[2645] | 1 | /*
|
---|
| 2 | * SVM.NET Library
|
---|
| 3 | * Copyright (C) 2008 Matthew Johnson
|
---|
| 4 | *
|
---|
| 5 | * This program is free software: you can redistribute it and/or modify
|
---|
| 6 | * it under the terms of the GNU General Public License as published by
|
---|
| 7 | * the Free Software Foundation, either version 3 of the License, or
|
---|
| 8 | * (at your option) any later version.
|
---|
| 9 | *
|
---|
| 10 | * This program is distributed in the hope that it will be useful,
|
---|
| 11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 13 | * GNU General Public License for more details.
|
---|
| 14 | *
|
---|
| 15 | * You should have received a copy of the GNU General Public License
|
---|
| 16 | * along with this program. If not, see <http://www.gnu.org/licenses/>.
|
---|
| 17 | */
|
---|
| 18 |
|
---|
| 19 |
|
---|
| 20 | using System;
|
---|
| 21 | using System.IO;
|
---|
| 22 |
|
---|
[4068] | 23 | namespace SVM {
|
---|
[2645] | 24 |
|
---|
[4068] | 25 | // An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
|
---|
| 26 | // Solves:
|
---|
| 27 | //
|
---|
| 28 | // Min 0.5(\alpha^T Q \alpha) + p^T \alpha
|
---|
| 29 | //
|
---|
| 30 | // y^T \alpha = \delta
|
---|
| 31 | // y_i = +1 or -1
|
---|
| 32 | // 0 <= alpha_i <= Cp for y_i = 1
|
---|
| 33 | // 0 <= alpha_i <= Cn for y_i = -1
|
---|
| 34 | //
|
---|
| 35 | // Given:
|
---|
| 36 | //
|
---|
| 37 | // Q, p, y, Cp, Cn, and an initial feasible point \alpha
|
---|
| 38 | // l is the size of vectors and matrices
|
---|
| 39 | // eps is the stopping tolerance
|
---|
| 40 | //
|
---|
| 41 | // solution will be put in \alpha, objective value will be put in obj
|
---|
| 42 | //
|
---|
| 43 | internal class Solver {
|
---|
| 44 | protected int active_size;
|
---|
| 45 | protected sbyte[] y;
|
---|
| 46 | protected double[] G; // gradient of objective function
|
---|
| 47 | private const byte LOWER_BOUND = 0;
|
---|
| 48 | private const byte UPPER_BOUND = 1;
|
---|
| 49 | private const byte FREE = 2;
|
---|
| 50 | private byte[] alpha_status; // LOWER_BOUND, UPPER_BOUND, FREE
|
---|
| 51 | private double[] alpha;
|
---|
| 52 | protected IQMatrix Q;
|
---|
| 53 | protected float[] QD;
|
---|
| 54 | protected double EPS;
|
---|
| 55 | private double Cp, Cn;
|
---|
| 56 | private double[] p;
|
---|
| 57 | private int[] active_set;
|
---|
| 58 | private double[] G_bar; // gradient, if we treat free variables as 0
|
---|
| 59 | protected int l;
|
---|
| 60 | protected bool unshrink; // XXX
|
---|
[2645] | 61 |
|
---|
[4068] | 62 | protected const double INF = double.PositiveInfinity;
|
---|
[2645] | 63 |
|
---|
[4068] | 64 | private double get_C(int i) {
|
---|
| 65 | return (y[i] > 0) ? Cp : Cn;
|
---|
| 66 | }
|
---|
[2645] | 67 |
|
---|
[4068] | 68 | private void update_alpha_status(int i) {
|
---|
| 69 | if (alpha[i] >= get_C(i))
|
---|
| 70 | alpha_status[i] = UPPER_BOUND;
|
---|
| 71 | else if (alpha[i] <= 0)
|
---|
| 72 | alpha_status[i] = LOWER_BOUND;
|
---|
| 73 | else alpha_status[i] = FREE;
|
---|
| 74 | }
|
---|
[2645] | 75 |
|
---|
[4068] | 76 | protected bool is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
|
---|
| 77 | protected bool is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }
|
---|
[2645] | 78 |
|
---|
[4068] | 79 | private bool is_free(int i) { return alpha_status[i] == FREE; }
|
---|
[2645] | 80 |
|
---|
[4068] | 81 | public class SolutionInfo {
|
---|
| 82 | public double obj;
|
---|
| 83 | public double rho;
|
---|
| 84 | public double upper_bound_p;
|
---|
| 85 | public double upper_bound_n;
|
---|
| 86 | public double r; // for Solver_NU
|
---|
| 87 | }
|
---|
[2645] | 88 |
|
---|
[4068] | 89 | protected void swap_index(int i, int j) {
|
---|
| 90 | Q.SwapIndex(i, j);
|
---|
| 91 | y.SwapIndex(i, j);
|
---|
| 92 | G.SwapIndex(i, j);
|
---|
| 93 | alpha_status.SwapIndex(i, j);
|
---|
| 94 | alpha.SwapIndex(i, j);
|
---|
| 95 | p.SwapIndex(i, j);
|
---|
| 96 | active_set.SwapIndex(i, j);
|
---|
| 97 | G_bar.SwapIndex(i, j);
|
---|
| 98 | }
|
---|
[2645] | 99 |
|
---|
[4068] | 100 | protected void reconstruct_gradient() {
|
---|
| 101 | // reconstruct inactive elements of G from G_bar and free variables
|
---|
[2645] | 102 |
|
---|
[4068] | 103 | if (active_size == l) return;
|
---|
[2645] | 104 |
|
---|
[4068] | 105 | int i, j;
|
---|
| 106 | int nr_free = 0;
|
---|
[2645] | 107 |
|
---|
[4068] | 108 | for (j = active_size; j < l; j++)
|
---|
| 109 | G[j] = G_bar[j] + p[j];
|
---|
[2645] | 110 |
|
---|
[4068] | 111 | for (j = 0; j < active_size; j++)
|
---|
| 112 | if (is_free(j))
|
---|
| 113 | nr_free++;
|
---|
[2645] | 114 |
|
---|
[4068] | 115 | if (2 * nr_free < active_size)
|
---|
| 116 | Procedures.info("\nWarning: using -h 0 may be faster\n");
|
---|
[2645] | 117 |
|
---|
[4068] | 118 | if (nr_free * l > 2 * active_size * (l - active_size)) {
|
---|
| 119 | for (i = active_size; i < l; i++) {
|
---|
| 120 | float[] Q_i = Q.GetQ(i, active_size);
|
---|
| 121 | for (j = 0; j < active_size; j++)
|
---|
| 122 | if (is_free(j))
|
---|
| 123 | G[i] += alpha[j] * Q_i[j];
|
---|
[2645] | 124 | }
|
---|
[4068] | 125 | } else {
|
---|
| 126 | for (i = 0; i < active_size; i++)
|
---|
| 127 | if (is_free(i)) {
|
---|
| 128 | float[] Q_i = Q.GetQ(i, l);
|
---|
| 129 | double alpha_i = alpha[i];
|
---|
| 130 | for (j = active_size; j < l; j++)
|
---|
| 131 | G[j] += alpha_i * Q_i[j];
|
---|
| 132 | }
|
---|
| 133 | }
|
---|
| 134 | }
|
---|
[2645] | 135 |
|
---|
[4068] | 136 | public virtual void Solve(int l, IQMatrix Q, double[] p_, sbyte[] y_, double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, bool shrinking) {
|
---|
| 137 | this.l = l;
|
---|
| 138 | this.Q = Q;
|
---|
| 139 | QD = Q.GetQD();
|
---|
| 140 | p = (double[])p_.Clone();
|
---|
| 141 | y = (sbyte[])y_.Clone();
|
---|
| 142 | alpha = (double[])alpha_.Clone();
|
---|
| 143 | this.Cp = Cp;
|
---|
| 144 | this.Cn = Cn;
|
---|
| 145 | this.EPS = eps;
|
---|
| 146 | this.unshrink = false;
|
---|
[2645] | 147 |
|
---|
[4068] | 148 | // initialize alpha_status
|
---|
| 149 | {
|
---|
| 150 | alpha_status = new byte[l];
|
---|
| 151 | for (int i = 0; i < l; i++)
|
---|
| 152 | update_alpha_status(i);
|
---|
| 153 | }
|
---|
[2645] | 154 |
|
---|
[4068] | 155 | // initialize active set (for shrinking)
|
---|
| 156 | {
|
---|
| 157 | active_set = new int[l];
|
---|
| 158 | for (int i = 0; i < l; i++)
|
---|
| 159 | active_set[i] = i;
|
---|
| 160 | active_size = l;
|
---|
| 161 | }
|
---|
[2645] | 162 |
|
---|
[4068] | 163 | // initialize gradient
|
---|
| 164 | {
|
---|
| 165 | G = new double[l];
|
---|
| 166 | G_bar = new double[l];
|
---|
| 167 | int i;
|
---|
| 168 | for (i = 0; i < l; i++) {
|
---|
| 169 | G[i] = p[i];
|
---|
| 170 | G_bar[i] = 0;
|
---|
| 171 | }
|
---|
| 172 | for (i = 0; i < l; i++)
|
---|
| 173 | if (!is_lower_bound(i)) {
|
---|
| 174 | float[] Q_i = Q.GetQ(i, l);
|
---|
| 175 | double alpha_i = alpha[i];
|
---|
| 176 | int j;
|
---|
| 177 | for (j = 0; j < l; j++)
|
---|
| 178 | G[j] += alpha_i * Q_i[j];
|
---|
| 179 | if (is_upper_bound(i))
|
---|
| 180 | for (j = 0; j < l; j++)
|
---|
| 181 | G_bar[j] += get_C(i) * Q_i[j];
|
---|
| 182 | }
|
---|
| 183 | }
|
---|
[2645] | 184 |
|
---|
[4068] | 185 | // optimization step
|
---|
[2645] | 186 |
|
---|
[4068] | 187 | int iter = 0;
|
---|
| 188 | int counter = Math.Min(l, 1000) + 1;
|
---|
| 189 | int[] working_set = new int[2];
|
---|
[2645] | 190 |
|
---|
[4068] | 191 | while (true) {
|
---|
| 192 | // show progress and do shrinking
|
---|
[2645] | 193 |
|
---|
[4068] | 194 | if (--counter == 0) {
|
---|
| 195 | counter = Math.Min(l, 1000);
|
---|
| 196 | if (shrinking) do_shrinking();
|
---|
| 197 | Procedures.info(".");
|
---|
| 198 | }
|
---|
[2645] | 199 |
|
---|
[4068] | 200 | if (select_working_set(working_set) != 0) {
|
---|
| 201 | // reconstruct the whole gradient
|
---|
| 202 | reconstruct_gradient();
|
---|
| 203 | // reset active set size and check
|
---|
| 204 | active_size = l;
|
---|
| 205 | Procedures.info("*");
|
---|
| 206 | if (select_working_set(working_set) != 0)
|
---|
| 207 | break;
|
---|
| 208 | else
|
---|
| 209 | counter = 1; // do shrinking next iteration
|
---|
| 210 | }
|
---|
[2645] | 211 |
|
---|
[4068] | 212 | int i = working_set[0];
|
---|
| 213 | int j = working_set[1];
|
---|
[2645] | 214 |
|
---|
[4068] | 215 | ++iter;
|
---|
[2645] | 216 |
|
---|
[4068] | 217 | // update alpha[i] and alpha[j], handle bounds carefully
|
---|
[2645] | 218 |
|
---|
[4068] | 219 | float[] Q_i = Q.GetQ(i, active_size);
|
---|
| 220 | float[] Q_j = Q.GetQ(j, active_size);
|
---|
[2645] | 221 |
|
---|
[4068] | 222 | double C_i = get_C(i);
|
---|
| 223 | double C_j = get_C(j);
|
---|
[2645] | 224 |
|
---|
[4068] | 225 | double old_alpha_i = alpha[i];
|
---|
| 226 | double old_alpha_j = alpha[j];
|
---|
[2645] | 227 |
|
---|
[4068] | 228 | if (y[i] != y[j]) {
|
---|
| 229 | double quad_coef = Q_i[i] + Q_j[j] + 2 * Q_i[j];
|
---|
| 230 | if (quad_coef <= 0)
|
---|
| 231 | quad_coef = 1e-12;
|
---|
| 232 | double delta = (-G[i] - G[j]) / quad_coef;
|
---|
| 233 | double diff = alpha[i] - alpha[j];
|
---|
| 234 | alpha[i] += delta;
|
---|
| 235 | alpha[j] += delta;
|
---|
[2645] | 236 |
|
---|
[4068] | 237 | if (diff > 0) {
|
---|
| 238 | if (alpha[j] < 0) {
|
---|
| 239 | alpha[j] = 0;
|
---|
| 240 | alpha[i] = diff;
|
---|
| 241 | }
|
---|
| 242 | } else {
|
---|
| 243 | if (alpha[i] < 0) {
|
---|
| 244 | alpha[i] = 0;
|
---|
| 245 | alpha[j] = -diff;
|
---|
| 246 | }
|
---|
| 247 | }
|
---|
| 248 | if (diff > C_i - C_j) {
|
---|
| 249 | if (alpha[i] > C_i) {
|
---|
| 250 | alpha[i] = C_i;
|
---|
| 251 | alpha[j] = C_i - diff;
|
---|
| 252 | }
|
---|
| 253 | } else {
|
---|
| 254 | if (alpha[j] > C_j) {
|
---|
| 255 | alpha[j] = C_j;
|
---|
| 256 | alpha[i] = C_j + diff;
|
---|
| 257 | }
|
---|
| 258 | }
|
---|
| 259 | } else {
|
---|
| 260 | double quad_coef = Q_i[i] + Q_j[j] - 2 * Q_i[j];
|
---|
| 261 | if (quad_coef <= 0)
|
---|
| 262 | quad_coef = 1e-12;
|
---|
| 263 | double delta = (G[i] - G[j]) / quad_coef;
|
---|
| 264 | double sum = alpha[i] + alpha[j];
|
---|
| 265 | alpha[i] -= delta;
|
---|
| 266 | alpha[j] += delta;
|
---|
[2645] | 267 |
|
---|
[4068] | 268 | if (sum > C_i) {
|
---|
| 269 | if (alpha[i] > C_i) {
|
---|
| 270 | alpha[i] = C_i;
|
---|
| 271 | alpha[j] = sum - C_i;
|
---|
| 272 | }
|
---|
| 273 | } else {
|
---|
| 274 | if (alpha[j] < 0) {
|
---|
| 275 | alpha[j] = 0;
|
---|
| 276 | alpha[i] = sum;
|
---|
| 277 | }
|
---|
| 278 | }
|
---|
| 279 | if (sum > C_j) {
|
---|
| 280 | if (alpha[j] > C_j) {
|
---|
| 281 | alpha[j] = C_j;
|
---|
| 282 | alpha[i] = sum - C_j;
|
---|
| 283 | }
|
---|
| 284 | } else {
|
---|
| 285 | if (alpha[i] < 0) {
|
---|
| 286 | alpha[i] = 0;
|
---|
| 287 | alpha[j] = sum;
|
---|
| 288 | }
|
---|
| 289 | }
|
---|
| 290 | }
|
---|
[2645] | 291 |
|
---|
[4068] | 292 | // update G
|
---|
[2645] | 293 |
|
---|
[4068] | 294 | double delta_alpha_i = alpha[i] - old_alpha_i;
|
---|
| 295 | double delta_alpha_j = alpha[j] - old_alpha_j;
|
---|
[2645] | 296 |
|
---|
[4068] | 297 | for (int k = 0; k < active_size; k++) {
|
---|
| 298 | G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
|
---|
| 299 | }
|
---|
[2645] | 300 |
|
---|
[4068] | 301 | // update alpha_status and G_bar
|
---|
[2645] | 302 |
|
---|
[4068] | 303 | {
|
---|
| 304 | bool ui = is_upper_bound(i);
|
---|
| 305 | bool uj = is_upper_bound(j);
|
---|
| 306 | update_alpha_status(i);
|
---|
| 307 | update_alpha_status(j);
|
---|
| 308 | int k;
|
---|
| 309 | if (ui != is_upper_bound(i)) {
|
---|
| 310 | Q_i = Q.GetQ(i, l);
|
---|
| 311 | if (ui)
|
---|
| 312 | for (k = 0; k < l; k++)
|
---|
| 313 | G_bar[k] -= C_i * Q_i[k];
|
---|
| 314 | else
|
---|
| 315 | for (k = 0; k < l; k++)
|
---|
| 316 | G_bar[k] += C_i * Q_i[k];
|
---|
| 317 | }
|
---|
[2645] | 318 |
|
---|
[4068] | 319 | if (uj != is_upper_bound(j)) {
|
---|
| 320 | Q_j = Q.GetQ(j, l);
|
---|
| 321 | if (uj)
|
---|
| 322 | for (k = 0; k < l; k++)
|
---|
| 323 | G_bar[k] -= C_j * Q_j[k];
|
---|
| 324 | else
|
---|
| 325 | for (k = 0; k < l; k++)
|
---|
| 326 | G_bar[k] += C_j * Q_j[k];
|
---|
| 327 | }
|
---|
| 328 | }
|
---|
[2645] | 329 |
|
---|
[4068] | 330 | }
|
---|
[2645] | 331 |
|
---|
[4068] | 332 | // calculate rho
|
---|
[2645] | 333 |
|
---|
[4068] | 334 | si.rho = calculate_rho();
|
---|
[2645] | 335 |
|
---|
[4068] | 336 | // calculate objective value
|
---|
| 337 | {
|
---|
| 338 | double v = 0;
|
---|
| 339 | int i;
|
---|
| 340 | for (i = 0; i < l; i++)
|
---|
| 341 | v += alpha[i] * (G[i] + p[i]);
|
---|
[2645] | 342 |
|
---|
[4068] | 343 | si.obj = v / 2;
|
---|
| 344 | }
|
---|
[2645] | 345 |
|
---|
[4068] | 346 | // put back the solution
|
---|
| 347 | {
|
---|
| 348 | for (int i = 0; i < l; i++)
|
---|
| 349 | alpha_[active_set[i]] = alpha[i];
|
---|
| 350 | }
|
---|
[2645] | 351 |
|
---|
[4068] | 352 | si.upper_bound_p = Cp;
|
---|
| 353 | si.upper_bound_n = Cn;
|
---|
[2645] | 354 |
|
---|
[4068] | 355 | Procedures.info("\noptimization finished, #iter = " + iter + "\n");
|
---|
| 356 | }
|
---|
[2645] | 357 |
|
---|
[4068] | 358 | // return 1 if already optimal, return 0 otherwise
|
---|
| 359 | protected virtual int select_working_set(int[] working_set) {
|
---|
| 360 | // return i,j such that
|
---|
| 361 | // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
|
---|
| 362 | // j: mimimizes the decrease of obj value
|
---|
| 363 | // (if quadratic coefficeint <= 0, replace it with tau)
|
---|
| 364 | // -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
|
---|
[2645] | 365 |
|
---|
[4068] | 366 | double GMax = -INF;
|
---|
| 367 | double GMax2 = -INF;
|
---|
| 368 | int GMax_idx = -1;
|
---|
| 369 | int GMin_idx = -1;
|
---|
| 370 | double obj_diff_Min = INF;
|
---|
[2645] | 371 |
|
---|
[4068] | 372 | for (int t = 0; t < active_size; t++)
|
---|
| 373 | if (y[t] == +1) {
|
---|
| 374 | if (!is_upper_bound(t))
|
---|
| 375 | if (-G[t] >= GMax) {
|
---|
| 376 | GMax = -G[t];
|
---|
| 377 | GMax_idx = t;
|
---|
| 378 | }
|
---|
| 379 | } else {
|
---|
| 380 | if (!is_lower_bound(t))
|
---|
| 381 | if (G[t] >= GMax) {
|
---|
| 382 | GMax = G[t];
|
---|
| 383 | GMax_idx = t;
|
---|
| 384 | }
|
---|
| 385 | }
|
---|
[2645] | 386 |
|
---|
[4068] | 387 | int i = GMax_idx;
|
---|
| 388 | float[] Q_i = null;
|
---|
| 389 | if (i != -1) // null Q_i not accessed: GMax=-INF if i=-1
|
---|
| 390 | Q_i = Q.GetQ(i, active_size);
|
---|
[2645] | 391 |
|
---|
[4068] | 392 | for (int j = 0; j < active_size; j++) {
|
---|
| 393 | if (y[j] == +1) {
|
---|
| 394 | if (!is_lower_bound(j)) {
|
---|
| 395 | double grad_diff = GMax + G[j];
|
---|
| 396 | if (G[j] >= GMax2)
|
---|
| 397 | GMax2 = G[j];
|
---|
| 398 | if (grad_diff > 0) {
|
---|
| 399 | double obj_diff;
|
---|
| 400 | double quad_coef = Q_i[i] + QD[j] - 2.0 * y[i] * Q_i[j];
|
---|
| 401 | if (quad_coef > 0)
|
---|
| 402 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
---|
| 403 | else
|
---|
| 404 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
---|
[2645] | 405 |
|
---|
[4068] | 406 | if (obj_diff <= obj_diff_Min) {
|
---|
| 407 | GMin_idx = j;
|
---|
| 408 | obj_diff_Min = obj_diff;
|
---|
| 409 | }
|
---|
[2645] | 410 | }
|
---|
[4068] | 411 | }
|
---|
| 412 | } else {
|
---|
| 413 | if (!is_upper_bound(j)) {
|
---|
| 414 | double grad_diff = GMax - G[j];
|
---|
| 415 | if (-G[j] >= GMax2)
|
---|
| 416 | GMax2 = -G[j];
|
---|
| 417 | if (grad_diff > 0) {
|
---|
| 418 | double obj_diff;
|
---|
| 419 | double quad_coef = Q_i[i] + QD[j] + 2.0 * y[i] * Q_i[j];
|
---|
| 420 | if (quad_coef > 0)
|
---|
| 421 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
---|
| 422 | else
|
---|
| 423 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
---|
[2645] | 424 |
|
---|
[4068] | 425 | if (obj_diff <= obj_diff_Min) {
|
---|
| 426 | GMin_idx = j;
|
---|
| 427 | obj_diff_Min = obj_diff;
|
---|
| 428 | }
|
---|
[2645] | 429 | }
|
---|
[4068] | 430 | }
|
---|
[2645] | 431 | }
|
---|
[4068] | 432 | }
|
---|
[2645] | 433 |
|
---|
[4068] | 434 | if (GMax + GMax2 < EPS)
|
---|
| 435 | return 1;
|
---|
[2645] | 436 |
|
---|
[4068] | 437 | working_set[0] = GMax_idx;
|
---|
| 438 | working_set[1] = GMin_idx;
|
---|
| 439 | return 0;
|
---|
| 440 | }
|
---|
[2645] | 441 |
|
---|
[4068] | 442 | private bool be_shrunk(int i, double GMax1, double GMax2) {
|
---|
| 443 | if (is_upper_bound(i)) {
|
---|
| 444 | if (y[i] == +1)
|
---|
| 445 | return (-G[i] > GMax1);
|
---|
| 446 | else
|
---|
| 447 | return (-G[i] > GMax2);
|
---|
| 448 | } else if (is_lower_bound(i)) {
|
---|
| 449 | if (y[i] == +1)
|
---|
| 450 | return (G[i] > GMax2);
|
---|
| 451 | else
|
---|
| 452 | return (G[i] > GMax1);
|
---|
| 453 | } else
|
---|
| 454 | return (false);
|
---|
| 455 | }
|
---|
[2645] | 456 |
|
---|
[4068] | 457 | protected virtual void do_shrinking() {
|
---|
| 458 | int i;
|
---|
| 459 | double GMax1 = -INF; // Max { -y_i * grad(f)_i | i in I_up(\alpha) }
|
---|
| 460 | double GMax2 = -INF; // Max { y_i * grad(f)_i | i in I_low(\alpha) }
|
---|
| 461 |
|
---|
| 462 | // find Maximal violating pair first
|
---|
| 463 | for (i = 0; i < active_size; i++) {
|
---|
| 464 | if (y[i] == +1) {
|
---|
| 465 | if (!is_upper_bound(i)) {
|
---|
| 466 | if (-G[i] >= GMax1)
|
---|
| 467 | GMax1 = -G[i];
|
---|
| 468 | }
|
---|
| 469 | if (!is_lower_bound(i)) {
|
---|
| 470 | if (G[i] >= GMax2)
|
---|
| 471 | GMax2 = G[i];
|
---|
| 472 | }
|
---|
| 473 | } else {
|
---|
| 474 | if (!is_upper_bound(i)) {
|
---|
| 475 | if (-G[i] >= GMax2)
|
---|
| 476 | GMax2 = -G[i];
|
---|
| 477 | }
|
---|
| 478 | if (!is_lower_bound(i)) {
|
---|
| 479 | if (G[i] >= GMax1)
|
---|
| 480 | GMax1 = G[i];
|
---|
| 481 | }
|
---|
[2645] | 482 | }
|
---|
[4068] | 483 | }
|
---|
[2645] | 484 |
|
---|
[4068] | 485 | if (unshrink == false && GMax1 + GMax2 <= EPS * 10) {
|
---|
| 486 | unshrink = true;
|
---|
| 487 | reconstruct_gradient();
|
---|
| 488 | active_size = l;
|
---|
| 489 | }
|
---|
[2645] | 490 |
|
---|
[4068] | 491 | for (i = 0; i < active_size; i++)
|
---|
| 492 | if (be_shrunk(i, GMax1, GMax2)) {
|
---|
| 493 | active_size--;
|
---|
| 494 | while (active_size > i) {
|
---|
| 495 | if (!be_shrunk(active_size, GMax1, GMax2)) {
|
---|
| 496 | swap_index(i, active_size);
|
---|
| 497 | break;
|
---|
[2645] | 498 | }
|
---|
[4068] | 499 | active_size--;
|
---|
| 500 | }
|
---|
[2645] | 501 | }
|
---|
| 502 | }
|
---|
| 503 |
|
---|
[4068] | 504 | protected virtual double calculate_rho() {
|
---|
| 505 | double r;
|
---|
| 506 | int nr_free = 0;
|
---|
| 507 | double ub = INF, lb = -INF, sum_free = 0;
|
---|
| 508 | for (int i = 0; i < active_size; i++) {
|
---|
| 509 | double yG = y[i] * G[i];
|
---|
[2645] | 510 |
|
---|
[4068] | 511 | if (is_lower_bound(i)) {
|
---|
| 512 | if (y[i] > 0)
|
---|
| 513 | ub = Math.Min(ub, yG);
|
---|
| 514 | else
|
---|
| 515 | lb = Math.Max(lb, yG);
|
---|
| 516 | } else if (is_upper_bound(i)) {
|
---|
| 517 | if (y[i] < 0)
|
---|
| 518 | ub = Math.Min(ub, yG);
|
---|
| 519 | else
|
---|
| 520 | lb = Math.Max(lb, yG);
|
---|
| 521 | } else {
|
---|
| 522 | ++nr_free;
|
---|
| 523 | sum_free += yG;
|
---|
[2645] | 524 | }
|
---|
[4068] | 525 | }
|
---|
[2645] | 526 |
|
---|
[4068] | 527 | if (nr_free > 0)
|
---|
| 528 | r = sum_free / nr_free;
|
---|
| 529 | else
|
---|
| 530 | r = (ub + lb) / 2;
|
---|
[2645] | 531 |
|
---|
[4068] | 532 | return r;
|
---|
| 533 | }
|
---|
[2645] | 534 |
|
---|
[4068] | 535 | }
|
---|
[2645] | 536 |
|
---|
[4068] | 537 | //
|
---|
| 538 | // Solver for nu-svm classification and regression
|
---|
| 539 | //
|
---|
| 540 | // additional constraint: e^T \alpha = constant
|
---|
| 541 | //
|
---|
| 542 | class Solver_NU : Solver {
|
---|
| 543 | private SolutionInfo si;
|
---|
[2645] | 544 |
|
---|
[4068] | 545 | public sealed override void Solve(int l, IQMatrix Q, double[] p, sbyte[] y,
|
---|
| 546 | double[] alpha, double Cp, double Cn, double eps,
|
---|
| 547 | SolutionInfo si, bool shrinking) {
|
---|
| 548 | this.si = si;
|
---|
| 549 | base.Solve(l, Q, p, y, alpha, Cp, Cn, eps, si, shrinking);
|
---|
| 550 | }
|
---|
[2645] | 551 |
|
---|
[4068] | 552 | // return 1 if already optimal, return 0 otherwise
|
---|
| 553 | protected override sealed int select_working_set(int[] working_set) {
|
---|
| 554 | // return i,j such that y_i = y_j and
|
---|
| 555 | // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
|
---|
| 556 | // j: Minimizes the decrease of obj value
|
---|
| 557 | // (if quadratic coefficeint <= 0, replace it with tau)
|
---|
| 558 | // -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
|
---|
[2645] | 559 |
|
---|
[4068] | 560 | double GMaxp = -INF;
|
---|
| 561 | double GMaxp2 = -INF;
|
---|
| 562 | int GMaxp_idx = -1;
|
---|
[2645] | 563 |
|
---|
[4068] | 564 | double GMaxn = -INF;
|
---|
| 565 | double GMaxn2 = -INF;
|
---|
| 566 | int GMaxn_idx = -1;
|
---|
[2645] | 567 |
|
---|
[4068] | 568 | int GMin_idx = -1;
|
---|
| 569 | double obj_diff_Min = INF;
|
---|
[2645] | 570 |
|
---|
[4068] | 571 | for (int t = 0; t < active_size; t++)
|
---|
| 572 | if (y[t] == +1) {
|
---|
| 573 | if (!is_upper_bound(t))
|
---|
| 574 | if (-G[t] >= GMaxp) {
|
---|
| 575 | GMaxp = -G[t];
|
---|
| 576 | GMaxp_idx = t;
|
---|
[2645] | 577 | }
|
---|
[4068] | 578 | } else {
|
---|
| 579 | if (!is_lower_bound(t))
|
---|
| 580 | if (G[t] >= GMaxn) {
|
---|
| 581 | GMaxn = G[t];
|
---|
| 582 | GMaxn_idx = t;
|
---|
[2645] | 583 | }
|
---|
| 584 | }
|
---|
| 585 |
|
---|
[4068] | 586 | int ip = GMaxp_idx;
|
---|
| 587 | int iN = GMaxn_idx;
|
---|
| 588 | float[] Q_ip = null;
|
---|
| 589 | float[] Q_in = null;
|
---|
| 590 | if (ip != -1) // null Q_ip not accessed: GMaxp=-INF if ip=-1
|
---|
| 591 | Q_ip = Q.GetQ(ip, active_size);
|
---|
| 592 | if (iN != -1)
|
---|
| 593 | Q_in = Q.GetQ(iN, active_size);
|
---|
[2645] | 594 |
|
---|
[4068] | 595 | for (int j = 0; j < active_size; j++) {
|
---|
| 596 | if (y[j] == +1) {
|
---|
| 597 | if (!is_lower_bound(j)) {
|
---|
| 598 | double grad_diff = GMaxp + G[j];
|
---|
| 599 | if (G[j] >= GMaxp2)
|
---|
| 600 | GMaxp2 = G[j];
|
---|
| 601 | if (grad_diff > 0) {
|
---|
| 602 | double obj_diff;
|
---|
| 603 | double quad_coef = Q_ip[ip] + QD[j] - 2 * Q_ip[j];
|
---|
| 604 | if (quad_coef > 0)
|
---|
| 605 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
---|
| 606 | else
|
---|
| 607 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
---|
| 608 |
|
---|
| 609 | if (obj_diff <= obj_diff_Min) {
|
---|
| 610 | GMin_idx = j;
|
---|
| 611 | obj_diff_Min = obj_diff;
|
---|
| 612 | }
|
---|
[2645] | 613 | }
|
---|
[4068] | 614 | }
|
---|
| 615 | } else {
|
---|
| 616 | if (!is_upper_bound(j)) {
|
---|
| 617 | double grad_diff = GMaxn - G[j];
|
---|
| 618 | if (-G[j] >= GMaxn2)
|
---|
| 619 | GMaxn2 = -G[j];
|
---|
| 620 | if (grad_diff > 0) {
|
---|
| 621 | double obj_diff;
|
---|
| 622 | double quad_coef = Q_in[iN] + QD[j] - 2 * Q_in[j];
|
---|
| 623 | if (quad_coef > 0)
|
---|
| 624 | obj_diff = -(grad_diff * grad_diff) / quad_coef;
|
---|
| 625 | else
|
---|
| 626 | obj_diff = -(grad_diff * grad_diff) / 1e-12;
|
---|
[2645] | 627 |
|
---|
[4068] | 628 | if (obj_diff <= obj_diff_Min) {
|
---|
| 629 | GMin_idx = j;
|
---|
| 630 | obj_diff_Min = obj_diff;
|
---|
| 631 | }
|
---|
[2645] | 632 | }
|
---|
[4068] | 633 | }
|
---|
[2645] | 634 | }
|
---|
[4068] | 635 | }
|
---|
[2645] | 636 |
|
---|
[4068] | 637 | if (Math.Max(GMaxp + GMaxp2, GMaxn + GMaxn2) < EPS)
|
---|
| 638 | return 1;
|
---|
[2645] | 639 |
|
---|
[4068] | 640 | if (y[GMin_idx] == +1)
|
---|
| 641 | working_set[0] = GMaxp_idx;
|
---|
| 642 | else
|
---|
| 643 | working_set[0] = GMaxn_idx;
|
---|
| 644 | working_set[1] = GMin_idx;
|
---|
[2645] | 645 |
|
---|
[4068] | 646 | return 0;
|
---|
| 647 | }
|
---|
[2645] | 648 |
|
---|
[4068] | 649 | private bool be_shrunk(int i, double GMax1, double GMax2, double GMax3, double GMax4) {
|
---|
| 650 | if (is_upper_bound(i)) {
|
---|
| 651 | if (y[i] == +1)
|
---|
| 652 | return (-G[i] > GMax1);
|
---|
| 653 | else
|
---|
| 654 | return (-G[i] > GMax4);
|
---|
| 655 | } else if (is_lower_bound(i)) {
|
---|
| 656 | if (y[i] == +1)
|
---|
| 657 | return (G[i] > GMax2);
|
---|
| 658 | else
|
---|
| 659 | return (G[i] > GMax3);
|
---|
| 660 | } else
|
---|
| 661 | return (false);
|
---|
[2645] | 662 | }
|
---|
| 663 |
|
---|
[4068] | 664 | protected override sealed void do_shrinking() {
|
---|
| 665 | double GMax1 = -INF; // Max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
|
---|
| 666 | double GMax2 = -INF; // Max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
|
---|
| 667 | double GMax3 = -INF; // Max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
|
---|
| 668 | double GMax4 = -INF; // Max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }
|
---|
[2645] | 669 |
|
---|
[4068] | 670 | // find Maximal violating pair first
|
---|
| 671 | int i;
|
---|
| 672 | for (i = 0; i < active_size; i++) {
|
---|
| 673 | if (!is_upper_bound(i)) {
|
---|
| 674 | if (y[i] == +1) {
|
---|
| 675 | if (-G[i] > GMax1) GMax1 = -G[i];
|
---|
| 676 | } else if (-G[i] > GMax4) GMax4 = -G[i];
|
---|
[2645] | 677 | }
|
---|
[4068] | 678 | if (!is_lower_bound(i)) {
|
---|
| 679 | if (y[i] == +1) {
|
---|
| 680 | if (G[i] > GMax2) GMax2 = G[i];
|
---|
| 681 | } else if (G[i] > GMax3) GMax3 = G[i];
|
---|
[2645] | 682 | }
|
---|
[4068] | 683 | }
|
---|
[2645] | 684 |
|
---|
[4068] | 685 | if (unshrink == false && Math.Max(GMax1 + GMax2, GMax3 + GMax4) <= EPS * 10) {
|
---|
| 686 | unshrink = true;
|
---|
| 687 | reconstruct_gradient();
|
---|
| 688 | active_size = l;
|
---|
| 689 | }
|
---|
[2645] | 690 |
|
---|
[4068] | 691 | for (i = 0; i < active_size; i++)
|
---|
| 692 | if (be_shrunk(i, GMax1, GMax2, GMax3, GMax4)) {
|
---|
| 693 | active_size--;
|
---|
| 694 | while (active_size > i) {
|
---|
| 695 | if (!be_shrunk(active_size, GMax1, GMax2, GMax3, GMax4)) {
|
---|
| 696 | swap_index(i, active_size);
|
---|
| 697 | break;
|
---|
| 698 | }
|
---|
| 699 | active_size--;
|
---|
| 700 | }
|
---|
[2645] | 701 | }
|
---|
| 702 | }
|
---|
| 703 |
|
---|
[4068] | 704 | protected override sealed double calculate_rho() {
|
---|
| 705 | int nr_free1 = 0, nr_free2 = 0;
|
---|
| 706 | double ub1 = INF, ub2 = INF;
|
---|
| 707 | double lb1 = -INF, lb2 = -INF;
|
---|
| 708 | double sum_free1 = 0, sum_free2 = 0;
|
---|
[2645] | 709 |
|
---|
[4068] | 710 | for (int i = 0; i < active_size; i++) {
|
---|
| 711 | if (y[i] == +1) {
|
---|
| 712 | if (is_lower_bound(i))
|
---|
| 713 | ub1 = Math.Min(ub1, G[i]);
|
---|
| 714 | else if (is_upper_bound(i))
|
---|
| 715 | lb1 = Math.Max(lb1, G[i]);
|
---|
| 716 | else {
|
---|
| 717 | ++nr_free1;
|
---|
| 718 | sum_free1 += G[i];
|
---|
| 719 | }
|
---|
| 720 | } else {
|
---|
| 721 | if (is_lower_bound(i))
|
---|
| 722 | ub2 = Math.Min(ub2, G[i]);
|
---|
| 723 | else if (is_upper_bound(i))
|
---|
| 724 | lb2 = Math.Max(lb2, G[i]);
|
---|
| 725 | else {
|
---|
| 726 | ++nr_free2;
|
---|
| 727 | sum_free2 += G[i];
|
---|
| 728 | }
|
---|
[2645] | 729 | }
|
---|
[4068] | 730 | }
|
---|
[2645] | 731 |
|
---|
[4068] | 732 | double r1, r2;
|
---|
| 733 | if (nr_free1 > 0)
|
---|
| 734 | r1 = sum_free1 / nr_free1;
|
---|
| 735 | else
|
---|
| 736 | r1 = (ub1 + lb1) / 2;
|
---|
[2645] | 737 |
|
---|
[4068] | 738 | if (nr_free2 > 0)
|
---|
| 739 | r2 = sum_free2 / nr_free2;
|
---|
| 740 | else
|
---|
| 741 | r2 = (ub2 + lb2) / 2;
|
---|
[2645] | 742 |
|
---|
[4068] | 743 | si.r = (r1 + r2) / 2;
|
---|
| 744 | return (r1 - r2) / 2;
|
---|
[2645] | 745 | }
|
---|
[4068] | 746 | }
|
---|
[2645] | 747 |
|
---|
[4068] | 748 | //
|
---|
| 749 | // Q matrices for various formulations
|
---|
| 750 | //
|
---|
| 751 | class SVC_Q : Kernel {
|
---|
| 752 | private sbyte[] y;
|
---|
| 753 | private Cache cache;
|
---|
| 754 | private float[] QD;
|
---|
[2645] | 755 |
|
---|
[4068] | 756 | public SVC_Q(Problem prob, Parameter param, sbyte[] y_)
|
---|
| 757 | : base(prob.Count, prob.X, param) {
|
---|
| 758 | y = (sbyte[])y_.Clone();
|
---|
| 759 | cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
|
---|
| 760 | QD = new float[prob.Count];
|
---|
| 761 | for (int i = 0; i < prob.Count; i++)
|
---|
| 762 | QD[i] = (float)KernelFunction(i, i);
|
---|
| 763 | }
|
---|
[2645] | 764 |
|
---|
[4068] | 765 | public override sealed float[] GetQ(int i, int len) {
|
---|
| 766 | float[] data = null;
|
---|
| 767 | int start, j;
|
---|
| 768 | if ((start = cache.GetData(i, ref data, len)) < len) {
|
---|
| 769 | for (j = start; j < len; j++)
|
---|
| 770 | data[j] = (float)(y[i] * y[j] * KernelFunction(i, j));
|
---|
| 771 | }
|
---|
| 772 | return data;
|
---|
| 773 | }
|
---|
[2645] | 774 |
|
---|
[4068] | 775 | public override sealed float[] GetQD() {
|
---|
| 776 | return QD;
|
---|
| 777 | }
|
---|
[2645] | 778 |
|
---|
[4068] | 779 | public override sealed void SwapIndex(int i, int j) {
|
---|
| 780 | cache.SwapIndex(i, j);
|
---|
| 781 | base.SwapIndex(i, j);
|
---|
| 782 | y.SwapIndex(i, j);
|
---|
| 783 | QD.SwapIndex(i, j);
|
---|
| 784 | }
|
---|
| 785 | }
|
---|
[2645] | 786 |
|
---|
[4068] | 787 | class ONE_CLASS_Q : Kernel {
|
---|
| 788 | private Cache cache;
|
---|
| 789 | private float[] QD;
|
---|
| 790 |
|
---|
| 791 | public ONE_CLASS_Q(Problem prob, Parameter param)
|
---|
| 792 | : base(prob.Count, prob.X, param) {
|
---|
| 793 | cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
|
---|
| 794 | QD = new float[prob.Count];
|
---|
| 795 | for (int i = 0; i < prob.Count; i++)
|
---|
| 796 | QD[i] = (float)KernelFunction(i, i);
|
---|
[2645] | 797 | }
|
---|
| 798 |
|
---|
[4068] | 799 | public override sealed float[] GetQ(int i, int len) {
|
---|
| 800 | float[] data = null;
|
---|
| 801 | int start, j;
|
---|
| 802 | if ((start = cache.GetData(i, ref data, len)) < len) {
|
---|
| 803 | for (j = start; j < len; j++)
|
---|
| 804 | data[j] = (float)KernelFunction(i, j);
|
---|
| 805 | }
|
---|
| 806 | return data;
|
---|
| 807 | }
|
---|
[2645] | 808 |
|
---|
[4068] | 809 | public override sealed float[] GetQD() {
|
---|
| 810 | return QD;
|
---|
| 811 | }
|
---|
[2645] | 812 |
|
---|
[4068] | 813 | public override sealed void SwapIndex(int i, int j) {
|
---|
| 814 | cache.SwapIndex(i, j);
|
---|
| 815 | base.SwapIndex(i, j);
|
---|
| 816 | QD.SwapIndex(i, j);
|
---|
| 817 | }
|
---|
| 818 | }
|
---|
[2645] | 819 |
|
---|
[4068] | 820 | class SVR_Q : Kernel {
|
---|
| 821 | private int l;
|
---|
| 822 | private Cache cache;
|
---|
| 823 | private sbyte[] sign;
|
---|
| 824 | private int[] index;
|
---|
| 825 | private int next_buffer;
|
---|
| 826 | private float[][] buffer;
|
---|
| 827 | private float[] QD;
|
---|
[2645] | 828 |
|
---|
[4068] | 829 | public SVR_Q(Problem prob, Parameter param)
|
---|
| 830 | : base(prob.Count, prob.X, param) {
|
---|
| 831 | l = prob.Count;
|
---|
| 832 | cache = new Cache(l, (long)(param.CacheSize * (1 << 20)));
|
---|
| 833 | QD = new float[2 * l];
|
---|
| 834 | sign = new sbyte[2 * l];
|
---|
| 835 | index = new int[2 * l];
|
---|
| 836 | for (int k = 0; k < l; k++) {
|
---|
| 837 | sign[k] = 1;
|
---|
| 838 | sign[k + l] = -1;
|
---|
| 839 | index[k] = k;
|
---|
| 840 | index[k + l] = k;
|
---|
| 841 | QD[k] = (float)KernelFunction(k, k);
|
---|
| 842 | QD[k + l] = QD[k];
|
---|
| 843 | }
|
---|
| 844 | buffer = new float[2][];
|
---|
| 845 | buffer[0] = new float[2 * l];
|
---|
| 846 | buffer[1] = new float[2 * l];
|
---|
| 847 | next_buffer = 0;
|
---|
| 848 | }
|
---|
[2645] | 849 |
|
---|
[4068] | 850 | public override sealed void SwapIndex(int i, int j) {
|
---|
| 851 | sign.SwapIndex(i, j);
|
---|
| 852 | index.SwapIndex(i, j);
|
---|
| 853 | QD.SwapIndex(i, j);
|
---|
| 854 | }
|
---|
[2645] | 855 |
|
---|
[4068] | 856 | public override sealed float[] GetQ(int i, int len) {
|
---|
| 857 | float[] data = null;
|
---|
| 858 | int j, real_i = index[i];
|
---|
| 859 | if (cache.GetData(real_i, ref data, l) < l) {
|
---|
| 860 | for (j = 0; j < l; j++)
|
---|
| 861 | data[j] = (float)KernelFunction(real_i, j);
|
---|
| 862 | }
|
---|
[2645] | 863 |
|
---|
[4068] | 864 | // reorder and copy
|
---|
| 865 | float[] buf = buffer[next_buffer];
|
---|
| 866 | next_buffer = 1 - next_buffer;
|
---|
| 867 | sbyte si = sign[i];
|
---|
| 868 | for (j = 0; j < len; j++)
|
---|
| 869 | buf[j] = (float)si * sign[j] * data[index[j]];
|
---|
| 870 | return buf;
|
---|
| 871 | }
|
---|
[2645] | 872 |
|
---|
[4068] | 873 | public override sealed float[] GetQD() {
|
---|
| 874 | return QD;
|
---|
| 875 | }
|
---|
| 876 | }
|
---|
[2645] | 877 |
|
---|
[4068] | 878 | internal class Procedures {
|
---|
| 879 | private static bool _verbose;
|
---|
| 880 | public static bool IsVerbose {
|
---|
| 881 | get {
|
---|
| 882 | return _verbose;
|
---|
| 883 | }
|
---|
| 884 | set {
|
---|
| 885 | _verbose = value;
|
---|
| 886 | }
|
---|
| 887 | }
|
---|
| 888 | //
|
---|
| 889 | // construct and solve various formulations
|
---|
| 890 | //
|
---|
| 891 | public const int LIBSVM_VERSION = 289;
|
---|
[2645] | 892 |
|
---|
[4068] | 893 | public static TextWriter svm_print_string = Console.Out;
|
---|
[2645] | 894 |
|
---|
[4068] | 895 | public static void info(string s) {
|
---|
| 896 | if (_verbose)
|
---|
| 897 | svm_print_string.Write(s);
|
---|
| 898 | }
|
---|
[2645] | 899 |
|
---|
[4068] | 900 | private static void solve_c_svc(Problem prob, Parameter param,
|
---|
| 901 | double[] alpha, Solver.SolutionInfo si,
|
---|
| 902 | double Cp, double Cn) {
|
---|
| 903 | int l = prob.Count;
|
---|
| 904 | double[] Minus_ones = new double[l];
|
---|
| 905 | sbyte[] y = new sbyte[l];
|
---|
[2645] | 906 |
|
---|
[4068] | 907 | int i;
|
---|
[2645] | 908 |
|
---|
[4068] | 909 | for (i = 0; i < l; i++) {
|
---|
| 910 | alpha[i] = 0;
|
---|
| 911 | Minus_ones[i] = -1;
|
---|
| 912 | if (prob.Y[i] > 0) y[i] = +1; else y[i] = -1;
|
---|
| 913 | }
|
---|
[2645] | 914 |
|
---|
[4068] | 915 | Solver s = new Solver();
|
---|
| 916 | s.Solve(l, new SVC_Q(prob, param, y), Minus_ones, y,
|
---|
| 917 | alpha, Cp, Cn, param.EPS, si, param.Shrinking);
|
---|
[2645] | 918 |
|
---|
[4068] | 919 | double sum_alpha = 0;
|
---|
| 920 | for (i = 0; i < l; i++)
|
---|
| 921 | sum_alpha += alpha[i];
|
---|
[2645] | 922 |
|
---|
[4068] | 923 | if (Cp == Cn)
|
---|
| 924 | Procedures.info("nu = " + sum_alpha / (Cp * prob.Count) + "\n");
|
---|
[2645] | 925 |
|
---|
[4068] | 926 | for (i = 0; i < l; i++)
|
---|
| 927 | alpha[i] *= y[i];
|
---|
| 928 | }
|
---|
[2645] | 929 |
|
---|
[4068] | 930 | private static void solve_nu_svc(Problem prob, Parameter param,
|
---|
| 931 | double[] alpha, Solver.SolutionInfo si) {
|
---|
| 932 | int i;
|
---|
| 933 | int l = prob.Count;
|
---|
| 934 | double nu = param.Nu;
|
---|
[2645] | 935 |
|
---|
[4068] | 936 | sbyte[] y = new sbyte[l];
|
---|
| 937 |
|
---|
| 938 | for (i = 0; i < l; i++)
|
---|
| 939 | if (prob.Y[i] > 0)
|
---|
| 940 | y[i] = +1;
|
---|
| 941 | else
|
---|
| 942 | y[i] = -1;
|
---|
| 943 |
|
---|
| 944 | double sum_pos = nu * l / 2;
|
---|
| 945 | double sum_neg = nu * l / 2;
|
---|
| 946 |
|
---|
| 947 | for (i = 0; i < l; i++)
|
---|
| 948 | if (y[i] == +1) {
|
---|
| 949 | alpha[i] = Math.Min(1.0, sum_pos);
|
---|
| 950 | sum_pos -= alpha[i];
|
---|
| 951 | } else {
|
---|
| 952 | alpha[i] = Math.Min(1.0, sum_neg);
|
---|
| 953 | sum_neg -= alpha[i];
|
---|
[2645] | 954 | }
|
---|
| 955 |
|
---|
[4068] | 956 | double[] zeros = new double[l];
|
---|
[2645] | 957 |
|
---|
[4068] | 958 | for (i = 0; i < l; i++)
|
---|
| 959 | zeros[i] = 0;
|
---|
[2645] | 960 |
|
---|
[4068] | 961 | Solver_NU s = new Solver_NU();
|
---|
| 962 | s.Solve(l, new SVC_Q(prob, param, y), zeros, y, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
|
---|
| 963 | double r = si.r;
|
---|
[2645] | 964 |
|
---|
[4068] | 965 | Procedures.info("C = " + 1 / r + "\n");
|
---|
[2645] | 966 |
|
---|
[4068] | 967 | for (i = 0; i < l; i++)
|
---|
| 968 | alpha[i] *= y[i] / r;
|
---|
[2645] | 969 |
|
---|
[4068] | 970 | si.rho /= r;
|
---|
| 971 | si.obj /= (r * r);
|
---|
| 972 | si.upper_bound_p = 1 / r;
|
---|
| 973 | si.upper_bound_n = 1 / r;
|
---|
| 974 | }
|
---|
[2645] | 975 |
|
---|
[4068] | 976 | private static void solve_one_class(Problem prob, Parameter param,
|
---|
| 977 | double[] alpha, Solver.SolutionInfo si) {
|
---|
| 978 | int l = prob.Count;
|
---|
| 979 | double[] zeros = new double[l];
|
---|
| 980 | sbyte[] ones = new sbyte[l];
|
---|
| 981 | int i;
|
---|
[2645] | 982 |
|
---|
[4068] | 983 | int n = (int)(param.Nu * prob.Count); // # of alpha's at upper bound
|
---|
[2645] | 984 |
|
---|
[4068] | 985 | for (i = 0; i < n; i++)
|
---|
| 986 | alpha[i] = 1;
|
---|
| 987 | if (n < prob.Count)
|
---|
| 988 | alpha[n] = param.Nu * prob.Count - n;
|
---|
| 989 | for (i = n + 1; i < l; i++)
|
---|
| 990 | alpha[i] = 0;
|
---|
[2645] | 991 |
|
---|
[4068] | 992 | for (i = 0; i < l; i++) {
|
---|
| 993 | zeros[i] = 0;
|
---|
| 994 | ones[i] = 1;
|
---|
| 995 | }
|
---|
[2645] | 996 |
|
---|
[4068] | 997 | Solver s = new Solver();
|
---|
| 998 | s.Solve(l, new ONE_CLASS_Q(prob, param), zeros, ones, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
|
---|
| 999 | }
|
---|
[2645] | 1000 |
|
---|
[4068] | 1001 | private static void solve_epsilon_svr(Problem prob, Parameter param, double[] alpha, Solver.SolutionInfo si) {
|
---|
| 1002 | int l = prob.Count;
|
---|
| 1003 | double[] alpha2 = new double[2 * l];
|
---|
| 1004 | double[] linear_term = new double[2 * l];
|
---|
| 1005 | sbyte[] y = new sbyte[2 * l];
|
---|
| 1006 | int i;
|
---|
[2645] | 1007 |
|
---|
[4068] | 1008 | for (i = 0; i < l; i++) {
|
---|
| 1009 | alpha2[i] = 0;
|
---|
| 1010 | linear_term[i] = param.P - prob.Y[i];
|
---|
| 1011 | y[i] = 1;
|
---|
[2645] | 1012 |
|
---|
[4068] | 1013 | alpha2[i + l] = 0;
|
---|
| 1014 | linear_term[i + l] = param.P + prob.Y[i];
|
---|
| 1015 | y[i + l] = -1;
|
---|
| 1016 | }
|
---|
[2645] | 1017 |
|
---|
[4068] | 1018 | Solver s = new Solver();
|
---|
| 1019 | s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, param.C, param.C, param.EPS, si, param.Shrinking);
|
---|
[2645] | 1020 |
|
---|
[4068] | 1021 | double sum_alpha = 0;
|
---|
| 1022 | for (i = 0; i < l; i++) {
|
---|
| 1023 | alpha[i] = alpha2[i] - alpha2[i + l];
|
---|
| 1024 | sum_alpha += Math.Abs(alpha[i]);
|
---|
| 1025 | }
|
---|
| 1026 | Procedures.info("nu = " + sum_alpha / (param.C * l) + "\n");
|
---|
| 1027 | }
|
---|
[2645] | 1028 |
|
---|
[4068] | 1029 | private static void solve_nu_svr(Problem prob, Parameter param,
|
---|
| 1030 | double[] alpha, Solver.SolutionInfo si) {
|
---|
| 1031 | int l = prob.Count;
|
---|
| 1032 | double C = param.C;
|
---|
| 1033 | double[] alpha2 = new double[2 * l];
|
---|
| 1034 | double[] linear_term = new double[2 * l];
|
---|
| 1035 | sbyte[] y = new sbyte[2 * l];
|
---|
| 1036 | int i;
|
---|
[2645] | 1037 |
|
---|
[4068] | 1038 | double sum = C * param.Nu * l / 2;
|
---|
| 1039 | for (i = 0; i < l; i++) {
|
---|
| 1040 | alpha2[i] = alpha2[i + l] = Math.Min(sum, C);
|
---|
| 1041 | sum -= alpha2[i];
|
---|
[2645] | 1042 |
|
---|
[4068] | 1043 | linear_term[i] = -prob.Y[i];
|
---|
| 1044 | y[i] = 1;
|
---|
[2645] | 1045 |
|
---|
[4068] | 1046 | linear_term[i + l] = prob.Y[i];
|
---|
| 1047 | y[i + l] = -1;
|
---|
| 1048 | }
|
---|
[2645] | 1049 |
|
---|
[4068] | 1050 | Solver_NU s = new Solver_NU();
|
---|
| 1051 | s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, C, C, param.EPS, si, param.Shrinking);
|
---|
[2645] | 1052 |
|
---|
[4068] | 1053 | Procedures.info("epsilon = " + (-si.r) + "\n");
|
---|
[2645] | 1054 |
|
---|
[4068] | 1055 | for (i = 0; i < l; i++)
|
---|
| 1056 | alpha[i] = alpha2[i] - alpha2[i + l];
|
---|
| 1057 | }
|
---|
[2645] | 1058 |
|
---|
[4068] | 1059 | //
|
---|
| 1060 | // decision_function
|
---|
| 1061 | //
|
---|
| 1062 | internal class decision_function {
|
---|
| 1063 | public double[] alpha;
|
---|
| 1064 | public double rho;
|
---|
| 1065 | };
|
---|
| 1066 |
|
---|
| 1067 | static decision_function svm_train_one(Problem prob, Parameter param, double Cp, double Cn) {
|
---|
| 1068 | double[] alpha = new double[prob.Count];
|
---|
| 1069 | Solver.SolutionInfo si = new Solver.SolutionInfo();
|
---|
| 1070 | switch (param.SvmType) {
|
---|
| 1071 | case SvmType.C_SVC:
|
---|
| 1072 | solve_c_svc(prob, param, alpha, si, Cp, Cn);
|
---|
| 1073 | break;
|
---|
| 1074 | case SvmType.NU_SVC:
|
---|
| 1075 | solve_nu_svc(prob, param, alpha, si);
|
---|
| 1076 | break;
|
---|
| 1077 | case SvmType.ONE_CLASS:
|
---|
| 1078 | solve_one_class(prob, param, alpha, si);
|
---|
| 1079 | break;
|
---|
| 1080 | case SvmType.EPSILON_SVR:
|
---|
| 1081 | solve_epsilon_svr(prob, param, alpha, si);
|
---|
| 1082 | break;
|
---|
| 1083 | case SvmType.NU_SVR:
|
---|
| 1084 | solve_nu_svr(prob, param, alpha, si);
|
---|
| 1085 | break;
|
---|
| 1086 | }
|
---|
| 1087 |
|
---|
| 1088 | Procedures.info("obj = " + si.obj + ", rho = " + si.rho + "\n");
|
---|
| 1089 |
|
---|
| 1090 | // output SVs
|
---|
| 1091 |
|
---|
| 1092 | int nSV = 0;
|
---|
| 1093 | int nBSV = 0;
|
---|
| 1094 | for (int i = 0; i < prob.Count; i++) {
|
---|
| 1095 | if (Math.Abs(alpha[i]) > 0) {
|
---|
| 1096 | ++nSV;
|
---|
| 1097 | if (prob.Y[i] > 0) {
|
---|
| 1098 | if (Math.Abs(alpha[i]) >= si.upper_bound_p)
|
---|
| 1099 | ++nBSV;
|
---|
| 1100 | } else {
|
---|
| 1101 | if (Math.Abs(alpha[i]) >= si.upper_bound_n)
|
---|
| 1102 | ++nBSV;
|
---|
| 1103 | }
|
---|
[2645] | 1104 | }
|
---|
[4068] | 1105 | }
|
---|
[2645] | 1106 |
|
---|
[4068] | 1107 | Procedures.info("nSV = " + nSV + ", nBSV = " + nBSV + "\n");
|
---|
[2645] | 1108 |
|
---|
[4068] | 1109 | decision_function f = new decision_function();
|
---|
| 1110 | f.alpha = alpha;
|
---|
| 1111 | f.rho = si.rho;
|
---|
| 1112 | return f;
|
---|
| 1113 | }
|
---|
[2645] | 1114 |
|
---|
[4068] | 1115 | // Platt's binary SVM Probablistic Output: an improvement from Lin et al.
|
---|
| 1116 | private static void sigmoid_train(int l, double[] dec_values, double[] labels,
|
---|
| 1117 | double[] probAB) {
|
---|
| 1118 | double A, B;
|
---|
| 1119 | double prior1 = 0, prior0 = 0;
|
---|
| 1120 | int i;
|
---|
[2645] | 1121 |
|
---|
[4068] | 1122 | for (i = 0; i < l; i++)
|
---|
| 1123 | if (labels[i] > 0) prior1 += 1;
|
---|
| 1124 | else prior0 += 1;
|
---|
[2645] | 1125 |
|
---|
[4068] | 1126 | int Max_iter = 100; // Maximal number of iterations
|
---|
| 1127 | double Min_step = 1e-10; // Minimal step taken in line search
|
---|
| 1128 | double sigma = 1e-12; // For numerically strict PD of Hessian
|
---|
| 1129 | double eps = 1e-5;
|
---|
| 1130 | double hiTarget = (prior1 + 1.0) / (prior1 + 2.0);
|
---|
| 1131 | double loTarget = 1 / (prior0 + 2.0);
|
---|
| 1132 | double[] t = new double[l];
|
---|
| 1133 | double fApB, p, q, h11, h22, h21, g1, g2, det, dA, dB, gd, stepsize;
|
---|
| 1134 | double newA, newB, newf, d1, d2;
|
---|
| 1135 | int iter;
|
---|
[2645] | 1136 |
|
---|
[4068] | 1137 | // Initial Point and Initial Fun Value
|
---|
| 1138 | A = 0.0; B = Math.Log((prior0 + 1.0) / (prior1 + 1.0));
|
---|
| 1139 | double fval = 0.0;
|
---|
[2645] | 1140 |
|
---|
[4068] | 1141 | for (i = 0; i < l; i++) {
|
---|
| 1142 | if (labels[i] > 0) t[i] = hiTarget;
|
---|
| 1143 | else t[i] = loTarget;
|
---|
| 1144 | fApB = dec_values[i] * A + B;
|
---|
| 1145 | if (fApB >= 0)
|
---|
| 1146 | fval += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
|
---|
| 1147 | else
|
---|
| 1148 | fval += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
|
---|
| 1149 | }
|
---|
| 1150 | for (iter = 0; iter < Max_iter; iter++) {
|
---|
| 1151 | // Update Gradient and Hessian (use H' = H + sigma I)
|
---|
| 1152 | h11 = sigma; // numerically ensures strict PD
|
---|
| 1153 | h22 = sigma;
|
---|
| 1154 | h21 = 0.0; g1 = 0.0; g2 = 0.0;
|
---|
| 1155 | for (i = 0; i < l; i++) {
|
---|
| 1156 | fApB = dec_values[i] * A + B;
|
---|
| 1157 | if (fApB >= 0) {
|
---|
| 1158 | p = Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
|
---|
| 1159 | q = 1.0 / (1.0 + Math.Exp(-fApB));
|
---|
| 1160 | } else {
|
---|
| 1161 | p = 1.0 / (1.0 + Math.Exp(fApB));
|
---|
| 1162 | q = Math.Exp(fApB) / (1.0 + Math.Exp(fApB));
|
---|
| 1163 | }
|
---|
| 1164 | d2 = p * q;
|
---|
| 1165 | h11 += dec_values[i] * dec_values[i] * d2;
|
---|
| 1166 | h22 += d2;
|
---|
| 1167 | h21 += dec_values[i] * d2;
|
---|
| 1168 | d1 = t[i] - p;
|
---|
| 1169 | g1 += dec_values[i] * d1;
|
---|
| 1170 | g2 += d1;
|
---|
| 1171 | }
|
---|
[2645] | 1172 |
|
---|
[4068] | 1173 | // Stopping Criteria
|
---|
| 1174 | if (Math.Abs(g1) < eps && Math.Abs(g2) < eps)
|
---|
| 1175 | break;
|
---|
[2645] | 1176 |
|
---|
[4068] | 1177 | // Finding Newton direction: -inv(H') * g
|
---|
| 1178 | det = h11 * h22 - h21 * h21;
|
---|
| 1179 | dA = -(h22 * g1 - h21 * g2) / det;
|
---|
| 1180 | dB = -(-h21 * g1 + h11 * g2) / det;
|
---|
| 1181 | gd = g1 * dA + g2 * dB;
|
---|
[2645] | 1182 |
|
---|
| 1183 |
|
---|
[4068] | 1184 | stepsize = 1; // Line Search
|
---|
| 1185 | while (stepsize >= Min_step) {
|
---|
| 1186 | newA = A + stepsize * dA;
|
---|
| 1187 | newB = B + stepsize * dB;
|
---|
[2645] | 1188 |
|
---|
[4068] | 1189 | // New function value
|
---|
| 1190 | newf = 0.0;
|
---|
| 1191 | for (i = 0; i < l; i++) {
|
---|
| 1192 | fApB = dec_values[i] * newA + newB;
|
---|
[2645] | 1193 | if (fApB >= 0)
|
---|
[4068] | 1194 | newf += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
|
---|
[2645] | 1195 | else
|
---|
[4068] | 1196 | newf += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
|
---|
| 1197 | }
|
---|
| 1198 | // Check sufficient decrease
|
---|
| 1199 | if (newf < fval + 0.0001 * stepsize * gd) {
|
---|
| 1200 | A = newA; B = newB; fval = newf;
|
---|
| 1201 | break;
|
---|
| 1202 | } else
|
---|
| 1203 | stepsize = stepsize / 2.0;
|
---|
[2645] | 1204 | }
|
---|
| 1205 |
|
---|
[4068] | 1206 | if (stepsize < Min_step) {
|
---|
| 1207 | Procedures.info("Line search fails in two-class probability estimates\n");
|
---|
| 1208 | break;
|
---|
| 1209 | }
|
---|
| 1210 | }
|
---|
[2645] | 1211 |
|
---|
[4068] | 1212 | if (iter >= Max_iter)
|
---|
| 1213 | Procedures.info("Reaching Maximal iterations in two-class probability estimates\n");
|
---|
| 1214 | probAB[0] = A; probAB[1] = B;
|
---|
| 1215 | }
|
---|
[2645] | 1216 |
|
---|
[4068] | 1217 | private static double sigmoid_predict(double decision_value, double A, double B) {
|
---|
| 1218 | double fApB = decision_value * A + B;
|
---|
| 1219 | if (fApB >= 0)
|
---|
| 1220 | return Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
|
---|
| 1221 | else
|
---|
| 1222 | return 1.0 / (1 + Math.Exp(fApB));
|
---|
| 1223 | }
|
---|
| 1224 |
|
---|
| 1225 | // Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
|
---|
| 1226 | private static void multiclass_probability(int k, double[,] r, double[] p) {
|
---|
| 1227 | int t, j;
|
---|
| 1228 | int iter = 0, Max_iter = Math.Max(100, k);
|
---|
| 1229 | double[,] Q = new double[k, k];
|
---|
| 1230 | double[] Qp = new double[k];
|
---|
| 1231 | double pQp, eps = 0.005 / k;
|
---|
| 1232 |
|
---|
| 1233 | for (t = 0; t < k; t++) {
|
---|
| 1234 | p[t] = 1.0 / k; // Valid if k = 1
|
---|
| 1235 | Q[t, t] = 0;
|
---|
| 1236 | for (j = 0; j < t; j++) {
|
---|
| 1237 | Q[t, t] += r[j, t] * r[j, t];
|
---|
| 1238 | Q[t, j] = Q[j, t];
|
---|
[2645] | 1239 | }
|
---|
[4068] | 1240 | for (j = t + 1; j < k; j++) {
|
---|
| 1241 | Q[t, t] += r[j, t] * r[j, t];
|
---|
| 1242 | Q[t, j] = -r[j, t] * r[t, j];
|
---|
| 1243 | }
|
---|
| 1244 | }
|
---|
| 1245 | for (iter = 0; iter < Max_iter; iter++) {
|
---|
| 1246 | // stopping condition, recalculate QP,pQP for numerical accuracy
|
---|
| 1247 | pQp = 0;
|
---|
| 1248 | for (t = 0; t < k; t++) {
|
---|
| 1249 | Qp[t] = 0;
|
---|
| 1250 | for (j = 0; j < k; j++)
|
---|
| 1251 | Qp[t] += Q[t, j] * p[j];
|
---|
| 1252 | pQp += p[t] * Qp[t];
|
---|
| 1253 | }
|
---|
| 1254 | double Max_error = 0;
|
---|
| 1255 | for (t = 0; t < k; t++) {
|
---|
| 1256 | double error = Math.Abs(Qp[t] - pQp);
|
---|
| 1257 | if (error > Max_error)
|
---|
| 1258 | Max_error = error;
|
---|
| 1259 | }
|
---|
| 1260 | if (Max_error < eps) break;
|
---|
[2645] | 1261 |
|
---|
[4068] | 1262 | for (t = 0; t < k; t++) {
|
---|
| 1263 | double diff = (-Qp[t] + pQp) / Q[t, t];
|
---|
| 1264 | p[t] += diff;
|
---|
| 1265 | pQp = (pQp + diff * (diff * Q[t, t] + 2 * Qp[t])) / (1 + diff) / (1 + diff);
|
---|
| 1266 | for (j = 0; j < k; j++) {
|
---|
| 1267 | Qp[j] = (Qp[j] + diff * Q[t, j]) / (1 + diff);
|
---|
| 1268 | p[j] /= (1 + diff);
|
---|
| 1269 | }
|
---|
| 1270 | }
|
---|
| 1271 | }
|
---|
| 1272 | if (iter >= Max_iter)
|
---|
| 1273 | Procedures.info("Exceeds Max_iter in multiclass_prob\n");
|
---|
| 1274 | }
|
---|
[2645] | 1275 |
|
---|
[4068] | 1276 | // Cross-validation decision values for probability estimates
|
---|
| 1277 | private static void svm_binary_svc_probability(Problem prob, Parameter param, double Cp, double Cn, double[] probAB) {
|
---|
| 1278 | int i;
|
---|
| 1279 | int nr_fold = 5;
|
---|
| 1280 | int[] perm = new int[prob.Count];
|
---|
| 1281 | double[] dec_values = new double[prob.Count];
|
---|
[2645] | 1282 |
|
---|
[4068] | 1283 | // random shuffle
|
---|
| 1284 | Random rand = new Random();
|
---|
| 1285 | for (i = 0; i < prob.Count; i++) perm[i] = i;
|
---|
| 1286 | for (i = 0; i < prob.Count; i++) {
|
---|
| 1287 | int j = i + (int)(rand.NextDouble() * (prob.Count - i));
|
---|
| 1288 | do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
|
---|
| 1289 | }
|
---|
| 1290 | for (i = 0; i < nr_fold; i++) {
|
---|
| 1291 | int begin = i * prob.Count / nr_fold;
|
---|
| 1292 | int end = (i + 1) * prob.Count / nr_fold;
|
---|
| 1293 | int j, k;
|
---|
| 1294 | Problem subprob = new Problem();
|
---|
[2645] | 1295 |
|
---|
[4068] | 1296 | subprob.Count = prob.Count - (end - begin);
|
---|
| 1297 | subprob.X = new Node[subprob.Count][];
|
---|
| 1298 | subprob.Y = new double[subprob.Count];
|
---|
[2645] | 1299 |
|
---|
[4068] | 1300 | k = 0;
|
---|
| 1301 | for (j = 0; j < begin; j++) {
|
---|
| 1302 | subprob.X[k] = prob.X[perm[j]];
|
---|
| 1303 | subprob.Y[k] = prob.Y[perm[j]];
|
---|
| 1304 | ++k;
|
---|
[2645] | 1305 | }
|
---|
[4068] | 1306 | for (j = end; j < prob.Count; j++) {
|
---|
| 1307 | subprob.X[k] = prob.X[perm[j]];
|
---|
| 1308 | subprob.Y[k] = prob.Y[perm[j]];
|
---|
| 1309 | ++k;
|
---|
| 1310 | }
|
---|
| 1311 | int p_count = 0, n_count = 0;
|
---|
| 1312 | for (j = 0; j < k; j++)
|
---|
| 1313 | if (subprob.Y[j] > 0)
|
---|
| 1314 | p_count++;
|
---|
| 1315 | else
|
---|
| 1316 | n_count++;
|
---|
[2645] | 1317 |
|
---|
[4068] | 1318 | if (p_count == 0 && n_count == 0)
|
---|
| 1319 | for (j = begin; j < end; j++)
|
---|
| 1320 | dec_values[perm[j]] = 0;
|
---|
| 1321 | else if (p_count > 0 && n_count == 0)
|
---|
| 1322 | for (j = begin; j < end; j++)
|
---|
| 1323 | dec_values[perm[j]] = 1;
|
---|
| 1324 | else if (p_count == 0 && n_count > 0)
|
---|
| 1325 | for (j = begin; j < end; j++)
|
---|
| 1326 | dec_values[perm[j]] = -1;
|
---|
| 1327 | else {
|
---|
| 1328 | Parameter subparam = (Parameter)param.Clone();
|
---|
| 1329 | subparam.Probability = false;
|
---|
| 1330 | subparam.C = 1.0;
|
---|
| 1331 | subparam.Weights[1] = Cp;
|
---|
| 1332 | subparam.Weights[-1] = Cn;
|
---|
| 1333 | Model submodel = svm_train(subprob, subparam);
|
---|
| 1334 | for (j = begin; j < end; j++) {
|
---|
| 1335 | double[] dec_value = new double[1];
|
---|
| 1336 | svm_predict_values(submodel, prob.X[perm[j]], dec_value);
|
---|
| 1337 | dec_values[perm[j]] = dec_value[0];
|
---|
| 1338 | // ensure +1 -1 order; reason not using CV subroutine
|
---|
| 1339 | dec_values[perm[j]] *= submodel.ClassLabels[0];
|
---|
| 1340 | }
|
---|
[2645] | 1341 | }
|
---|
[4068] | 1342 | }
|
---|
| 1343 | sigmoid_train(prob.Count, dec_values, prob.Y, probAB);
|
---|
| 1344 | }
|
---|
[2645] | 1345 |
|
---|
[4068] | 1346 | // Return parameter of a Laplace distribution
|
---|
| 1347 | private static double svm_svr_probability(Problem prob, Parameter param) {
|
---|
| 1348 | int i;
|
---|
| 1349 | int nr_fold = 5;
|
---|
| 1350 | double[] ymv = new double[prob.Count];
|
---|
| 1351 | double mae = 0;
|
---|
[2645] | 1352 |
|
---|
[4068] | 1353 | Parameter newparam = (Parameter)param.Clone();
|
---|
| 1354 | newparam.Probability = false;
|
---|
| 1355 | svm_cross_validation(prob, newparam, nr_fold, ymv, true);
|
---|
| 1356 | for (i = 0; i < prob.Count; i++) {
|
---|
| 1357 | ymv[i] = prob.Y[i] - ymv[i];
|
---|
| 1358 | mae += Math.Abs(ymv[i]);
|
---|
| 1359 | }
|
---|
| 1360 | mae /= prob.Count;
|
---|
| 1361 | double std = Math.Sqrt(2 * mae * mae);
|
---|
| 1362 | int count = 0;
|
---|
| 1363 | mae = 0;
|
---|
| 1364 | for (i = 0; i < prob.Count; i++)
|
---|
| 1365 | if (Math.Abs(ymv[i]) > 5 * std)
|
---|
| 1366 | count = count + 1;
|
---|
| 1367 | else
|
---|
| 1368 | mae += Math.Abs(ymv[i]);
|
---|
| 1369 | mae /= (prob.Count - count);
|
---|
| 1370 | Procedures.info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma=" + mae + "\n");
|
---|
| 1371 | return mae;
|
---|
| 1372 | }
|
---|
[2645] | 1373 |
|
---|
[4068] | 1374 | // label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
|
---|
| 1375 | // perm, length l, must be allocated before calling this subroutine
|
---|
| 1376 | private static void svm_group_classes(Problem prob, int[] nr_class_ret, int[][] label_ret, int[][] start_ret, int[][] count_ret, int[] perm) {
|
---|
| 1377 | int l = prob.Count;
|
---|
| 1378 | int Max_nr_class = 16;
|
---|
| 1379 | int nr_class = 0;
|
---|
| 1380 | int[] label = new int[Max_nr_class];
|
---|
| 1381 | int[] count = new int[Max_nr_class];
|
---|
| 1382 | int[] data_label = new int[l];
|
---|
| 1383 | int i;
|
---|
[2645] | 1384 |
|
---|
[4068] | 1385 | for (i = 0; i < l; i++) {
|
---|
| 1386 | int this_label = (int)(prob.Y[i]);
|
---|
| 1387 | int j;
|
---|
| 1388 | for (j = 0; j < nr_class; j++) {
|
---|
| 1389 | if (this_label == label[j]) {
|
---|
| 1390 | ++count[j];
|
---|
| 1391 | break;
|
---|
| 1392 | }
|
---|
[2645] | 1393 | }
|
---|
[4068] | 1394 | data_label[i] = j;
|
---|
| 1395 | if (j == nr_class) {
|
---|
| 1396 | if (nr_class == Max_nr_class) {
|
---|
| 1397 | Max_nr_class *= 2;
|
---|
| 1398 | int[] new_data = new int[Max_nr_class];
|
---|
| 1399 | Array.Copy(label, 0, new_data, 0, label.Length);
|
---|
| 1400 | label = new_data;
|
---|
| 1401 | new_data = new int[Max_nr_class];
|
---|
| 1402 | Array.Copy(count, 0, new_data, 0, count.Length);
|
---|
| 1403 | count = new_data;
|
---|
| 1404 | }
|
---|
| 1405 | label[nr_class] = this_label;
|
---|
| 1406 | count[nr_class] = 1;
|
---|
| 1407 | ++nr_class;
|
---|
| 1408 | }
|
---|
| 1409 | }
|
---|
[2645] | 1410 |
|
---|
[4068] | 1411 | int[] start = new int[nr_class];
|
---|
| 1412 | start[0] = 0;
|
---|
| 1413 | for (i = 1; i < nr_class; i++)
|
---|
| 1414 | start[i] = start[i - 1] + count[i - 1];
|
---|
| 1415 | for (i = 0; i < l; i++) {
|
---|
| 1416 | perm[start[data_label[i]]] = i;
|
---|
| 1417 | ++start[data_label[i]];
|
---|
| 1418 | }
|
---|
| 1419 | start[0] = 0;
|
---|
| 1420 | for (i = 1; i < nr_class; i++)
|
---|
| 1421 | start[i] = start[i - 1] + count[i - 1];
|
---|
[2645] | 1422 |
|
---|
[4068] | 1423 | nr_class_ret[0] = nr_class;
|
---|
| 1424 | label_ret[0] = label;
|
---|
| 1425 | start_ret[0] = start;
|
---|
| 1426 | count_ret[0] = count;
|
---|
| 1427 | }
|
---|
[2645] | 1428 |
|
---|
[4068] | 1429 | //
|
---|
| 1430 | // Interface functions
|
---|
| 1431 | //
|
---|
| 1432 | public static Model svm_train(Problem prob, Parameter param) {
|
---|
| 1433 | Model model = new Model();
|
---|
| 1434 | model.Parameter = param;
|
---|
[2645] | 1435 |
|
---|
[4068] | 1436 | if (param.SvmType == SvmType.ONE_CLASS ||
|
---|
| 1437 | param.SvmType == SvmType.EPSILON_SVR ||
|
---|
| 1438 | param.SvmType == SvmType.NU_SVR) {
|
---|
| 1439 | // regression or one-class-svm
|
---|
| 1440 | model.NumberOfClasses = 2;
|
---|
| 1441 | model.ClassLabels = null;
|
---|
| 1442 | model.NumberOfSVPerClass = null;
|
---|
| 1443 | model.PairwiseProbabilityA = null; model.PairwiseProbabilityB = null;
|
---|
| 1444 | model.SupportVectorCoefficients = new double[1][];
|
---|
[2645] | 1445 |
|
---|
[4068] | 1446 | if (param.Probability &&
|
---|
| 1447 | (param.SvmType == SvmType.EPSILON_SVR ||
|
---|
| 1448 | param.SvmType == SvmType.NU_SVR)) {
|
---|
| 1449 | model.PairwiseProbabilityA = new double[1];
|
---|
| 1450 | model.PairwiseProbabilityA[0] = svm_svr_probability(prob, param);
|
---|
| 1451 | }
|
---|
[2645] | 1452 |
|
---|
[4068] | 1453 | decision_function f = svm_train_one(prob, param, 0, 0);
|
---|
| 1454 | model.Rho = new double[1];
|
---|
| 1455 | model.Rho[0] = f.rho;
|
---|
[2645] | 1456 |
|
---|
[4068] | 1457 | int nSV = 0;
|
---|
| 1458 | int i;
|
---|
| 1459 | for (i = 0; i < prob.Count; i++)
|
---|
| 1460 | if (Math.Abs(f.alpha[i]) > 0) ++nSV;
|
---|
| 1461 | model.SupportVectorCount = nSV;
|
---|
| 1462 | model.SupportVectorIndizes = new int[nSV];
|
---|
| 1463 | model.SupportVectors = new Node[nSV][];
|
---|
| 1464 | model.SupportVectorCoefficients[0] = new double[nSV];
|
---|
[2645] | 1465 |
|
---|
[4068] | 1466 | int j = 0;
|
---|
| 1467 | for (i = 0; i < prob.Count; i++)
|
---|
| 1468 | if (Math.Abs(f.alpha[i]) > 0) {
|
---|
| 1469 | model.SupportVectors[j] = prob.X[i];
|
---|
| 1470 | model.SupportVectorIndizes[j] = i;
|
---|
| 1471 | model.SupportVectorCoefficients[0][j] = f.alpha[i];
|
---|
[2645] | 1472 |
|
---|
[4068] | 1473 | ++j;
|
---|
| 1474 | }
|
---|
| 1475 | } else {
|
---|
| 1476 | // classification
|
---|
| 1477 | int l = prob.Count;
|
---|
| 1478 | int[] tmp_nr_class = new int[1];
|
---|
| 1479 | int[][] tmp_label = new int[1][];
|
---|
| 1480 | int[][] tmp_start = new int[1][];
|
---|
| 1481 | int[][] tmp_count = new int[1][];
|
---|
| 1482 | int[] perm = new int[l];
|
---|
[2645] | 1483 |
|
---|
[4068] | 1484 | // group training data of the same class
|
---|
| 1485 | svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);
|
---|
| 1486 | int nr_class = tmp_nr_class[0];
|
---|
| 1487 | int[] label = tmp_label[0];
|
---|
| 1488 | int[] start = tmp_start[0];
|
---|
| 1489 | int[] count = tmp_count[0];
|
---|
| 1490 | Node[][] x = new Node[l][];
|
---|
| 1491 | int i;
|
---|
| 1492 | for (i = 0; i < l; i++)
|
---|
| 1493 | x[i] = prob.X[perm[i]];
|
---|
[2645] | 1494 |
|
---|
[4068] | 1495 | // calculate weighted C
|
---|
[2645] | 1496 |
|
---|
[4068] | 1497 | double[] weighted_C = new double[nr_class];
|
---|
| 1498 | for (i = 0; i < nr_class; i++)
|
---|
| 1499 | weighted_C[i] = param.C;
|
---|
| 1500 | foreach (int weightedLabel in param.Weights.Keys) {
|
---|
| 1501 | int index = Array.IndexOf<int>(label, weightedLabel);
|
---|
| 1502 | if (index < 0)
|
---|
| 1503 | Console.Error.WriteLine("warning: class label " + weightedLabel + " specified in weight is not found");
|
---|
| 1504 | else weighted_C[index] *= param.Weights[weightedLabel];
|
---|
| 1505 | }
|
---|
[2645] | 1506 |
|
---|
[4068] | 1507 | // train k*(k-1)/2 models
|
---|
[2645] | 1508 |
|
---|
[4068] | 1509 | bool[] nonzero = new bool[l];
|
---|
| 1510 | for (i = 0; i < l; i++)
|
---|
| 1511 | nonzero[i] = false;
|
---|
| 1512 | decision_function[] f = new decision_function[nr_class * (nr_class - 1) / 2];
|
---|
[2645] | 1513 |
|
---|
[4068] | 1514 | double[] probA = null, probB = null;
|
---|
| 1515 | if (param.Probability) {
|
---|
| 1516 | probA = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1517 | probB = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1518 | }
|
---|
[2645] | 1519 |
|
---|
[4068] | 1520 | int p = 0;
|
---|
| 1521 | for (i = 0; i < nr_class; i++)
|
---|
| 1522 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1523 | Problem sub_prob = new Problem();
|
---|
| 1524 | int si = start[i], sj = start[j];
|
---|
| 1525 | int ci = count[i], cj = count[j];
|
---|
| 1526 | sub_prob.Count = ci + cj;
|
---|
| 1527 | sub_prob.X = new Node[sub_prob.Count][];
|
---|
| 1528 | sub_prob.Y = new double[sub_prob.Count];
|
---|
| 1529 | int k;
|
---|
| 1530 | for (k = 0; k < ci; k++) {
|
---|
| 1531 | sub_prob.X[k] = x[si + k];
|
---|
| 1532 | sub_prob.Y[k] = +1;
|
---|
| 1533 | }
|
---|
| 1534 | for (k = 0; k < cj; k++) {
|
---|
| 1535 | sub_prob.X[ci + k] = x[sj + k];
|
---|
| 1536 | sub_prob.Y[ci + k] = -1;
|
---|
| 1537 | }
|
---|
[2645] | 1538 |
|
---|
[4068] | 1539 | if (param.Probability) {
|
---|
| 1540 | double[] probAB = new double[2];
|
---|
| 1541 | svm_binary_svc_probability(sub_prob, param, weighted_C[i], weighted_C[j], probAB);
|
---|
| 1542 | probA[p] = probAB[0];
|
---|
| 1543 | probB[p] = probAB[1];
|
---|
| 1544 | }
|
---|
[2645] | 1545 |
|
---|
[4068] | 1546 | f[p] = svm_train_one(sub_prob, param, weighted_C[i], weighted_C[j]);
|
---|
| 1547 | for (k = 0; k < ci; k++)
|
---|
| 1548 | if (!nonzero[si + k] && Math.Abs(f[p].alpha[k]) > 0)
|
---|
| 1549 | nonzero[si + k] = true;
|
---|
| 1550 | for (k = 0; k < cj; k++)
|
---|
| 1551 | if (!nonzero[sj + k] && Math.Abs(f[p].alpha[ci + k]) > 0)
|
---|
| 1552 | nonzero[sj + k] = true;
|
---|
| 1553 | ++p;
|
---|
| 1554 | }
|
---|
[2645] | 1555 |
|
---|
[4068] | 1556 | // build output
|
---|
[2645] | 1557 |
|
---|
[4068] | 1558 | model.NumberOfClasses = nr_class;
|
---|
[2645] | 1559 |
|
---|
[4068] | 1560 | model.ClassLabels = new int[nr_class];
|
---|
| 1561 | for (i = 0; i < nr_class; i++)
|
---|
| 1562 | model.ClassLabels[i] = label[i];
|
---|
[2645] | 1563 |
|
---|
[4068] | 1564 | model.Rho = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1565 | for (i = 0; i < nr_class * (nr_class - 1) / 2; i++)
|
---|
| 1566 | model.Rho[i] = f[i].rho;
|
---|
[2645] | 1567 |
|
---|
[4068] | 1568 | if (param.Probability) {
|
---|
| 1569 | model.PairwiseProbabilityA = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1570 | model.PairwiseProbabilityB = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1571 | for (i = 0; i < nr_class * (nr_class - 1) / 2; i++) {
|
---|
| 1572 | model.PairwiseProbabilityA[i] = probA[i];
|
---|
| 1573 | model.PairwiseProbabilityB[i] = probB[i];
|
---|
| 1574 | }
|
---|
| 1575 | } else {
|
---|
| 1576 | model.PairwiseProbabilityA = null;
|
---|
| 1577 | model.PairwiseProbabilityB = null;
|
---|
| 1578 | }
|
---|
[2645] | 1579 |
|
---|
[4068] | 1580 | int nnz = 0;
|
---|
| 1581 | int[] nz_count = new int[nr_class];
|
---|
| 1582 | model.NumberOfSVPerClass = new int[nr_class];
|
---|
| 1583 | for (i = 0; i < nr_class; i++) {
|
---|
| 1584 | int nSV = 0;
|
---|
| 1585 | for (int j = 0; j < count[i]; j++)
|
---|
| 1586 | if (nonzero[start[i] + j]) {
|
---|
| 1587 | ++nSV;
|
---|
| 1588 | ++nnz;
|
---|
| 1589 | }
|
---|
| 1590 | model.NumberOfSVPerClass[i] = nSV;
|
---|
| 1591 | nz_count[i] = nSV;
|
---|
| 1592 | }
|
---|
[2645] | 1593 |
|
---|
[4068] | 1594 | Procedures.info("Total nSV = " + nnz + "\n");
|
---|
[2645] | 1595 |
|
---|
[4068] | 1596 | model.SupportVectorCount = nnz;
|
---|
| 1597 | model.SupportVectors = new Node[nnz][];
|
---|
| 1598 | model.SupportVectorIndizes = new int[nnz];
|
---|
| 1599 | p = 0;
|
---|
| 1600 | for (i = 0; i < l; i++) {
|
---|
| 1601 | if (nonzero[i]) {
|
---|
| 1602 | model.SupportVectors[p] = x[i];
|
---|
| 1603 | model.SupportVectorIndizes[p] = i;
|
---|
| 1604 | p++;
|
---|
| 1605 | }
|
---|
[2645] | 1606 | }
|
---|
| 1607 |
|
---|
[4068] | 1608 | int[] nz_start = new int[nr_class];
|
---|
| 1609 | nz_start[0] = 0;
|
---|
| 1610 | for (i = 1; i < nr_class; i++)
|
---|
| 1611 | nz_start[i] = nz_start[i - 1] + nz_count[i - 1];
|
---|
[2645] | 1612 |
|
---|
[4068] | 1613 | model.SupportVectorCoefficients = new double[nr_class - 1][];
|
---|
| 1614 | for (i = 0; i < nr_class - 1; i++)
|
---|
| 1615 | model.SupportVectorCoefficients[i] = new double[nnz];
|
---|
[2645] | 1616 |
|
---|
[4068] | 1617 | p = 0;
|
---|
| 1618 | for (i = 0; i < nr_class; i++)
|
---|
| 1619 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1620 | // classifier (i,j): coefficients with
|
---|
| 1621 | // i are in sv_coef[j-1][nz_start[i]...],
|
---|
| 1622 | // j are in sv_coef[i][nz_start[j]...]
|
---|
[2645] | 1623 |
|
---|
[4068] | 1624 | int si = start[i];
|
---|
| 1625 | int sj = start[j];
|
---|
| 1626 | int ci = count[i];
|
---|
| 1627 | int cj = count[j];
|
---|
[2645] | 1628 |
|
---|
[4068] | 1629 | int q = nz_start[i];
|
---|
| 1630 | int k;
|
---|
| 1631 | for (k = 0; k < ci; k++)
|
---|
| 1632 | if (nonzero[si + k])
|
---|
| 1633 | model.SupportVectorCoefficients[j - 1][q++] = f[p].alpha[k];
|
---|
| 1634 | q = nz_start[j];
|
---|
| 1635 | for (k = 0; k < cj; k++)
|
---|
| 1636 | if (nonzero[sj + k])
|
---|
| 1637 | model.SupportVectorCoefficients[i][q++] = f[p].alpha[ci + k];
|
---|
| 1638 | ++p;
|
---|
| 1639 | }
|
---|
| 1640 | }
|
---|
| 1641 | return model;
|
---|
| 1642 | }
|
---|
[2645] | 1643 |
|
---|
[4068] | 1644 | // Stratified cross validation
|
---|
| 1645 | public static void svm_cross_validation(Problem prob, Parameter param, int nr_fold, double[] target, bool shuffleTraining) {
|
---|
| 1646 | Random rand = new Random();
|
---|
| 1647 | int i;
|
---|
| 1648 | int[] fold_start = new int[nr_fold + 1];
|
---|
| 1649 | int l = prob.Count;
|
---|
| 1650 | int[] perm = new int[l];
|
---|
[2645] | 1651 |
|
---|
[4068] | 1652 | // stratified cv may not give leave-one-out rate
|
---|
| 1653 | // Each class to l folds -> some folds may have zero elements
|
---|
| 1654 | if ((param.SvmType == SvmType.C_SVC ||
|
---|
| 1655 | param.SvmType == SvmType.NU_SVC) && nr_fold < l) {
|
---|
| 1656 | int[] tmp_nr_class = new int[1];
|
---|
| 1657 | int[][] tmp_label = new int[1][];
|
---|
| 1658 | int[][] tmp_start = new int[1][];
|
---|
| 1659 | int[][] tmp_count = new int[1][];
|
---|
[2645] | 1660 |
|
---|
[4068] | 1661 | svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);
|
---|
| 1662 |
|
---|
| 1663 | int nr_class = tmp_nr_class[0];
|
---|
| 1664 | int[] label = tmp_label[0];
|
---|
| 1665 | int[] start = tmp_start[0];
|
---|
| 1666 | int[] count = tmp_count[0];
|
---|
| 1667 |
|
---|
| 1668 | // random shuffle and then data grouped by fold using the array perm
|
---|
| 1669 | int[] fold_count = new int[nr_fold];
|
---|
| 1670 | int c;
|
---|
| 1671 | int[] index = new int[l];
|
---|
| 1672 | for (i = 0; i < l; i++)
|
---|
| 1673 | index[i] = perm[i];
|
---|
| 1674 | for (c = 0; c < nr_class; c++)
|
---|
| 1675 | for (i = 0; i < count[c]; i++) {
|
---|
| 1676 | int j = i + (int)(rand.NextDouble() * (count[c] - i));
|
---|
| 1677 | do { int _ = index[start[c] + j]; index[start[c] + j] = index[start[c] + i]; index[start[c] + i] = _; } while (false);
|
---|
| 1678 | }
|
---|
| 1679 | for (i = 0; i < nr_fold; i++) {
|
---|
| 1680 | fold_count[i] = 0;
|
---|
| 1681 | for (c = 0; c < nr_class; c++)
|
---|
| 1682 | fold_count[i] += (i + 1) * count[c] / nr_fold - i * count[c] / nr_fold;
|
---|
| 1683 | }
|
---|
| 1684 | fold_start[0] = 0;
|
---|
| 1685 | for (i = 1; i <= nr_fold; i++)
|
---|
| 1686 | fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
|
---|
| 1687 | for (c = 0; c < nr_class; c++)
|
---|
| 1688 | for (i = 0; i < nr_fold; i++) {
|
---|
| 1689 | int begin = start[c] + i * count[c] / nr_fold;
|
---|
| 1690 | int end = start[c] + (i + 1) * count[c] / nr_fold;
|
---|
| 1691 | for (int j = begin; j < end; j++) {
|
---|
| 1692 | perm[fold_start[i]] = index[j];
|
---|
| 1693 | fold_start[i]++;
|
---|
[2645] | 1694 | }
|
---|
[4068] | 1695 | }
|
---|
| 1696 | fold_start[0] = 0;
|
---|
| 1697 | for (i = 1; i <= nr_fold; i++)
|
---|
| 1698 | fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
|
---|
| 1699 | } else {
|
---|
| 1700 | for (i = 0; i < l; i++) perm[i] = i;
|
---|
| 1701 | if (shuffleTraining) {
|
---|
| 1702 | for (i = 0; i < l; i++) {
|
---|
| 1703 | int j = i + (int)(rand.NextDouble() * (l - i));
|
---|
| 1704 | do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
|
---|
| 1705 | }
|
---|
[2645] | 1706 | }
|
---|
[4068] | 1707 | for (i = 0; i <= nr_fold; i++)
|
---|
| 1708 | fold_start[i] = i * l / nr_fold;
|
---|
| 1709 | }
|
---|
[2645] | 1710 |
|
---|
[4068] | 1711 | for (i = 0; i < nr_fold; i++) {
|
---|
| 1712 | int begin = fold_start[i];
|
---|
| 1713 | int end = fold_start[i + 1];
|
---|
| 1714 | int j, k;
|
---|
| 1715 | Problem subprob = new Problem();
|
---|
[2645] | 1716 |
|
---|
[4068] | 1717 | subprob.Count = l - (end - begin);
|
---|
| 1718 | subprob.X = new Node[subprob.Count][];
|
---|
| 1719 | subprob.Y = new double[subprob.Count];
|
---|
[2645] | 1720 |
|
---|
[4068] | 1721 | k = 0;
|
---|
| 1722 | for (j = 0; j < begin; j++) {
|
---|
| 1723 | subprob.X[k] = prob.X[perm[j]];
|
---|
| 1724 | subprob.Y[k] = prob.Y[perm[j]];
|
---|
| 1725 | ++k;
|
---|
[2645] | 1726 | }
|
---|
[4068] | 1727 | for (j = end; j < l; j++) {
|
---|
| 1728 | subprob.X[k] = prob.X[perm[j]];
|
---|
| 1729 | subprob.Y[k] = prob.Y[perm[j]];
|
---|
| 1730 | ++k;
|
---|
[2645] | 1731 | }
|
---|
[4068] | 1732 | Model submodel = svm_train(subprob, param);
|
---|
| 1733 | if (param.Probability &&
|
---|
| 1734 | (param.SvmType == SvmType.C_SVC ||
|
---|
| 1735 | param.SvmType == SvmType.NU_SVC)) {
|
---|
| 1736 | double[] prob_estimates = new double[svm_get_nr_class(submodel)];
|
---|
| 1737 | for (j = begin; j < end; j++)
|
---|
| 1738 | target[perm[j]] = svm_predict_probability(submodel, prob.X[perm[j]], prob_estimates);
|
---|
| 1739 | } else
|
---|
| 1740 | for (j = begin; j < end; j++)
|
---|
| 1741 | target[perm[j]] = svm_predict(submodel, prob.X[perm[j]]);
|
---|
| 1742 | }
|
---|
| 1743 | }
|
---|
[2645] | 1744 |
|
---|
[4068] | 1745 | public static SvmType svm_get_svm_type(Model model) {
|
---|
| 1746 | return model.Parameter.SvmType;
|
---|
| 1747 | }
|
---|
[2645] | 1748 |
|
---|
[4068] | 1749 | public static int svm_get_nr_class(Model model) {
|
---|
| 1750 | return model.NumberOfClasses;
|
---|
| 1751 | }
|
---|
[2645] | 1752 |
|
---|
[4068] | 1753 | public static void svm_get_labels(Model model, int[] label) {
|
---|
| 1754 | if (model.ClassLabels != null)
|
---|
| 1755 | for (int i = 0; i < model.NumberOfClasses; i++)
|
---|
| 1756 | label[i] = model.ClassLabels[i];
|
---|
| 1757 | }
|
---|
[2645] | 1758 |
|
---|
[4068] | 1759 | public static double svm_get_svr_probability(Model model) {
|
---|
| 1760 | if ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
|
---|
| 1761 | model.PairwiseProbabilityA != null)
|
---|
| 1762 | return model.PairwiseProbabilityA[0];
|
---|
| 1763 | else {
|
---|
| 1764 | Console.Error.WriteLine("Model doesn't contain information for SVR probability inference");
|
---|
| 1765 | return 0;
|
---|
| 1766 | }
|
---|
| 1767 | }
|
---|
[2645] | 1768 |
|
---|
[4068] | 1769 | public static void svm_predict_values(Model model, Node[] x, double[] dec_values) {
|
---|
| 1770 | if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
|
---|
| 1771 | model.Parameter.SvmType == SvmType.EPSILON_SVR ||
|
---|
| 1772 | model.Parameter.SvmType == SvmType.NU_SVR) {
|
---|
| 1773 | double[] sv_coef = model.SupportVectorCoefficients[0];
|
---|
| 1774 | double sum = 0;
|
---|
| 1775 | for (int i = 0; i < model.SupportVectorCount; i++)
|
---|
| 1776 | sum += sv_coef[i] * Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);
|
---|
| 1777 | sum -= model.Rho[0];
|
---|
| 1778 | dec_values[0] = sum;
|
---|
| 1779 | } else {
|
---|
| 1780 | int i;
|
---|
| 1781 | int nr_class = model.NumberOfClasses;
|
---|
| 1782 | int l = model.SupportVectorCount;
|
---|
[2645] | 1783 |
|
---|
[4068] | 1784 | double[] kvalue = new double[l];
|
---|
| 1785 | for (i = 0; i < l; i++)
|
---|
| 1786 | kvalue[i] = Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);
|
---|
[2645] | 1787 |
|
---|
[4068] | 1788 | int[] start = new int[nr_class];
|
---|
| 1789 | start[0] = 0;
|
---|
| 1790 | for (i = 1; i < nr_class; i++)
|
---|
| 1791 | start[i] = start[i - 1] + model.NumberOfSVPerClass[i - 1];
|
---|
[2645] | 1792 |
|
---|
[4068] | 1793 | int p = 0;
|
---|
| 1794 | for (i = 0; i < nr_class; i++)
|
---|
| 1795 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1796 | double sum = 0;
|
---|
| 1797 | int si = start[i];
|
---|
| 1798 | int sj = start[j];
|
---|
| 1799 | int ci = model.NumberOfSVPerClass[i];
|
---|
| 1800 | int cj = model.NumberOfSVPerClass[j];
|
---|
[2645] | 1801 |
|
---|
[4068] | 1802 | int k;
|
---|
| 1803 | double[] coef1 = model.SupportVectorCoefficients[j - 1];
|
---|
| 1804 | double[] coef2 = model.SupportVectorCoefficients[i];
|
---|
| 1805 | for (k = 0; k < ci; k++)
|
---|
| 1806 | sum += coef1[si + k] * kvalue[si + k];
|
---|
| 1807 | for (k = 0; k < cj; k++)
|
---|
| 1808 | sum += coef2[sj + k] * kvalue[sj + k];
|
---|
| 1809 | sum -= model.Rho[p];
|
---|
| 1810 | dec_values[p] = sum;
|
---|
| 1811 | p++;
|
---|
| 1812 | }
|
---|
| 1813 | }
|
---|
| 1814 | }
|
---|
[2645] | 1815 |
|
---|
[4068] | 1816 | public static double svm_predict(Model model, Node[] x) {
|
---|
| 1817 | if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
|
---|
| 1818 | model.Parameter.SvmType == SvmType.EPSILON_SVR ||
|
---|
| 1819 | model.Parameter.SvmType == SvmType.NU_SVR) {
|
---|
| 1820 | double[] res = new double[1];
|
---|
| 1821 | svm_predict_values(model, x, res);
|
---|
[2645] | 1822 |
|
---|
[4068] | 1823 | if (model.Parameter.SvmType == SvmType.ONE_CLASS)
|
---|
| 1824 | return (res[0] > 0) ? 1 : -1;
|
---|
| 1825 | else
|
---|
| 1826 | return res[0];
|
---|
| 1827 | } else {
|
---|
| 1828 | int i;
|
---|
| 1829 | int nr_class = model.NumberOfClasses;
|
---|
| 1830 | double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1831 | svm_predict_values(model, x, dec_values);
|
---|
[2645] | 1832 |
|
---|
[4068] | 1833 | int[] vote = new int[nr_class];
|
---|
| 1834 | for (i = 0; i < nr_class; i++)
|
---|
| 1835 | vote[i] = 0;
|
---|
| 1836 | int pos = 0;
|
---|
| 1837 | for (i = 0; i < nr_class; i++)
|
---|
| 1838 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1839 | if (dec_values[pos++] > 0)
|
---|
| 1840 | ++vote[i];
|
---|
| 1841 | else
|
---|
| 1842 | ++vote[j];
|
---|
| 1843 | }
|
---|
[2645] | 1844 |
|
---|
[4068] | 1845 | int vote_Max_idx = 0;
|
---|
| 1846 | for (i = 1; i < nr_class; i++)
|
---|
| 1847 | if (vote[i] > vote[vote_Max_idx])
|
---|
| 1848 | vote_Max_idx = i;
|
---|
| 1849 | return model.ClassLabels[vote_Max_idx];
|
---|
| 1850 | }
|
---|
| 1851 | }
|
---|
| 1852 |
|
---|
| 1853 | public static double svm_predict_probability(Model model, Node[] x, double[] prob_estimates) {
|
---|
| 1854 | if ((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
|
---|
| 1855 | model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null) {
|
---|
| 1856 | int i;
|
---|
| 1857 | int nr_class = model.NumberOfClasses;
|
---|
| 1858 | double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
|
---|
| 1859 | svm_predict_values(model, x, dec_values);
|
---|
| 1860 |
|
---|
| 1861 | double Min_prob = 1e-7;
|
---|
| 1862 | double[,] pairwise_prob = new double[nr_class, nr_class];
|
---|
| 1863 |
|
---|
| 1864 | int k = 0;
|
---|
| 1865 | for (i = 0; i < nr_class; i++) {
|
---|
| 1866 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1867 | pairwise_prob[i, j] = Math.Min(Math.Max(sigmoid_predict(dec_values[k], model.PairwiseProbabilityA[k], model.PairwiseProbabilityB[k]), Min_prob), 1 - Min_prob);
|
---|
| 1868 | pairwise_prob[j, i] = 1 - pairwise_prob[i, j];
|
---|
| 1869 | k++;
|
---|
| 1870 | }
|
---|
[2645] | 1871 | }
|
---|
[4068] | 1872 | multiclass_probability(nr_class, pairwise_prob, prob_estimates);
|
---|
[2645] | 1873 |
|
---|
[4068] | 1874 | int prob_Max_idx = 0;
|
---|
| 1875 | for (i = 1; i < nr_class; i++)
|
---|
| 1876 | if (prob_estimates[i] > prob_estimates[prob_Max_idx])
|
---|
| 1877 | prob_Max_idx = i;
|
---|
| 1878 | return model.ClassLabels[prob_Max_idx];
|
---|
| 1879 | } else
|
---|
| 1880 | return svm_predict(model, x);
|
---|
| 1881 | }
|
---|
[2645] | 1882 |
|
---|
[4068] | 1883 | public static string svm_check_parameter(Problem prob, Parameter param) {
|
---|
| 1884 | // svm_type
|
---|
[2645] | 1885 |
|
---|
[4068] | 1886 | SvmType svm_type = param.SvmType;
|
---|
[2645] | 1887 |
|
---|
[4068] | 1888 | // kernel_type, degree
|
---|
[2645] | 1889 |
|
---|
[4068] | 1890 | KernelType kernel_type = param.KernelType;
|
---|
[2645] | 1891 |
|
---|
[4068] | 1892 | if (param.Degree < 0)
|
---|
| 1893 | return "degree of polynomial kernel < 0";
|
---|
[2645] | 1894 |
|
---|
[4068] | 1895 | // cache_size,eps,C,nu,p,shrinking
|
---|
[2645] | 1896 |
|
---|
[4068] | 1897 | if (param.CacheSize <= 0)
|
---|
| 1898 | return "cache_size <= 0";
|
---|
[2645] | 1899 |
|
---|
[4068] | 1900 | if (param.EPS <= 0)
|
---|
| 1901 | return "eps <= 0";
|
---|
[2645] | 1902 |
|
---|
[4068] | 1903 | if (param.Gamma == 0)
|
---|
| 1904 | param.Gamma = 1.0 / prob.MaxIndex;
|
---|
[2645] | 1905 |
|
---|
[4068] | 1906 | if (svm_type == SvmType.C_SVC ||
|
---|
| 1907 | svm_type == SvmType.EPSILON_SVR ||
|
---|
| 1908 | svm_type == SvmType.NU_SVR)
|
---|
| 1909 | if (param.C <= 0)
|
---|
| 1910 | return "C <= 0";
|
---|
[2645] | 1911 |
|
---|
[4068] | 1912 | if (svm_type == SvmType.NU_SVC ||
|
---|
| 1913 | svm_type == SvmType.ONE_CLASS ||
|
---|
| 1914 | svm_type == SvmType.NU_SVR)
|
---|
| 1915 | if (param.Nu <= 0 || param.Nu > 1)
|
---|
| 1916 | return "nu <= 0 or nu > 1";
|
---|
[2645] | 1917 |
|
---|
[4068] | 1918 | if (svm_type == SvmType.EPSILON_SVR)
|
---|
| 1919 | if (param.P < 0)
|
---|
| 1920 | return "p < 0";
|
---|
[2645] | 1921 |
|
---|
[4068] | 1922 | if (param.Probability &&
|
---|
| 1923 | svm_type == SvmType.ONE_CLASS)
|
---|
| 1924 | return "one-class SVM probability output not supported yet";
|
---|
[2645] | 1925 |
|
---|
[4068] | 1926 | // check whether nu-svc is feasible
|
---|
[2645] | 1927 |
|
---|
[4068] | 1928 | if (svm_type == SvmType.NU_SVC) {
|
---|
| 1929 | int l = prob.Count;
|
---|
| 1930 | int Max_nr_class = 16;
|
---|
| 1931 | int nr_class = 0;
|
---|
| 1932 | int[] label = new int[Max_nr_class];
|
---|
| 1933 | int[] count = new int[Max_nr_class];
|
---|
[2645] | 1934 |
|
---|
[4068] | 1935 | int i;
|
---|
| 1936 | for (i = 0; i < l; i++) {
|
---|
| 1937 | int this_label = (int)prob.Y[i];
|
---|
| 1938 | int j;
|
---|
| 1939 | for (j = 0; j < nr_class; j++)
|
---|
| 1940 | if (this_label == label[j]) {
|
---|
| 1941 | ++count[j];
|
---|
| 1942 | break;
|
---|
| 1943 | }
|
---|
[2645] | 1944 |
|
---|
[4068] | 1945 | if (j == nr_class) {
|
---|
| 1946 | if (nr_class == Max_nr_class) {
|
---|
| 1947 | Max_nr_class *= 2;
|
---|
| 1948 | int[] new_data = new int[Max_nr_class];
|
---|
| 1949 | Array.Copy(label, 0, new_data, 0, label.Length);
|
---|
| 1950 | label = new_data;
|
---|
[2645] | 1951 |
|
---|
[4068] | 1952 | new_data = new int[Max_nr_class];
|
---|
| 1953 | Array.Copy(count, 0, new_data, 0, count.Length);
|
---|
| 1954 | count = new_data;
|
---|
[2645] | 1955 | }
|
---|
[4068] | 1956 | label[nr_class] = this_label;
|
---|
| 1957 | count[nr_class] = 1;
|
---|
| 1958 | ++nr_class;
|
---|
| 1959 | }
|
---|
| 1960 | }
|
---|
[2645] | 1961 |
|
---|
[4068] | 1962 | for (i = 0; i < nr_class; i++) {
|
---|
| 1963 | int n1 = count[i];
|
---|
| 1964 | for (int j = i + 1; j < nr_class; j++) {
|
---|
| 1965 | int n2 = count[j];
|
---|
| 1966 | if (param.Nu * (n1 + n2) / 2 > Math.Min(n1, n2))
|
---|
| 1967 | return "specified nu is infeasible";
|
---|
| 1968 | }
|
---|
[2645] | 1969 | }
|
---|
[4068] | 1970 | }
|
---|
[2645] | 1971 |
|
---|
[4068] | 1972 | return null;
|
---|
[2645] | 1973 | }
|
---|
[4068] | 1974 |
|
---|
| 1975 | public static int svm_check_probability_model(Model model) {
|
---|
| 1976 | if (((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
|
---|
| 1977 | model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null) ||
|
---|
| 1978 | ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
|
---|
| 1979 | model.PairwiseProbabilityA != null))
|
---|
| 1980 | return 1;
|
---|
| 1981 | else
|
---|
| 1982 | return 0;
|
---|
| 1983 | }
|
---|
| 1984 | }
|
---|
[2645] | 1985 | }
|
---|