count;
|
|---|
| 973 | cache = new Cache(l, (long)(param.CacheSize * (1 << 20)));
|
|---|
| 974 | QD = new float[2 * l];
|
|---|
| 975 | sign = new sbyte[2 * l];
|
|---|
| 976 | index = new int[2 * l];
|
|---|
| 977 | for (int k = 0; k < l; k++)
|
|---|
| 978 | {
|
|---|
| 979 | sign[k] = 1;
|
|---|
| 980 | sign[k + l] = -1;
|
|---|
| 981 | index[k] = k;
|
|---|
| 982 | index[k + l] = k;
|
|---|
| 983 | QD[k] = (float)KernelFunction(k, k);
|
|---|
| 984 | QD[k + l] = QD[k];
|
|---|
| 985 | }
|
|---|
| 986 | buffer = new float[2][];
|
|---|
| 987 | buffer[0] = new float[2 * l];
|
|---|
| 988 | buffer[1] = new float[2 * l];
|
|---|
| 989 | next_buffer = 0;
|
|---|
| 990 | }
|
|---|
| 991 |
|
|---|
| 992 | public override sealed void SwapIndex(int i, int j)
|
|---|
| 993 | {
|
|---|
| 994 | sign.SwapIndex(i, j);
|
|---|
| 995 | index.SwapIndex(i, j);
|
|---|
| 996 | QD.SwapIndex(i, j);
|
|---|
| 997 | }
|
|---|
| 998 |
|
|---|
| 999 | public override sealed float[] GetQ(int i, int len)
|
|---|
| 1000 | {
|
|---|
| 1001 | float[] data = null;
|
|---|
| 1002 | int j, real_i = index[i];
|
|---|
| 1003 | if (cache.GetData(real_i, ref data, l) < l)
|
|---|
| 1004 | {
|
|---|
| 1005 | for (j = 0; j < l; j++)
|
|---|
| 1006 | data[j] = (float)KernelFunction(real_i, j);
|
|---|
| 1007 | }
|
|---|
| 1008 |
|
|---|
| 1009 | // reorder and copy
|
|---|
| 1010 | float[] buf = buffer[next_buffer];
|
|---|
| 1011 | next_buffer = 1 - next_buffer;
|
|---|
| 1012 | sbyte si = sign[i];
|
|---|
| 1013 | for (j = 0; j < len; j++)
|
|---|
| 1014 | buf[j] = (float)si * sign[j] * data[index[j]];
|
|---|
| 1015 | return buf;
|
|---|
| 1016 | }
|
|---|
| 1017 |
|
|---|
| 1018 | public override sealed float[] GetQD()
|
|---|
| 1019 | {
|
|---|
| 1020 | return QD;
|
|---|
| 1021 | }
|
|---|
| 1022 | }
|
|---|
| 1023 |
|
|---|
| 1024 | internal class Procedures
|
|---|
| 1025 | {
|
|---|
| 1026 | private static bool _verbose;
|
|---|
| 1027 | public static bool IsVerbose
|
|---|
| 1028 | {
|
|---|
| 1029 | get
|
|---|
| 1030 | {
|
|---|
| 1031 | return _verbose;
|
|---|
| 1032 | }
|
|---|
| 1033 | set
|
|---|
| 1034 | {
|
|---|
| 1035 | _verbose = value;
|
|---|
| 1036 | }
|
|---|
| 1037 | }
|
|---|
| 1038 | //
|
|---|
| 1039 | // construct and solve various formulations
|
|---|
| 1040 | //
|
|---|
| 1041 | public const int LIBSVM_VERSION = 289;
|
|---|
| 1042 |
|
|---|
| 1043 | public static TextWriter svm_print_string = Console.Out;
|
|---|
| 1044 |
|
|---|
| 1045 | public static void info(string s)
|
|---|
| 1046 | {
|
|---|
| 1047 | if(_verbose)
|
|---|
| 1048 | svm_print_string.Write(s);
|
|---|
| 1049 | }
|
|---|
| 1050 |
|
|---|
| 1051 | private static void solve_c_svc(Problem prob, Parameter param,
|
|---|
| 1052 | double[] alpha, Solver.SolutionInfo si,
|
|---|
| 1053 | double Cp, double Cn)
|
|---|
| 1054 | {
|
|---|
| 1055 | int l = prob.Count;
|
|---|
| 1056 | double[] Minus_ones = new double[l];
|
|---|
| 1057 | sbyte[] y = new sbyte[l];
|
|---|
| 1058 |
|
|---|
| 1059 | int i;
|
|---|
| 1060 |
|
|---|
| 1061 | for (i = 0; i < l; i++)
|
|---|
| 1062 | {
|
|---|
| 1063 | alpha[i] = 0;
|
|---|
| 1064 | Minus_ones[i] = -1;
|
|---|
| 1065 | if (prob.Y[i] > 0) y[i] = +1; else y[i] = -1;
|
|---|
| 1066 | }
|
|---|
| 1067 |
|
|---|
| 1068 | Solver s = new Solver();
|
|---|
| 1069 | s.Solve(l, new SVC_Q(prob, param, y), Minus_ones, y,
|
|---|
| 1070 | alpha, Cp, Cn, param.EPS, si, param.Shrinking);
|
|---|
| 1071 |
|
|---|
| 1072 | double sum_alpha = 0;
|
|---|
| 1073 | for (i = 0; i < l; i++)
|
|---|
| 1074 | sum_alpha += alpha[i];
|
|---|
| 1075 |
|
|---|
| 1076 | if (Cp == Cn)
|
|---|
| 1077 | Procedures.info("nu = " + sum_alpha / (Cp * prob.Count) + "\n");
|
|---|
| 1078 |
|
|---|
| 1079 | for (i = 0; i < l; i++)
|
|---|
| 1080 | alpha[i] *= y[i];
|
|---|
| 1081 | }
|
|---|
| 1082 |
|
|---|
| 1083 | private static void solve_nu_svc(Problem prob, Parameter param,
|
|---|
| 1084 | double[] alpha, Solver.SolutionInfo si)
|
|---|
| 1085 | {
|
|---|
| 1086 | int i;
|
|---|
| 1087 | int l = prob.Count;
|
|---|
| 1088 | double nu = param.Nu;
|
|---|
| 1089 |
|
|---|
| 1090 | sbyte[] y = new sbyte[l];
|
|---|
| 1091 |
|
|---|
| 1092 | for (i = 0; i < l; i++)
|
|---|
| 1093 | if (prob.Y[i] > 0)
|
|---|
| 1094 | y[i] = +1;
|
|---|
| 1095 | else
|
|---|
| 1096 | y[i] = -1;
|
|---|
| 1097 |
|
|---|
| 1098 | double sum_pos = nu * l / 2;
|
|---|
| 1099 | double sum_neg = nu * l / 2;
|
|---|
| 1100 |
|
|---|
| 1101 | for (i = 0; i < l; i++)
|
|---|
| 1102 | if (y[i] == +1)
|
|---|
| 1103 | {
|
|---|
| 1104 | alpha[i] = Math.Min(1.0, sum_pos);
|
|---|
| 1105 | sum_pos -= alpha[i];
|
|---|
| 1106 | }
|
|---|
| 1107 | else
|
|---|
| 1108 | {
|
|---|
| 1109 | alpha[i] = Math.Min(1.0, sum_neg);
|
|---|
| 1110 | sum_neg -= alpha[i];
|
|---|
| 1111 | }
|
|---|
| 1112 |
|
|---|
| 1113 | double[] zeros = new double[l];
|
|---|
| 1114 |
|
|---|
| 1115 | for (i = 0; i < l; i++)
|
|---|
| 1116 | zeros[i] = 0;
|
|---|
| 1117 |
|
|---|
| 1118 | Solver_NU s = new Solver_NU();
|
|---|
| 1119 | s.Solve(l, new SVC_Q(prob, param, y), zeros, y, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
|
|---|
| 1120 | double r = si.r;
|
|---|
| 1121 |
|
|---|
| 1122 | Procedures.info("C = " + 1 / r + "\n");
|
|---|
| 1123 |
|
|---|
| 1124 | for (i = 0; i < l; i++)
|
|---|
| 1125 | alpha[i] *= y[i] / r;
|
|---|
| 1126 |
|
|---|
| 1127 | si.rho /= r;
|
|---|
| 1128 | si.obj /= (r * r);
|
|---|
| 1129 | si.upper_bound_p = 1 / r;
|
|---|
| 1130 | si.upper_bound_n = 1 / r;
|
|---|
| 1131 | }
|
|---|
| 1132 |
|
|---|
| 1133 | private static void solve_one_class(Problem prob, Parameter param,
|
|---|
| 1134 | double[] alpha, Solver.SolutionInfo si)
|
|---|
| 1135 | {
|
|---|
| 1136 | int l = prob.Count;
|
|---|
| 1137 | double[] zeros = new double[l];
|
|---|
| 1138 | sbyte[] ones = new sbyte[l];
|
|---|
| 1139 | int i;
|
|---|
| 1140 |
|
|---|
| 1141 | int n = (int)(param.Nu * prob.Count); // # of alpha's at upper bound
|
|---|
| 1142 |
|
|---|
| 1143 | for (i = 0; i < n; i++)
|
|---|
| 1144 | alpha[i] = 1;
|
|---|
| 1145 | if (n < prob.Count)
|
|---|
| 1146 | alpha[n] = param.Nu * prob.Count - n;
|
|---|
| 1147 | for (i = n + 1; i < l; i++)
|
|---|
| 1148 | alpha[i] = 0;
|
|---|
| 1149 |
|
|---|
| 1150 | for (i = 0; i < l; i++)
|
|---|
| 1151 | {
|
|---|
| 1152 | zeros[i] = 0;
|
|---|
| 1153 | ones[i] = 1;
|
|---|
| 1154 | }
|
|---|
| 1155 |
|
|---|
| 1156 | Solver s = new Solver();
|
|---|
| 1157 | s.Solve(l, new ONE_CLASS_Q(prob, param), zeros, ones, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
|
|---|
| 1158 | }
|
|---|
| 1159 |
|
|---|
| 1160 | private static void solve_epsilon_svr(Problem prob, Parameter param, double[] alpha, Solver.SolutionInfo si)
|
|---|
| 1161 | {
|
|---|
| 1162 | int l = prob.Count;
|
|---|
| 1163 | double[] alpha2 = new double[2 * l];
|
|---|
| 1164 | double[] linear_term = new double[2 * l];
|
|---|
| 1165 | sbyte[] y = new sbyte[2 * l];
|
|---|
| 1166 | int i;
|
|---|
| 1167 |
|
|---|
| 1168 | for (i = 0; i < l; i++)
|
|---|
| 1169 | {
|
|---|
| 1170 | alpha2[i] = 0;
|
|---|
| 1171 | linear_term[i] = param.P - prob.Y[i];
|
|---|
| 1172 | y[i] = 1;
|
|---|
| 1173 |
|
|---|
| 1174 | alpha2[i + l] = 0;
|
|---|
| 1175 | linear_term[i + l] = param.P + prob.Y[i];
|
|---|
| 1176 | y[i + l] = -1;
|
|---|
| 1177 | }
|
|---|
| 1178 |
|
|---|
| 1179 | Solver s = new Solver();
|
|---|
| 1180 | s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, param.C, param.C, param.EPS, si, param.Shrinking);
|
|---|
| 1181 |
|
|---|
| 1182 | double sum_alpha = 0;
|
|---|
| 1183 | for (i = 0; i < l; i++)
|
|---|
| 1184 | {
|
|---|
| 1185 | alpha[i] = alpha2[i] - alpha2[i + l];
|
|---|
| 1186 | sum_alpha += Math.Abs(alpha[i]);
|
|---|
| 1187 | }
|
|---|
| 1188 | Procedures.info("nu = " + sum_alpha / (param.C * l) + "\n");
|
|---|
| 1189 | }
|
|---|
| 1190 |
|
|---|
| 1191 | private static void solve_nu_svr(Problem prob, Parameter param,
|
|---|
| 1192 | double[] alpha, Solver.SolutionInfo si)
|
|---|
| 1193 | {
|
|---|
| 1194 | int l = prob.Count;
|
|---|
| 1195 | double C = param.C;
|
|---|
| 1196 | double[] alpha2 = new double[2 * l];
|
|---|
| 1197 | double[] linear_term = new double[2 * l];
|
|---|
| 1198 | sbyte[] y = new sbyte[2 * l];
|
|---|
| 1199 | int i;
|
|---|
| 1200 |
|
|---|
| 1201 | double sum = C * param.Nu * l / 2;
|
|---|
| 1202 | for (i = 0; i < l; i++)
|
|---|
| 1203 | {
|
|---|
| 1204 | alpha2[i] = alpha2[i + l] = Math.Min(sum, C);
|
|---|
| 1205 | sum -= alpha2[i];
|
|---|
| 1206 |
|
|---|
| 1207 | linear_term[i] = -prob.Y[i];
|
|---|
| 1208 | y[i] = 1;
|
|---|
| 1209 |
|
|---|
| 1210 | linear_term[i + l] = prob.Y[i];
|
|---|
| 1211 | y[i + l] = -1;
|
|---|
| 1212 | }
|
|---|
| 1213 |
|
|---|
| 1214 | Solver_NU s = new Solver_NU();
|
|---|
| 1215 | s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, C, C, param.EPS, si, param.Shrinking);
|
|---|
| 1216 |
|
|---|
| 1217 | Procedures.info("epsilon = " + (-si.r) + "\n");
|
|---|
| 1218 |
|
|---|
| 1219 | for (i = 0; i < l; i++)
|
|---|
| 1220 | alpha[i] = alpha2[i] - alpha2[i + l];
|
|---|
| 1221 | }
|
|---|
| 1222 |
|
|---|
| 1223 | //
|
|---|
| 1224 | // decision_function
|
|---|
| 1225 | //
|
|---|
| 1226 | internal class decision_function
|
|---|
| 1227 | {
|
|---|
| 1228 | public double[] alpha;
|
|---|
| 1229 | public double rho;
|
|---|
| 1230 | };
|
|---|
| 1231 |
|
|---|
| 1232 | static decision_function svm_train_one(Problem prob, Parameter param, double Cp, double Cn)
|
|---|
| 1233 | {
|
|---|
| 1234 | double[] alpha = new double[prob.Count];
|
|---|
| 1235 | Solver.SolutionInfo si = new Solver.SolutionInfo();
|
|---|
| 1236 | switch (param.SvmType)
|
|---|
| 1237 | {
|
|---|
| 1238 | case SvmType.C_SVC:
|
|---|
| 1239 | solve_c_svc(prob, param, alpha, si, Cp, Cn);
|
|---|
| 1240 | break;
|
|---|
| 1241 | case SvmType.NU_SVC:
|
|---|
| 1242 | solve_nu_svc(prob, param, alpha, si);
|
|---|
| 1243 | break;
|
|---|
| 1244 | case SvmType.ONE_CLASS:
|
|---|
| 1245 | solve_one_class(prob, param, alpha, si);
|
|---|
| 1246 | break;
|
|---|
| 1247 | case SvmType.EPSILON_SVR:
|
|---|
| 1248 | solve_epsilon_svr(prob, param, alpha, si);
|
|---|
| 1249 | break;
|
|---|
| 1250 | case SvmType.NU_SVR:
|
|---|
| 1251 | solve_nu_svr(prob, param, alpha, si);
|
|---|
| 1252 | break;
|
|---|
| 1253 | }
|
|---|
| 1254 |
|
|---|
| 1255 | Procedures.info("obj = " + si.obj + ", rho = " + si.rho + "\n");
|
|---|
| 1256 |
|
|---|
| 1257 | // output SVs
|
|---|
| 1258 |
|
|---|
| 1259 | int nSV = 0;
|
|---|
| 1260 | int nBSV = 0;
|
|---|
| 1261 | for (int i = 0; i < prob.Count; i++)
|
|---|
| 1262 | {
|
|---|
| 1263 | if (Math.Abs(alpha[i]) > 0)
|
|---|
| 1264 | {
|
|---|
| 1265 | ++nSV;
|
|---|
| 1266 | if (prob.Y[i] > 0)
|
|---|
| 1267 | {
|
|---|
| 1268 | if (Math.Abs(alpha[i]) >= si.upper_bound_p)
|
|---|
| 1269 | ++nBSV;
|
|---|
| 1270 | }
|
|---|
| 1271 | else
|
|---|
| 1272 | {
|
|---|
| 1273 | if (Math.Abs(alpha[i]) >= si.upper_bound_n)
|
|---|
| 1274 | ++nBSV;
|
|---|
| 1275 | }
|
|---|
| 1276 | }
|
|---|
| 1277 | }
|
|---|
| 1278 |
|
|---|
| 1279 | Procedures.info("nSV = " + nSV + ", nBSV = " + nBSV + "\n");
|
|---|
| 1280 |
|
|---|
| 1281 | decision_function f = new decision_function();
|
|---|
| 1282 | f.alpha = alpha;
|
|---|
| 1283 | f.rho = si.rho;
|
|---|
| 1284 | return f;
|
|---|
| 1285 | }
|
|---|
| 1286 |
|
|---|
| 1287 | // Platt's binary SVM Probablistic Output: an improvement from Lin et al.
|
|---|
| 1288 | private static void sigmoid_train(int l, double[] dec_values, double[] labels,
|
|---|
| 1289 | double[] probAB)
|
|---|
| 1290 | {
|
|---|
| 1291 | double A, B;
|
|---|
| 1292 | double prior1 = 0, prior0 = 0;
|
|---|
| 1293 | int i;
|
|---|
| 1294 |
|
|---|
| 1295 | for (i = 0; i < l; i++)
|
|---|
| 1296 | if (labels[i] > 0) prior1 += 1;
|
|---|
| 1297 | else prior0 += 1;
|
|---|
| 1298 |
|
|---|
| 1299 | int Max_iter = 100; // Maximal number of iterations
|
|---|
| 1300 | double Min_step = 1e-10; // Minimal step taken in line search
|
|---|
| 1301 | double sigma = 1e-12; // For numerically strict PD of Hessian
|
|---|
| 1302 | double eps = 1e-5;
|
|---|
| 1303 | double hiTarget = (prior1 + 1.0) / (prior1 + 2.0);
|
|---|
| 1304 | double loTarget = 1 / (prior0 + 2.0);
|
|---|
| 1305 | double[] t = new double[l];
|
|---|
| 1306 | double fApB, p, q, h11, h22, h21, g1, g2, det, dA, dB, gd, stepsize;
|
|---|
| 1307 | double newA, newB, newf, d1, d2;
|
|---|
| 1308 | int iter;
|
|---|
| 1309 |
|
|---|
| 1310 | // Initial Point and Initial Fun Value
|
|---|
| 1311 | A = 0.0; B = Math.Log((prior0 + 1.0) / (prior1 + 1.0));
|
|---|
| 1312 | double fval = 0.0;
|
|---|
| 1313 |
|
|---|
| 1314 | for (i = 0; i < l; i++)
|
|---|
| 1315 | {
|
|---|
| 1316 | if (labels[i] > 0) t[i] = hiTarget;
|
|---|
| 1317 | else t[i] = loTarget;
|
|---|
| 1318 | fApB = dec_values[i] * A + B;
|
|---|
| 1319 | if (fApB >= 0)
|
|---|
| 1320 | fval += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
|
|---|
| 1321 | else
|
|---|
| 1322 | fval += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
|
|---|
| 1323 | }
|
|---|
| 1324 | for (iter = 0; iter < Max_iter; iter++)
|
|---|
| 1325 | {
|
|---|
| 1326 | // Update Gradient and Hessian (use H' = H + sigma I)
|
|---|
| 1327 | h11 = sigma; // numerically ensures strict PD
|
|---|
| 1328 | h22 = sigma;
|
|---|
| 1329 | h21 = 0.0; g1 = 0.0; g2 = 0.0;
|
|---|
| 1330 | for (i = 0; i < l; i++)
|
|---|
| 1331 | {
|
|---|
| 1332 | fApB = dec_values[i] * A + B;
|
|---|
| 1333 | if (fApB >= 0)
|
|---|
| 1334 | {
|
|---|
| 1335 | p = Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
|
|---|
| 1336 | q = 1.0 / (1.0 + Math.Exp(-fApB));
|
|---|
| 1337 | }
|
|---|
| 1338 | else
|
|---|
| 1339 | {
|
|---|
| 1340 | p = 1.0 / (1.0 + Math.Exp(fApB));
|
|---|
| 1341 | q = Math.Exp(fApB) / (1.0 + Math.Exp(fApB));
|
|---|
| 1342 | }
|
|---|
| 1343 | d2 = p * q;
|
|---|
| 1344 | h11 += dec_values[i] * dec_values[i] * d2;
|
|---|
| 1345 | h22 += d2;
|
|---|
| 1346 | h21 += dec_values[i] * d2;
|
|---|
| 1347 | d1 = t[i] - p;
|
|---|
| 1348 | g1 += dec_values[i] * d1;
|
|---|
| 1349 | g2 += d1;
|
|---|
| 1350 | }
|
|---|
| 1351 |
|
|---|
| 1352 | // Stopping Criteria
|
|---|
| 1353 | if (Math.Abs(g1) < eps && Math.Abs(g2) < eps)
|
|---|
| 1354 | break;
|
|---|
| 1355 |
|
|---|
| 1356 | // Finding Newton direction: -inv(H') * g
|
|---|
| 1357 | det = h11 * h22 - h21 * h21;
|
|---|
| 1358 | dA = -(h22 * g1 - h21 * g2) / det;
|
|---|
| 1359 | dB = -(-h21 * g1 + h11 * g2) / det;
|
|---|
| 1360 | gd = g1 * dA + g2 * dB;
|
|---|
| 1361 |
|
|---|
| 1362 |
|
|---|
| 1363 | stepsize = 1; // Line Search
|
|---|
| 1364 | while (stepsize >= Min_step)
|
|---|
| 1365 | {
|
|---|
| 1366 | newA = A + stepsize * dA;
|
|---|
| 1367 | newB = B + stepsize * dB;
|
|---|
| 1368 |
|
|---|
| 1369 | // New function value
|
|---|
| 1370 | newf = 0.0;
|
|---|
| 1371 | for (i = 0; i < l; i++)
|
|---|
| 1372 | {
|
|---|
| 1373 | fApB = dec_values[i] * newA + newB;
|
|---|
| 1374 | if (fApB >= 0)
|
|---|
| 1375 | newf += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
|
|---|
| 1376 | else
|
|---|
| 1377 | newf += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
|
|---|
| 1378 | }
|
|---|
| 1379 | // Check sufficient decrease
|
|---|
| 1380 | if (newf < fval + 0.0001 * stepsize * gd)
|
|---|
| 1381 | {
|
|---|
| 1382 | A = newA; B = newB; fval = newf;
|
|---|
| 1383 | break;
|
|---|
| 1384 | }
|
|---|
| 1385 | else
|
|---|
| 1386 | stepsize = stepsize / 2.0;
|
|---|
| 1387 | }
|
|---|
| 1388 |
|
|---|
| 1389 | if (stepsize < Min_step)
|
|---|
| 1390 | {
|
|---|
| 1391 | Procedures.info("Line search fails in two-class probability estimates\n");
|
|---|
| 1392 | break;
|
|---|
| 1393 | }
|
|---|
| 1394 | }
|
|---|
| 1395 |
|
|---|
| 1396 | if (iter >= Max_iter)
|
|---|
| 1397 | Procedures.info("Reaching Maximal iterations in two-class probability estimates\n");
|
|---|
| 1398 | probAB[0] = A; probAB[1] = B;
|
|---|
| 1399 | }
|
|---|
| 1400 |
|
|---|
| 1401 | private static double sigmoid_predict(double decision_value, double A, double B)
|
|---|
| 1402 | {
|
|---|
| 1403 | double fApB = decision_value * A + B;
|
|---|
| 1404 | if (fApB >= 0)
|
|---|
| 1405 | return Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
|
|---|
| 1406 | else
|
|---|
| 1407 | return 1.0 / (1 + Math.Exp(fApB));
|
|---|
| 1408 | }
|
|---|
| 1409 |
|
|---|
| 1410 | // Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
|
|---|
| 1411 | private static void multiclass_probability(int k, double[,] r, double[] p)
|
|---|
| 1412 | {
|
|---|
| 1413 | int t, j;
|
|---|
| 1414 | int iter = 0, Max_iter = Math.Max(100, k);
|
|---|
| 1415 | double[,] Q = new double[k,k];
|
|---|
| 1416 | double[] Qp = new double[k];
|
|---|
| 1417 | double pQp, eps = 0.005 / k;
|
|---|
| 1418 |
|
|---|
| 1419 | for (t = 0; t < k; t++)
|
|---|
| 1420 | {
|
|---|
| 1421 | p[t] = 1.0 / k; // Valid if k = 1
|
|---|
| 1422 | Q[t,t] = 0;
|
|---|
| 1423 | for (j = 0; j < t; j++)
|
|---|
| 1424 | {
|
|---|
| 1425 | Q[t,t] += r[j,t] * r[j,t];
|
|---|
| 1426 | Q[t,j] = Q[j,t];
|
|---|
| 1427 | }
|
|---|
| 1428 | for (j = t + 1; j < k; j++)
|
|---|
| 1429 | {
|
|---|
| 1430 | Q[t,t] += r[j,t] * r[j,t];
|
|---|
| 1431 | Q[t,j] = -r[j,t] * r[t,j];
|
|---|
| 1432 | }
|
|---|
| 1433 | }
|
|---|
| 1434 | for (iter = 0; iter < Max_iter; iter++)
|
|---|
| 1435 | {
|
|---|
| 1436 | // stopping condition, recalculate QP,pQP for numerical accuracy
|
|---|
| 1437 | pQp = 0;
|
|---|
| 1438 | for (t = 0; t < k; t++)
|
|---|
| 1439 | {
|
|---|
| 1440 | Qp[t] = 0;
|
|---|
| 1441 | for (j = 0; j < k; j++)
|
|---|
| 1442 | Qp[t] += Q[t,j] * p[j];
|
|---|
| 1443 | pQp += p[t] * Qp[t];
|
|---|
| 1444 | }
|
|---|
| 1445 | double Max_error = 0;
|
|---|
| 1446 | for (t = 0; t < k; t++)
|
|---|
| 1447 | {
|
|---|
| 1448 | double error = Math.Abs(Qp[t] - pQp);
|
|---|
| 1449 | if (error > Max_error)
|
|---|
| 1450 | Max_error = error;
|
|---|
| 1451 | }
|
|---|
| 1452 | if (Max_error < eps) break;
|
|---|
| 1453 |
|
|---|
| 1454 | for (t = 0; t < k; t++)
|
|---|
| 1455 | {
|
|---|
| 1456 | double diff = (-Qp[t] + pQp) / Q[t,t];
|
|---|
| 1457 | p[t] += diff;
|
|---|
| 1458 | pQp = (pQp + diff * (diff * Q[t,t] + 2 * Qp[t])) / (1 + diff) / (1 + diff);
|
|---|
| 1459 | for (j = 0; j < k; j++)
|
|---|
| 1460 | {
|
|---|
| 1461 | Qp[j] = (Qp[j] + diff * Q[t,j]) / (1 + diff);
|
|---|
| 1462 | p[j] /= (1 + diff);
|
|---|
| 1463 | }
|
|---|
| 1464 | }
|
|---|
| 1465 | }
|
|---|
| 1466 | if (iter >= Max_iter)
|
|---|
| 1467 | Procedures.info("Exceeds Max_iter in multiclass_prob\n");
|
|---|
| 1468 | }
|
|---|
| 1469 |
|
|---|
| 1470 | // Cross-validation decision values for probability estimates
|
|---|
| 1471 | private static void svm_binary_svc_probability(Problem prob, Parameter param, double Cp, double Cn, double[] probAB)
|
|---|
| 1472 | {
|
|---|
| 1473 | int i;
|
|---|
| 1474 | int nr_fold = 5;
|
|---|
| 1475 | int[] perm = new int[prob.Count];
|
|---|
| 1476 | double[] dec_values = new double[prob.Count];
|
|---|
| 1477 |
|
|---|
| 1478 | // random shuffle
|
|---|
| 1479 | Random rand = new Random();
|
|---|
| 1480 | for (i = 0; i < prob.Count; i++) perm[i] = i;
|
|---|
| 1481 | for (i = 0; i < prob.Count; i++)
|
|---|
| 1482 | {
|
|---|
| 1483 | int j = i + (int)(rand.NextDouble() * (prob.Count - i));
|
|---|
| 1484 | do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
|
|---|
| 1485 | }
|
|---|
| 1486 | for (i = 0; i < nr_fold; i++)
|
|---|
| 1487 | {
|
|---|
| 1488 | int begin = i * prob.Count / nr_fold;
|
|---|
| 1489 | int end = (i + 1) * prob.Count / nr_fold;
|
|---|
| 1490 | int j, k;
|
|---|
| 1491 | Problem subprob = new Problem();
|
|---|
| 1492 |
|
|---|
| 1493 | subprob.Count = prob.Count - (end - begin);
|
|---|
| 1494 | subprob.X = new Node[subprob.Count][];
|
|---|
| 1495 | subprob.Y = new double[subprob.Count];
|
|---|
| 1496 |
|
|---|
| 1497 | k = 0;
|
|---|
| 1498 | for (j = 0; j < begin; j++)
|
|---|
| 1499 | {
|
|---|
| 1500 | subprob.X[k] = prob.X[perm[j]];
|
|---|
| 1501 | subprob.Y[k] = prob.Y[perm[j]];
|
|---|
| 1502 | ++k;
|
|---|
| 1503 | }
|
|---|
| 1504 | for (j = end; j < prob.Count; j++)
|
|---|
| 1505 | {
|
|---|
| 1506 | subprob.X[k] = prob.X[perm[j]];
|
|---|
| 1507 | subprob.Y[k] = prob.Y[perm[j]];
|
|---|
| 1508 | ++k;
|
|---|
| 1509 | }
|
|---|
| 1510 | int p_count = 0, n_count = 0;
|
|---|
| 1511 | for (j = 0; j < k; j++)
|
|---|
| 1512 | if (subprob.Y[j] > 0)
|
|---|
| 1513 | p_count++;
|
|---|
| 1514 | else
|
|---|
| 1515 | n_count++;
|
|---|
| 1516 |
|
|---|
| 1517 | if (p_count == 0 && n_count == 0)
|
|---|
| 1518 | for (j = begin; j < end; j++)
|
|---|
| 1519 | dec_values[perm[j]] = 0;
|
|---|
| 1520 | else if (p_count > 0 && n_count == 0)
|
|---|
| 1521 | for (j = begin; j < end; j++)
|
|---|
| 1522 | dec_values[perm[j]] = 1;
|
|---|
| 1523 | else if (p_count == 0 && n_count > 0)
|
|---|
| 1524 | for (j = begin; j < end; j++)
|
|---|
| 1525 | dec_values[perm[j]] = -1;
|
|---|
| 1526 | else
|
|---|
| 1527 | {
|
|---|
| 1528 | Parameter subparam = (Parameter)param.Clone();
|
|---|
| 1529 | subparam.Probability = false;
|
|---|
| 1530 | subparam.C = 1.0;
|
|---|
| 1531 | subparam.Weights[1] = Cp;
|
|---|
| 1532 | subparam.Weights[-1] = Cn;
|
|---|
| 1533 | Model submodel = svm_train(subprob, subparam);
|
|---|
| 1534 | for (j = begin; j < end; j++)
|
|---|
| 1535 | {
|
|---|
| 1536 | double[] dec_value = new double[1];
|
|---|
| 1537 | svm_predict_values(submodel, prob.X[perm[j]], dec_value);
|
|---|
| 1538 | dec_values[perm[j]] = dec_value[0];
|
|---|
| 1539 | // ensure +1 -1 order; reason not using CV subroutine
|
|---|
| 1540 | dec_values[perm[j]] *= submodel.ClassLabels[0];
|
|---|
| 1541 | }
|
|---|
| 1542 | }
|
|---|
| 1543 | }
|
|---|
| 1544 | sigmoid_train(prob.Count, dec_values, prob.Y, probAB);
|
|---|
| 1545 | }
|
|---|
| 1546 |
|
|---|
| 1547 | // Return parameter of a Laplace distribution
|
|---|
| 1548 | private static double svm_svr_probability(Problem prob, Parameter param)
|
|---|
| 1549 | {
|
|---|
| 1550 | int i;
|
|---|
| 1551 | int nr_fold = 5;
|
|---|
| 1552 | double[] ymv = new double[prob.Count];
|
|---|
| 1553 | double mae = 0;
|
|---|
| 1554 |
|
|---|
| 1555 | Parameter newparam = (Parameter)param.Clone();
|
|---|
| 1556 | newparam.Probability = false;
|
|---|
| 1557 | svm_cross_validation(prob, newparam, nr_fold, ymv, true);
|
|---|
| 1558 | for (i = 0; i < prob.Count; i++)
|
|---|
| 1559 | {
|
|---|
| 1560 | ymv[i] = prob.Y[i] - ymv[i];
|
|---|
| 1561 | mae += Math.Abs(ymv[i]);
|
|---|
| 1562 | }
|
|---|
| 1563 | mae /= prob.Count;
|
|---|
| 1564 | double std = Math.Sqrt(2 * mae * mae);
|
|---|
| 1565 | int count = 0;
|
|---|
| 1566 | mae = 0;
|
|---|
| 1567 | for (i = 0; i < prob.Count; i++)
|
|---|
| 1568 | if (Math.Abs(ymv[i]) > 5 * std)
|
|---|
| 1569 | count = count + 1;
|
|---|
| 1570 | else
|
|---|
| 1571 | mae += Math.Abs(ymv[i]);
|
|---|
| 1572 | mae /= (prob.Count - count);
|
|---|
| 1573 | Procedures.info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma=" + mae + "\n");
|
|---|
| 1574 | return mae;
|
|---|
| 1575 | }
|
|---|
| 1576 |
|
|---|
| 1577 | // label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
|
|---|
| 1578 | // perm, length l, must be allocated before calling this subroutine
|
|---|
| 1579 | private static void svm_group_classes(Problem prob, int[] nr_class_ret, int[][] label_ret, int[][] start_ret, int[][] count_ret, int[] perm)
|
|---|
| 1580 | {
|
|---|
| 1581 | int l = prob.Count;
|
|---|
| 1582 | int Max_nr_class = 16;
|
|---|
| 1583 | int nr_class = 0;
|
|---|
| 1584 | int[] label = new int[Max_nr_class];
|
|---|
| 1585 | int[] count = new int[Max_nr_class];
|
|---|
| 1586 | int[] data_label = new int[l];
|
|---|
| 1587 | int i;
|
|---|
| 1588 |
|
|---|
| 1589 | for (i = 0; i < l; i++)
|
|---|
| 1590 | {
|
|---|
| 1591 | int this_label = (int)(prob.Y[i]);
|
|---|
| 1592 | int j;
|
|---|
| 1593 | for (j = 0; j < nr_class; j++)
|
|---|
| 1594 | {
|
|---|
| 1595 | if (this_label == label[j])
|
|---|
| 1596 | {
|
|---|
| 1597 | ++count[j];
|
|---|
| 1598 | break;
|
|---|
| 1599 | }
|
|---|
| 1600 | }
|
|---|
| 1601 | data_label[i] = j;
|
|---|
| 1602 | if (j == nr_class)
|
|---|
| 1603 | {
|
|---|
| 1604 | if (nr_class == Max_nr_class)
|
|---|
| 1605 | {
|
|---|
| 1606 | Max_nr_class *= 2;
|
|---|
| 1607 | int[] new_data = new int[Max_nr_class];
|
|---|
| 1608 | Array.Copy(label, 0, new_data, 0, label.Length);
|
|---|
| 1609 | label = new_data;
|
|---|
| 1610 | new_data = new int[Max_nr_class];
|
|---|
| 1611 | Array.Copy(count, 0, new_data, 0, count.Length);
|
|---|
| 1612 | count = new_data;
|
|---|
| 1613 | }
|
|---|
| 1614 | label[nr_class] = this_label;
|
|---|
| 1615 | count[nr_class] = 1;
|
|---|
| 1616 | ++nr_class;
|
|---|
| 1617 | }
|
|---|
| 1618 | }
|
|---|
| 1619 |
|
|---|
| 1620 | int[] start = new int[nr_class];
|
|---|
| 1621 | start[0] = 0;
|
|---|
| 1622 | for (i = 1; i < nr_class; i++)
|
|---|
| 1623 | start[i] = start[i - 1] + count[i - 1];
|
|---|
| 1624 | for (i = 0; i < l; i++)
|
|---|
| 1625 | {
|
|---|
| 1626 | perm[start[data_label[i]]] = i;
|
|---|
| 1627 | ++start[data_label[i]];
|
|---|
| 1628 | }
|
|---|
| 1629 | start[0] = 0;
|
|---|
| 1630 | for (i = 1; i < nr_class; i++)
|
|---|
| 1631 | start[i] = start[i - 1] + count[i - 1];
|
|---|
| 1632 |
|
|---|
| 1633 | nr_class_ret[0] = nr_class;
|
|---|
| 1634 | label_ret[0] = label;
|
|---|
| 1635 | start_ret[0] = start;
|
|---|
| 1636 | count_ret[0] = count;
|
|---|
| 1637 | }
|
|---|
| 1638 |
|
|---|
| 1639 | //
|
|---|
| 1640 | // Interface functions
|
|---|
| 1641 | //
|
|---|
| 1642 | public static Model svm_train(Problem prob, Parameter param)
|
|---|
| 1643 | {
|
|---|
| 1644 | Model model = new Model();
|
|---|
| 1645 | model.Parameter = param;
|
|---|
| 1646 |
|
|---|
| 1647 | if (param.SvmType == SvmType.ONE_CLASS ||
|
|---|
| 1648 | param.SvmType == SvmType.EPSILON_SVR ||
|
|---|
| 1649 | param.SvmType == SvmType.NU_SVR)
|
|---|
| 1650 | {
|
|---|
| 1651 | // regression or one-class-svm
|
|---|
| 1652 | model.NumberOfClasses = 2;
|
|---|
| 1653 | model.ClassLabels = null;
|
|---|
| 1654 | model.NumberOfSVPerClass = null;
|
|---|
| 1655 | model.PairwiseProbabilityA = null; model.PairwiseProbabilityB = null;
|
|---|
| 1656 | model.SupportVectorCoefficients = new double[1][];
|
|---|
| 1657 |
|
|---|
| 1658 | if (param.Probability &&
|
|---|
| 1659 | (param.SvmType == SvmType.EPSILON_SVR ||
|
|---|
| 1660 | param.SvmType == SvmType.NU_SVR))
|
|---|
| 1661 | {
|
|---|
| 1662 | model.PairwiseProbabilityA = new double[1];
|
|---|
| 1663 | model.PairwiseProbabilityA[0] = svm_svr_probability(prob, param);
|
|---|
| 1664 | }
|
|---|
| 1665 |
|
|---|
| 1666 | decision_function f = svm_train_one(prob, param, 0, 0);
|
|---|
| 1667 | model.Rho = new double[1];
|
|---|
| 1668 | model.Rho[0] = f.rho;
|
|---|
| 1669 |
|
|---|
| 1670 | int nSV = 0;
|
|---|
| 1671 | int i;
|
|---|
| 1672 | for (i = 0; i < prob.Count; i++)
|
|---|
| 1673 | if (Math.Abs(f.alpha[i]) > 0) ++nSV;
|
|---|
| 1674 | model.SupportVectorCount = nSV;
|
|---|
| 1675 | model.SupportVectorIndizes = new int[nSV];
|
|---|
| 1676 | model.SupportVectors = new Node[nSV][];
|
|---|
| 1677 | model.SupportVectorCoefficients[0] = new double[nSV];
|
|---|
| 1678 |
|
|---|
| 1679 | int j = 0;
|
|---|
| 1680 | for (i = 0; i < prob.Count; i++)
|
|---|
| 1681 | if (Math.Abs(f.alpha[i]) > 0)
|
|---|
| 1682 | {
|
|---|
| 1683 | model.SupportVectors[j] = prob.X[i];
|
|---|
| 1684 | model.SupportVectorIndizes[j] = i;
|
|---|
| 1685 | model.SupportVectorCoefficients[0][j] = f.alpha[i];
|
|---|
| 1686 |
|
|---|
| 1687 | ++j;
|
|---|
| 1688 | }
|
|---|
| 1689 | }
|
|---|
| 1690 | else
|
|---|
| 1691 | {
|
|---|
| 1692 | // classification
|
|---|
| 1693 | int l = prob.Count;
|
|---|
| 1694 | int[] tmp_nr_class = new int[1];
|
|---|
| 1695 | int[][] tmp_label = new int[1][];
|
|---|
| 1696 | int[][] tmp_start = new int[1][];
|
|---|
| 1697 | int[][] tmp_count = new int[1][];
|
|---|
| 1698 | int[] perm = new int[l];
|
|---|
| 1699 |
|
|---|
| 1700 | // group training data of the same class
|
|---|
| 1701 | svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);
|
|---|
| 1702 | int nr_class = tmp_nr_class[0];
|
|---|
| 1703 | int[] label = tmp_label[0];
|
|---|
| 1704 | int[] start = tmp_start[0];
|
|---|
| 1705 | int[] count = tmp_count[0];
|
|---|
| 1706 | Node[][] x = new Node[l][];
|
|---|
| 1707 | int i;
|
|---|
| 1708 | for (i = 0; i < l; i++)
|
|---|
| 1709 | x[i] = prob.X[perm[i]];
|
|---|
| 1710 |
|
|---|
| 1711 | // calculate weighted C
|
|---|
| 1712 |
|
|---|
| 1713 | double[] weighted_C = new double[nr_class];
|
|---|
| 1714 | for (i = 0; i < nr_class; i++)
|
|---|
| 1715 | weighted_C[i] = param.C;
|
|---|
| 1716 | foreach (int weightedLabel in param.Weights.Keys)
|
|---|
| 1717 | {
|
|---|
| 1718 | int index = Array.IndexOf<int>(label, weightedLabel);
|
|---|
| 1719 | if (index < 0)
|
|---|
| 1720 | Console.Error.WriteLine("warning: class label " + weightedLabel + " specified in weight is not found");
|
|---|
| 1721 | else weighted_C[index] *= param.Weights[weightedLabel];
|
|---|
| 1722 | }
|
|---|
| 1723 |
|
|---|
| 1724 | // train k*(k-1)/2 models
|
|---|
| 1725 |
|
|---|
| 1726 | bool[] nonzero = new bool[l];
|
|---|
| 1727 | for (i = 0; i < l; i++)
|
|---|
| 1728 | nonzero[i] = false;
|
|---|
| 1729 | decision_function[] f = new decision_function[nr_class * (nr_class - 1) / 2];
|
|---|
| 1730 |
|
|---|
| 1731 | double[] probA = null, probB = null;
|
|---|
| 1732 | if (param.Probability)
|
|---|
| 1733 | {
|
|---|
| 1734 | probA = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 1735 | probB = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 1736 | }
|
|---|
| 1737 |
|
|---|
| 1738 | int p = 0;
|
|---|
| 1739 | for (i = 0; i < nr_class; i++)
|
|---|
| 1740 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 1741 | {
|
|---|
| 1742 | Problem sub_prob = new Problem();
|
|---|
| 1743 | int si = start[i], sj = start[j];
|
|---|
| 1744 | int ci = count[i], cj = count[j];
|
|---|
| 1745 | sub_prob.Count = ci + cj;
|
|---|
| 1746 | sub_prob.X = new Node[sub_prob.Count][];
|
|---|
| 1747 | sub_prob.Y = new double[sub_prob.Count];
|
|---|
| 1748 | int k;
|
|---|
| 1749 | for (k = 0; k < ci; k++)
|
|---|
| 1750 | {
|
|---|
| 1751 | sub_prob.X[k] = x[si + k];
|
|---|
| 1752 | sub_prob.Y[k] = +1;
|
|---|
| 1753 | }
|
|---|
| 1754 | for (k = 0; k < cj; k++)
|
|---|
| 1755 | {
|
|---|
| 1756 | sub_prob.X[ci + k] = x[sj + k];
|
|---|
| 1757 | sub_prob.Y[ci + k] = -1;
|
|---|
| 1758 | }
|
|---|
| 1759 |
|
|---|
| 1760 | if (param.Probability)
|
|---|
| 1761 | {
|
|---|
| 1762 | double[] probAB = new double[2];
|
|---|
| 1763 | svm_binary_svc_probability(sub_prob, param, weighted_C[i], weighted_C[j], probAB);
|
|---|
| 1764 | probA[p] = probAB[0];
|
|---|
| 1765 | probB[p] = probAB[1];
|
|---|
| 1766 | }
|
|---|
| 1767 |
|
|---|
| 1768 | f[p] = svm_train_one(sub_prob, param, weighted_C[i], weighted_C[j]);
|
|---|
| 1769 | for (k = 0; k < ci; k++)
|
|---|
| 1770 | if (!nonzero[si + k] && Math.Abs(f[p].alpha[k]) > 0)
|
|---|
| 1771 | nonzero[si + k] = true;
|
|---|
| 1772 | for (k = 0; k < cj; k++)
|
|---|
| 1773 | if (!nonzero[sj + k] && Math.Abs(f[p].alpha[ci + k]) > 0)
|
|---|
| 1774 | nonzero[sj + k] = true;
|
|---|
| 1775 | ++p;
|
|---|
| 1776 | }
|
|---|
| 1777 |
|
|---|
| 1778 | // build output
|
|---|
| 1779 |
|
|---|
| 1780 | model.NumberOfClasses = nr_class;
|
|---|
| 1781 |
|
|---|
| 1782 | model.ClassLabels = new int[nr_class];
|
|---|
| 1783 | for (i = 0; i < nr_class; i++)
|
|---|
| 1784 | model.ClassLabels[i] = label[i];
|
|---|
| 1785 |
|
|---|
| 1786 | model.Rho = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 1787 | for (i = 0; i < nr_class * (nr_class - 1) / 2; i++)
|
|---|
| 1788 | model.Rho[i] = f[i].rho;
|
|---|
| 1789 |
|
|---|
| 1790 | if (param.Probability)
|
|---|
| 1791 | {
|
|---|
| 1792 | model.PairwiseProbabilityA = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 1793 | model.PairwiseProbabilityB = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 1794 | for (i = 0; i < nr_class * (nr_class - 1) / 2; i++)
|
|---|
| 1795 | {
|
|---|
| 1796 | model.PairwiseProbabilityA[i] = probA[i];
|
|---|
| 1797 | model.PairwiseProbabilityB[i] = probB[i];
|
|---|
| 1798 | }
|
|---|
| 1799 | }
|
|---|
| 1800 | else
|
|---|
| 1801 | {
|
|---|
| 1802 | model.PairwiseProbabilityA = null;
|
|---|
| 1803 | model.PairwiseProbabilityB = null;
|
|---|
| 1804 | }
|
|---|
| 1805 |
|
|---|
| 1806 | int nnz = 0;
|
|---|
| 1807 | int[] nz_count = new int[nr_class];
|
|---|
| 1808 | model.NumberOfSVPerClass = new int[nr_class];
|
|---|
| 1809 | for (i = 0; i < nr_class; i++)
|
|---|
| 1810 | {
|
|---|
| 1811 | int nSV = 0;
|
|---|
| 1812 | for (int j = 0; j < count[i]; j++)
|
|---|
| 1813 | if (nonzero[start[i] + j])
|
|---|
| 1814 | {
|
|---|
| 1815 | ++nSV;
|
|---|
| 1816 | ++nnz;
|
|---|
| 1817 | }
|
|---|
| 1818 | model.NumberOfSVPerClass[i] = nSV;
|
|---|
| 1819 | nz_count[i] = nSV;
|
|---|
| 1820 | }
|
|---|
| 1821 |
|
|---|
| 1822 | Procedures.info("Total nSV = " + nnz + "\n");
|
|---|
| 1823 |
|
|---|
| 1824 | model.SupportVectorCount = nnz;
|
|---|
| 1825 | model.SupportVectors = new Node[nnz][];
|
|---|
| 1826 | model.SupportVectorIndizes = new int[nnz];
|
|---|
| 1827 | p = 0;
|
|---|
| 1828 | for (i = 0; i < l; i++) {
|
|---|
| 1829 | if (nonzero[i]) {
|
|---|
| 1830 | model.SupportVectors[p] = x[i];
|
|---|
| 1831 | model.SupportVectorIndizes[p] = i;
|
|---|
| 1832 | p++;
|
|---|
| 1833 | }
|
|---|
| 1834 | }
|
|---|
| 1835 |
|
|---|
| 1836 | int[] nz_start = new int[nr_class];
|
|---|
| 1837 | nz_start[0] = 0;
|
|---|
| 1838 | for (i = 1; i < nr_class; i++)
|
|---|
| 1839 | nz_start[i] = nz_start[i - 1] + nz_count[i - 1];
|
|---|
| 1840 |
|
|---|
| 1841 | model.SupportVectorCoefficients = new double[nr_class - 1][];
|
|---|
| 1842 | for (i = 0; i < nr_class - 1; i++)
|
|---|
| 1843 | model.SupportVectorCoefficients[i] = new double[nnz];
|
|---|
| 1844 |
|
|---|
| 1845 | p = 0;
|
|---|
| 1846 | for (i = 0; i < nr_class; i++)
|
|---|
| 1847 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 1848 | {
|
|---|
| 1849 | // classifier (i,j): coefficients with
|
|---|
| 1850 | // i are in sv_coef[j-1][nz_start[i]...],
|
|---|
| 1851 | // j are in sv_coef[i][nz_start[j]...]
|
|---|
| 1852 |
|
|---|
| 1853 | int si = start[i];
|
|---|
| 1854 | int sj = start[j];
|
|---|
| 1855 | int ci = count[i];
|
|---|
| 1856 | int cj = count[j];
|
|---|
| 1857 |
|
|---|
| 1858 | int q = nz_start[i];
|
|---|
| 1859 | int k;
|
|---|
| 1860 | for (k = 0; k < ci; k++)
|
|---|
| 1861 | if (nonzero[si + k])
|
|---|
| 1862 | model.SupportVectorCoefficients[j - 1][q++] = f[p].alpha[k];
|
|---|
| 1863 | q = nz_start[j];
|
|---|
| 1864 | for (k = 0; k < cj; k++)
|
|---|
| 1865 | if (nonzero[sj + k])
|
|---|
| 1866 | model.SupportVectorCoefficients[i][q++] = f[p].alpha[ci + k];
|
|---|
| 1867 | ++p;
|
|---|
| 1868 | }
|
|---|
| 1869 | }
|
|---|
| 1870 | return model;
|
|---|
| 1871 | }
|
|---|
| 1872 |
|
|---|
| 1873 | // Stratified cross validation
|
|---|
| 1874 | public static void svm_cross_validation(Problem prob, Parameter param, int nr_fold, double[] target, bool shuffleTraining)
|
|---|
| 1875 | {
|
|---|
| 1876 | Random rand = new Random();
|
|---|
| 1877 | int i;
|
|---|
| 1878 | int[] fold_start = new int[nr_fold + 1];
|
|---|
| 1879 | int l = prob.Count;
|
|---|
| 1880 | int[] perm = new int[l];
|
|---|
| 1881 |
|
|---|
| 1882 | // stratified cv may not give leave-one-out rate
|
|---|
| 1883 | // Each class to l folds -> some folds may have zero elements
|
|---|
| 1884 | if ((param.SvmType == SvmType.C_SVC ||
|
|---|
| 1885 | param.SvmType == SvmType.NU_SVC) && nr_fold < l)
|
|---|
| 1886 | {
|
|---|
| 1887 | int[] tmp_nr_class = new int[1];
|
|---|
| 1888 | int[][] tmp_label = new int[1][];
|
|---|
| 1889 | int[][] tmp_start = new int[1][];
|
|---|
| 1890 | int[][] tmp_count = new int[1][];
|
|---|
| 1891 |
|
|---|
| 1892 | svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);
|
|---|
| 1893 |
|
|---|
| 1894 | int nr_class = tmp_nr_class[0];
|
|---|
| 1895 | int[] label = tmp_label[0];
|
|---|
| 1896 | int[] start = tmp_start[0];
|
|---|
| 1897 | int[] count = tmp_count[0];
|
|---|
| 1898 |
|
|---|
| 1899 | // random shuffle and then data grouped by fold using the array perm
|
|---|
| 1900 | int[] fold_count = new int[nr_fold];
|
|---|
| 1901 | int c;
|
|---|
| 1902 | int[] index = new int[l];
|
|---|
| 1903 | for (i = 0; i < l; i++)
|
|---|
| 1904 | index[i] = perm[i];
|
|---|
| 1905 | for (c = 0; c < nr_class; c++)
|
|---|
| 1906 | for (i = 0; i < count[c]; i++)
|
|---|
| 1907 | {
|
|---|
| 1908 | int j = i + (int)(rand.NextDouble() * (count[c] - i));
|
|---|
| 1909 | do { int _ = index[start[c] + j]; index[start[c] + j] = index[start[c] + i]; index[start[c] + i] = _; } while (false);
|
|---|
| 1910 | }
|
|---|
| 1911 | for (i = 0; i < nr_fold; i++)
|
|---|
| 1912 | {
|
|---|
| 1913 | fold_count[i] = 0;
|
|---|
| 1914 | for (c = 0; c < nr_class; c++)
|
|---|
| 1915 | fold_count[i] += (i + 1) * count[c] / nr_fold - i * count[c] / nr_fold;
|
|---|
| 1916 | }
|
|---|
| 1917 | fold_start[0] = 0;
|
|---|
| 1918 | for (i = 1; i <= nr_fold; i++)
|
|---|
| 1919 | fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
|
|---|
| 1920 | for (c = 0; c < nr_class; c++)
|
|---|
| 1921 | for (i = 0; i < nr_fold; i++)
|
|---|
| 1922 | {
|
|---|
| 1923 | int begin = start[c] + i * count[c] / nr_fold;
|
|---|
| 1924 | int end = start[c] + (i + 1) * count[c] / nr_fold;
|
|---|
| 1925 | for (int j = begin; j < end; j++)
|
|---|
| 1926 | {
|
|---|
| 1927 | perm[fold_start[i]] = index[j];
|
|---|
| 1928 | fold_start[i]++;
|
|---|
| 1929 | }
|
|---|
| 1930 | }
|
|---|
| 1931 | fold_start[0] = 0;
|
|---|
| 1932 | for (i = 1; i <= nr_fold; i++)
|
|---|
| 1933 | fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
|
|---|
| 1934 | }
|
|---|
| 1935 | else
|
|---|
| 1936 | {
|
|---|
| 1937 | for (i = 0; i < l; i++) perm[i] = i;
|
|---|
| 1938 | if (shuffleTraining) {
|
|---|
| 1939 | for (i = 0; i < l; i++) {
|
|---|
| 1940 | int j = i + (int)(rand.NextDouble() * (l - i));
|
|---|
| 1941 | do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
|
|---|
| 1942 | }
|
|---|
| 1943 | }
|
|---|
| 1944 | for (i = 0; i <= nr_fold; i++)
|
|---|
| 1945 | fold_start[i] = i * l / nr_fold;
|
|---|
| 1946 | }
|
|---|
| 1947 |
|
|---|
| 1948 | for (i = 0; i < nr_fold; i++)
|
|---|
| 1949 | {
|
|---|
| 1950 | int begin = fold_start[i];
|
|---|
| 1951 | int end = fold_start[i + 1];
|
|---|
| 1952 | int j, k;
|
|---|
| 1953 | Problem subprob = new Problem();
|
|---|
| 1954 |
|
|---|
| 1955 | subprob.Count = l - (end - begin);
|
|---|
| 1956 | subprob.X = new Node[subprob.Count][];
|
|---|
| 1957 | subprob.Y = new double[subprob.Count];
|
|---|
| 1958 |
|
|---|
| 1959 | k = 0;
|
|---|
| 1960 | for (j = 0; j < begin; j++)
|
|---|
| 1961 | {
|
|---|
| 1962 | subprob.X[k] = prob.X[perm[j]];
|
|---|
| 1963 | subprob.Y[k] = prob.Y[perm[j]];
|
|---|
| 1964 | ++k;
|
|---|
| 1965 | }
|
|---|
| 1966 | for (j = end; j < l; j++)
|
|---|
| 1967 | {
|
|---|
| 1968 | subprob.X[k] = prob.X[perm[j]];
|
|---|
| 1969 | subprob.Y[k] = prob.Y[perm[j]];
|
|---|
| 1970 | ++k;
|
|---|
| 1971 | }
|
|---|
| 1972 | Model submodel = svm_train(subprob, param);
|
|---|
| 1973 | if (param.Probability &&
|
|---|
| 1974 | (param.SvmType == SvmType.C_SVC ||
|
|---|
| 1975 | param.SvmType == SvmType.NU_SVC))
|
|---|
| 1976 | {
|
|---|
| 1977 | double[] prob_estimates = new double[svm_get_nr_class(submodel)];
|
|---|
| 1978 | for (j = begin; j < end; j++)
|
|---|
| 1979 | target[perm[j]] = svm_predict_probability(submodel, prob.X[perm[j]], prob_estimates);
|
|---|
| 1980 | }
|
|---|
| 1981 | else
|
|---|
| 1982 | for (j = begin; j < end; j++)
|
|---|
| 1983 | target[perm[j]] = svm_predict(submodel, prob.X[perm[j]]);
|
|---|
| 1984 | }
|
|---|
| 1985 | }
|
|---|
| 1986 |
|
|---|
| 1987 | public static SvmType svm_get_svm_type(Model model)
|
|---|
| 1988 | {
|
|---|
| 1989 | return model.Parameter.SvmType;
|
|---|
| 1990 | }
|
|---|
| 1991 |
|
|---|
| 1992 | public static int svm_get_nr_class(Model model)
|
|---|
| 1993 | {
|
|---|
| 1994 | return model.NumberOfClasses;
|
|---|
| 1995 | }
|
|---|
| 1996 |
|
|---|
| 1997 | public static void svm_get_labels(Model model, int[] label)
|
|---|
| 1998 | {
|
|---|
| 1999 | if (model.ClassLabels != null)
|
|---|
| 2000 | for (int i = 0; i < model.NumberOfClasses; i++)
|
|---|
| 2001 | label[i] = model.ClassLabels[i];
|
|---|
| 2002 | }
|
|---|
| 2003 |
|
|---|
| 2004 | public static double svm_get_svr_probability(Model model)
|
|---|
| 2005 | {
|
|---|
| 2006 | if ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
|
|---|
| 2007 | model.PairwiseProbabilityA != null)
|
|---|
| 2008 | return model.PairwiseProbabilityA[0];
|
|---|
| 2009 | else
|
|---|
| 2010 | {
|
|---|
| 2011 | Console.Error.WriteLine("Model doesn't contain information for SVR probability inference");
|
|---|
| 2012 | return 0;
|
|---|
| 2013 | }
|
|---|
| 2014 | }
|
|---|
| 2015 |
|
|---|
| 2016 | public static void svm_predict_values(Model model, Node[] x, double[] dec_values)
|
|---|
| 2017 | {
|
|---|
| 2018 | if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
|
|---|
| 2019 | model.Parameter.SvmType == SvmType.EPSILON_SVR ||
|
|---|
| 2020 | model.Parameter.SvmType == SvmType.NU_SVR)
|
|---|
| 2021 | {
|
|---|
| 2022 | double[] sv_coef = model.SupportVectorCoefficients[0];
|
|---|
| 2023 | double sum = 0;
|
|---|
| 2024 | for (int i = 0; i < model.SupportVectorCount; i++)
|
|---|
| 2025 | sum += sv_coef[i] * Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);
|
|---|
| 2026 | sum -= model.Rho[0];
|
|---|
| 2027 | dec_values[0] = sum;
|
|---|
| 2028 | }
|
|---|
| 2029 | else
|
|---|
| 2030 | {
|
|---|
| 2031 | int i;
|
|---|
| 2032 | int nr_class = model.NumberOfClasses;
|
|---|
| 2033 | int l = model.SupportVectorCount;
|
|---|
| 2034 |
|
|---|
| 2035 | double[] kvalue = new double[l];
|
|---|
| 2036 | for (i = 0; i < l; i++)
|
|---|
| 2037 | kvalue[i] = Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);
|
|---|
| 2038 |
|
|---|
| 2039 | int[] start = new int[nr_class];
|
|---|
| 2040 | start[0] = 0;
|
|---|
| 2041 | for (i = 1; i < nr_class; i++)
|
|---|
| 2042 | start[i] = start[i - 1] + model.NumberOfSVPerClass[i - 1];
|
|---|
| 2043 |
|
|---|
| 2044 | int p = 0;
|
|---|
| 2045 | for (i = 0; i < nr_class; i++)
|
|---|
| 2046 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 2047 | {
|
|---|
| 2048 | double sum = 0;
|
|---|
| 2049 | int si = start[i];
|
|---|
| 2050 | int sj = start[j];
|
|---|
| 2051 | int ci = model.NumberOfSVPerClass[i];
|
|---|
| 2052 | int cj = model.NumberOfSVPerClass[j];
|
|---|
| 2053 |
|
|---|
| 2054 | int k;
|
|---|
| 2055 | double[] coef1 = model.SupportVectorCoefficients[j - 1];
|
|---|
| 2056 | double[] coef2 = model.SupportVectorCoefficients[i];
|
|---|
| 2057 | for (k = 0; k < ci; k++)
|
|---|
| 2058 | sum += coef1[si + k] * kvalue[si + k];
|
|---|
| 2059 | for (k = 0; k < cj; k++)
|
|---|
| 2060 | sum += coef2[sj + k] * kvalue[sj + k];
|
|---|
| 2061 | sum -= model.Rho[p];
|
|---|
| 2062 | dec_values[p] = sum;
|
|---|
| 2063 | p++;
|
|---|
| 2064 | }
|
|---|
| 2065 | }
|
|---|
| 2066 | }
|
|---|
| 2067 |
|
|---|
| 2068 | public static double svm_predict(Model model, Node[] x)
|
|---|
| 2069 | {
|
|---|
| 2070 | if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
|
|---|
| 2071 | model.Parameter.SvmType == SvmType.EPSILON_SVR ||
|
|---|
| 2072 | model.Parameter.SvmType == SvmType.NU_SVR)
|
|---|
| 2073 | {
|
|---|
| 2074 | double[] res = new double[1];
|
|---|
| 2075 | svm_predict_values(model, x, res);
|
|---|
| 2076 |
|
|---|
| 2077 | if (model.Parameter.SvmType == SvmType.ONE_CLASS)
|
|---|
| 2078 | return (res[0] > 0) ? 1 : -1;
|
|---|
| 2079 | else
|
|---|
| 2080 | return res[0];
|
|---|
| 2081 | }
|
|---|
| 2082 | else
|
|---|
| 2083 | {
|
|---|
| 2084 | int i;
|
|---|
| 2085 | int nr_class = model.NumberOfClasses;
|
|---|
| 2086 | double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 2087 | svm_predict_values(model, x, dec_values);
|
|---|
| 2088 |
|
|---|
| 2089 | int[] vote = new int[nr_class];
|
|---|
| 2090 | for (i = 0; i < nr_class; i++)
|
|---|
| 2091 | vote[i] = 0;
|
|---|
| 2092 | int pos = 0;
|
|---|
| 2093 | for (i = 0; i < nr_class; i++)
|
|---|
| 2094 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 2095 | {
|
|---|
| 2096 | if (dec_values[pos++] > 0)
|
|---|
| 2097 | ++vote[i];
|
|---|
| 2098 | else
|
|---|
| 2099 | ++vote[j];
|
|---|
| 2100 | }
|
|---|
| 2101 |
|
|---|
| 2102 | int vote_Max_idx = 0;
|
|---|
| 2103 | for (i = 1; i < nr_class; i++)
|
|---|
| 2104 | if (vote[i] > vote[vote_Max_idx])
|
|---|
| 2105 | vote_Max_idx = i;
|
|---|
| 2106 | return model.ClassLabels[vote_Max_idx];
|
|---|
| 2107 | }
|
|---|
| 2108 | }
|
|---|
| 2109 |
|
|---|
| 2110 | public static double svm_predict_probability(Model model, Node[] x, double[] prob_estimates)
|
|---|
| 2111 | {
|
|---|
| 2112 | if ((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
|
|---|
| 2113 | model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null)
|
|---|
| 2114 | {
|
|---|
| 2115 | int i;
|
|---|
| 2116 | int nr_class = model.NumberOfClasses;
|
|---|
| 2117 | double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
|
|---|
| 2118 | svm_predict_values(model, x, dec_values);
|
|---|
| 2119 |
|
|---|
| 2120 | double Min_prob = 1e-7;
|
|---|
| 2121 | double[,] pairwise_prob = new double[nr_class, nr_class];
|
|---|
| 2122 |
|
|---|
| 2123 | int k = 0;
|
|---|
| 2124 | for (i = 0; i < nr_class; i++)
|
|---|
| 2125 | {
|
|---|
| 2126 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 2127 | {
|
|---|
| 2128 | pairwise_prob[i, j] = Math.Min(Math.Max(sigmoid_predict(dec_values[k], model.PairwiseProbabilityA[k], model.PairwiseProbabilityB[k]), Min_prob), 1 - Min_prob);
|
|---|
| 2129 | pairwise_prob[j, i] = 1 - pairwise_prob[i, j];
|
|---|
| 2130 | k++;
|
|---|
| 2131 | }
|
|---|
| 2132 | }
|
|---|
| 2133 | multiclass_probability(nr_class, pairwise_prob, prob_estimates);
|
|---|
| 2134 |
|
|---|
| 2135 | int prob_Max_idx = 0;
|
|---|
| 2136 | for (i = 1; i < nr_class; i++)
|
|---|
| 2137 | if (prob_estimates[i] > prob_estimates[prob_Max_idx])
|
|---|
| 2138 | prob_Max_idx = i;
|
|---|
| 2139 | return model.ClassLabels[prob_Max_idx];
|
|---|
| 2140 | }
|
|---|
| 2141 | else
|
|---|
| 2142 | return svm_predict(model, x);
|
|---|
| 2143 | }
|
|---|
| 2144 |
|
|---|
| 2145 | public static string svm_check_parameter(Problem prob, Parameter param)
|
|---|
| 2146 | {
|
|---|
| 2147 | // svm_type
|
|---|
| 2148 |
|
|---|
| 2149 | SvmType svm_type = param.SvmType;
|
|---|
| 2150 |
|
|---|
| 2151 | // kernel_type, degree
|
|---|
| 2152 |
|
|---|
| 2153 | KernelType kernel_type = param.KernelType;
|
|---|
| 2154 |
|
|---|
| 2155 | if (param.Degree < 0)
|
|---|
| 2156 | return "degree of polynomial kernel < 0";
|
|---|
| 2157 |
|
|---|
| 2158 | // cache_size,eps,C,nu,p,shrinking
|
|---|
| 2159 |
|
|---|
| 2160 | if (param.CacheSize <= 0)
|
|---|
| 2161 | return "cache_size <= 0";
|
|---|
| 2162 |
|
|---|
| 2163 | if (param.EPS <= 0)
|
|---|
| 2164 | return "eps <= 0";
|
|---|
| 2165 |
|
|---|
| 2166 | if (param.Gamma == 0)
|
|---|
| 2167 | param.Gamma = 1.0 / prob.MaxIndex;
|
|---|
| 2168 |
|
|---|
| 2169 | if (svm_type == SvmType.C_SVC ||
|
|---|
| 2170 | svm_type == SvmType.EPSILON_SVR ||
|
|---|
| 2171 | svm_type == SvmType.NU_SVR)
|
|---|
| 2172 | if (param.C <= 0)
|
|---|
| 2173 | return "C <= 0";
|
|---|
| 2174 |
|
|---|
| 2175 | if (svm_type == SvmType.NU_SVC ||
|
|---|
| 2176 | svm_type == SvmType.ONE_CLASS ||
|
|---|
| 2177 | svm_type == SvmType.NU_SVR)
|
|---|
| 2178 | if (param.Nu <= 0 || param.Nu > 1)
|
|---|
| 2179 | return "nu <= 0 or nu > 1";
|
|---|
| 2180 |
|
|---|
| 2181 | if (svm_type == SvmType.EPSILON_SVR)
|
|---|
| 2182 | if (param.P < 0)
|
|---|
| 2183 | return "p < 0";
|
|---|
| 2184 |
|
|---|
| 2185 | if (param.Probability &&
|
|---|
| 2186 | svm_type == SvmType.ONE_CLASS)
|
|---|
| 2187 | return "one-class SVM probability output not supported yet";
|
|---|
| 2188 |
|
|---|
| 2189 | // check whether nu-svc is feasible
|
|---|
| 2190 |
|
|---|
| 2191 | if (svm_type == SvmType.NU_SVC)
|
|---|
| 2192 | {
|
|---|
| 2193 | int l = prob.Count;
|
|---|
| 2194 | int Max_nr_class = 16;
|
|---|
| 2195 | int nr_class = 0;
|
|---|
| 2196 | int[] label = new int[Max_nr_class];
|
|---|
| 2197 | int[] count = new int[Max_nr_class];
|
|---|
| 2198 |
|
|---|
| 2199 | int i;
|
|---|
| 2200 | for (i = 0; i < l; i++)
|
|---|
| 2201 | {
|
|---|
| 2202 | int this_label = (int)prob.Y[i];
|
|---|
| 2203 | int j;
|
|---|
| 2204 | for (j = 0; j < nr_class; j++)
|
|---|
| 2205 | if (this_label == label[j])
|
|---|
| 2206 | {
|
|---|
| 2207 | ++count[j];
|
|---|
| 2208 | break;
|
|---|
| 2209 | }
|
|---|
| 2210 |
|
|---|
| 2211 | if (j == nr_class)
|
|---|
| 2212 | {
|
|---|
| 2213 | if (nr_class == Max_nr_class)
|
|---|
| 2214 | {
|
|---|
| 2215 | Max_nr_class *= 2;
|
|---|
| 2216 | int[] new_data = new int[Max_nr_class];
|
|---|
| 2217 | Array.Copy(label, 0, new_data, 0, label.Length);
|
|---|
| 2218 | label = new_data;
|
|---|
| 2219 |
|
|---|
| 2220 | new_data = new int[Max_nr_class];
|
|---|
| 2221 | Array.Copy(count, 0, new_data, 0, count.Length);
|
|---|
| 2222 | count = new_data;
|
|---|
| 2223 | }
|
|---|
| 2224 | label[nr_class] = this_label;
|
|---|
| 2225 | count[nr_class] = 1;
|
|---|
| 2226 | ++nr_class;
|
|---|
| 2227 | }
|
|---|
| 2228 | }
|
|---|
| 2229 |
|
|---|
| 2230 | for (i = 0; i < nr_class; i++)
|
|---|
| 2231 | {
|
|---|
| 2232 | int n1 = count[i];
|
|---|
| 2233 | for (int j = i + 1; j < nr_class; j++)
|
|---|
| 2234 | {
|
|---|
| 2235 | int n2 = count[j];
|
|---|
| 2236 | if (param.Nu * (n1 + n2) / 2 > Math.Min(n1, n2))
|
|---|
| 2237 | return "specified nu is infeasible";
|
|---|
| 2238 | }
|
|---|
| 2239 | }
|
|---|
| 2240 | }
|
|---|
| 2241 |
|
|---|
| 2242 | return null;
|
|---|
| 2243 | }
|
|---|
| 2244 |
|
|---|
| 2245 | public static int svm_check_probability_model(Model model)
|
|---|
| 2246 | {
|
|---|
| 2247 | if (((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
|
|---|
| 2248 | model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null) ||
|
|---|
| 2249 | ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
|
|---|
| 2250 | model.PairwiseProbabilityA != null))
|
|---|
| 2251 | return 1;
|
|---|
| 2252 | else
|
|---|
| 2253 | return 0;
|
|---|
| 2254 | }
|
|---|
| 2255 | }
|
|---|
| 2256 | }
|
|---|
