1 /*M/////////////////////////////////////////////////////////////////////////////////////// 2 // 3 // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. 4 // 5 // By downloading, copying, installing or using the software you agree to this license. 6 // If you do not agree to this license, do not download, install, 7 // copy or use the software. 8 // 9 // 10 // Intel License Agreement 11 // For Open Source Computer Vision Library 12 // 13 // Copyright( C) 2000, Intel Corporation, all rights reserved. 14 // Third party copyrights are property of their respective owners. 15 // 16 // Redistribution and use in source and binary forms, with or without modification, 17 // are permitted provided that the following conditions are met: 18 // 19 // * Redistribution's of source code must retain the above copyright notice, 20 // this list of conditions and the following disclaimer. 21 // 22 // * Redistribution's in binary form must reproduce the above copyright notice, 23 // this list of conditions and the following disclaimer in the documentation 24 // and/or other materials provided with the distribution. 25 // 26 // * The name of Intel Corporation may not be used to endorse or promote products 27 // derived from this software without specific prior written permission. 28 // 29 // This software is provided by the copyright holders and contributors "as is" and 30 // any express or implied warranties, including, but not limited to, the implied 31 // warranties of merchantability and fitness for a particular purpose are disclaimed. 32 // In no event shall the Intel Corporation or contributors be liable for any direct, 33 // indirect, incidental, special, exemplary, or consequential damages 34 //(including, but not limited to, procurement of substitute goods or services; 35 // loss of use, data, or profits; or business interruption) however caused 36 // and on any theory of liability, whether in contract, strict liability, 37 // or tort(including negligence or otherwise) arising in any way out of 38 // the use of this software, even ifadvised of the possibility of such damage. 39 // 40 //M*/ 41 42 #include "_ml.h" 43 44 45 /* 46 CvEM: 47 * params.nclusters - number of clusters to cluster samples to. 48 * means - calculated by the EM algorithm set of gaussians' means. 49 * log_weight_div_det - auxilary vector that k-th component is equal to 50 (-2)*ln(weights_k/det(Sigma_k)^0.5), 51 where <weights_k> is the weight, 52 <Sigma_k> is the covariation matrice of k-th cluster. 53 * inv_eigen_values - set of 1*dims matrices, <inv_eigen_values>[k] contains 54 inversed eigen values of covariation matrice of the k-th cluster. 55 In the case of <cov_mat_type> == COV_MAT_DIAGONAL, 56 inv_eigen_values[k] = Sigma_k^(-1). 57 * covs_rotate_mats - used only if cov_mat_type == COV_MAT_GENERIC, in all the 58 other cases it is NULL. <covs_rotate_mats>[k] is the orthogonal 59 matrice, obtained by the SVD-decomposition of Sigma_k. 60 Both <inv_eigen_values> and <covs_rotate_mats> fields are used for representation of 61 covariation matrices and simplifying EM calculations. 62 For fixed k denote 63 u = covs_rotate_mats[k], 64 v = inv_eigen_values[k], 65 w = v^(-1); 66 if <cov_mat_type> == COV_MAT_GENERIC, then Sigma_k = u w u', 67 else Sigma_k = w. 68 Symbol ' means transposition. 69 */ 70 71 72 CvEM::CvEM() 73 { 74 means = weights = probs = inv_eigen_values = log_weight_div_det = 0; 75 covs = cov_rotate_mats = 0; 76 } 77 78 CvEM::CvEM( const CvMat* samples, const CvMat* sample_idx, 79 CvEMParams params, CvMat* labels ) 80 { 81 means = weights = probs = inv_eigen_values = log_weight_div_det = 0; 82 covs = cov_rotate_mats = 0; 83 84 // just invoke the train() method 85 train(samples, sample_idx, params, labels); 86 } 87 88 CvEM::~CvEM() 89 { 90 clear(); 91 } 92 93 94 void CvEM::clear() 95 { 96 int i; 97 98 cvReleaseMat( &means ); 99 cvReleaseMat( &weights ); 100 cvReleaseMat( &probs ); 101 cvReleaseMat( &inv_eigen_values ); 102 cvReleaseMat( &log_weight_div_det ); 103 104 if( covs || cov_rotate_mats ) 105 { 106 for( i = 0; i < params.nclusters; i++ ) 107 { 108 if( covs ) 109 cvReleaseMat( &covs[i] ); 110 if( cov_rotate_mats ) 111 cvReleaseMat( &cov_rotate_mats[i] ); 112 } 113 cvFree( &covs ); 114 cvFree( &cov_rotate_mats ); 115 } 116 } 117 118 119 void CvEM::set_params( const CvEMParams& _params, const CvVectors& train_data ) 120 { 121 CV_FUNCNAME( "CvEM::set_params" ); 122 123 __BEGIN__; 124 125 int k; 126 127 params = _params; 128 params.term_crit = cvCheckTermCriteria( params.term_crit, 1e-6, 10000 ); 129 130 if( params.cov_mat_type != COV_MAT_SPHERICAL && 131 params.cov_mat_type != COV_MAT_DIAGONAL && 132 params.cov_mat_type != COV_MAT_GENERIC ) 133 CV_ERROR( CV_StsBadArg, "Unknown covariation matrix type" ); 134 135 switch( params.start_step ) 136 { 137 case START_M_STEP: 138 if( !params.probs ) 139 CV_ERROR( CV_StsNullPtr, "Probabilities must be specified when EM algorithm starts with M-step" ); 140 break; 141 case START_E_STEP: 142 if( !params.means ) 143 CV_ERROR( CV_StsNullPtr, "Mean's must be specified when EM algorithm starts with E-step" ); 144 break; 145 case START_AUTO_STEP: 146 break; 147 default: 148 CV_ERROR( CV_StsBadArg, "Unknown start_step" ); 149 } 150 151 if( params.nclusters < 1 ) 152 CV_ERROR( CV_StsOutOfRange, "The number of clusters (mixtures) should be > 0" ); 153 154 if( params.probs ) 155 { 156 const CvMat* p = params.weights; 157 if( !CV_IS_MAT(p) || 158 CV_MAT_TYPE(p->type) != CV_32FC1 && 159 CV_MAT_TYPE(p->type) != CV_64FC1 || 160 p->rows != train_data.count || 161 p->cols != params.nclusters ) 162 CV_ERROR( CV_StsBadArg, "The array of probabilities must be a valid " 163 "floating-point matrix (CvMat) of 'nsamples' x 'nclusters' size" ); 164 } 165 166 if( params.means ) 167 { 168 const CvMat* m = params.means; 169 if( !CV_IS_MAT(m) || 170 CV_MAT_TYPE(m->type) != CV_32FC1 && 171 CV_MAT_TYPE(m->type) != CV_64FC1 || 172 m->rows != params.nclusters || 173 m->cols != train_data.dims ) 174 CV_ERROR( CV_StsBadArg, "The array of mean's must be a valid " 175 "floating-point matrix (CvMat) of 'nsamples' x 'dims' size" ); 176 } 177 178 if( params.weights ) 179 { 180 const CvMat* w = params.weights; 181 if( !CV_IS_MAT(w) || 182 CV_MAT_TYPE(w->type) != CV_32FC1 && 183 CV_MAT_TYPE(w->type) != CV_64FC1 || 184 w->rows != 1 && w->cols != 1 || 185 w->rows + w->cols - 1 != params.nclusters ) 186 CV_ERROR( CV_StsBadArg, "The array of weights must be a valid " 187 "1d floating-point vector (CvMat) of 'nclusters' elements" ); 188 } 189 190 if( params.covs ) 191 for( k = 0; k < params.nclusters; k++ ) 192 { 193 const CvMat* cov = params.covs[k]; 194 if( !CV_IS_MAT(cov) || 195 CV_MAT_TYPE(cov->type) != CV_32FC1 && 196 CV_MAT_TYPE(cov->type) != CV_64FC1 || 197 cov->rows != cov->cols || cov->cols != train_data.dims ) 198 CV_ERROR( CV_StsBadArg, 199 "Each of covariation matrices must be a valid square " 200 "floating-point matrix (CvMat) of 'dims' x 'dims'" ); 201 } 202 203 __END__; 204 } 205 206 207 /****************************************************************************************/ 208 float 209 CvEM::predict( const CvMat* _sample, CvMat* _probs ) const 210 { 211 float* sample_data = 0; 212 void* buffer = 0; 213 int allocated_buffer = 0; 214 int cls = 0; 215 216 CV_FUNCNAME( "CvEM::predict" ); 217 __BEGIN__; 218 219 int i, k, dims; 220 int nclusters; 221 int cov_mat_type = params.cov_mat_type; 222 double opt = FLT_MAX; 223 size_t size; 224 CvMat diff, expo; 225 226 dims = means->cols; 227 nclusters = params.nclusters; 228 229 CV_CALL( cvPreparePredictData( _sample, dims, 0, params.nclusters, _probs, &sample_data )); 230 231 // allocate memory and initializing headers for calculating 232 size = sizeof(double) * (nclusters + dims); 233 if( size <= CV_MAX_LOCAL_SIZE ) 234 buffer = cvStackAlloc( size ); 235 else 236 { 237 CV_CALL( buffer = cvAlloc( size )); 238 allocated_buffer = 1; 239 } 240 expo = cvMat( 1, nclusters, CV_64FC1, buffer ); 241 diff = cvMat( 1, dims, CV_64FC1, (double*)buffer + nclusters ); 242 243 // calculate the probabilities 244 for( k = 0; k < nclusters; k++ ) 245 { 246 const double* mean_k = (const double*)(means->data.ptr + means->step*k); 247 const double* w = (const double*)(inv_eigen_values->data.ptr + inv_eigen_values->step*k); 248 double cur = log_weight_div_det->data.db[k]; 249 CvMat* u = cov_rotate_mats[k]; 250 // cov = u w u' --> cov^(-1) = u w^(-1) u' 251 if( cov_mat_type == COV_MAT_SPHERICAL ) 252 { 253 double w0 = w[0]; 254 for( i = 0; i < dims; i++ ) 255 { 256 double val = sample_data[i] - mean_k[i]; 257 cur += val*val*w0; 258 } 259 } 260 else 261 { 262 for( i = 0; i < dims; i++ ) 263 diff.data.db[i] = sample_data[i] - mean_k[i]; 264 if( cov_mat_type == COV_MAT_GENERIC ) 265 cvGEMM( &diff, u, 1, 0, 0, &diff, CV_GEMM_B_T ); 266 for( i = 0; i < dims; i++ ) 267 { 268 double val = diff.data.db[i]; 269 cur += val*val*w[i]; 270 } 271 } 272 273 expo.data.db[k] = cur; 274 if( cur < opt ) 275 { 276 cls = k; 277 opt = cur; 278 } 279 /* probability = (2*pi)^(-dims/2)*exp( -0.5 * cur ) */ 280 } 281 282 if( _probs ) 283 { 284 CV_CALL( cvConvertScale( &expo, &expo, -0.5 )); 285 CV_CALL( cvExp( &expo, &expo )); 286 if( _probs->cols == 1 ) 287 CV_CALL( cvReshape( &expo, &expo, 0, nclusters )); 288 CV_CALL( cvConvertScale( &expo, _probs, 1./cvSum( &expo ).val[0] )); 289 } 290 291 __END__; 292 293 if( sample_data != _sample->data.fl ) 294 cvFree( &sample_data ); 295 if( allocated_buffer ) 296 cvFree( &buffer ); 297 298 return (float)cls; 299 } 300 301 302 303 bool CvEM::train( const CvMat* _samples, const CvMat* _sample_idx, 304 CvEMParams _params, CvMat* labels ) 305 { 306 bool result = false; 307 CvVectors train_data; 308 CvMat* sample_idx = 0; 309 310 train_data.data.fl = 0; 311 train_data.count = 0; 312 313 CV_FUNCNAME("cvEM"); 314 315 __BEGIN__; 316 317 int i, nsamples, nclusters, dims; 318 319 clear(); 320 321 CV_CALL( cvPrepareTrainData( "cvEM", 322 _samples, CV_ROW_SAMPLE, 0, CV_VAR_CATEGORICAL, 323 0, _sample_idx, false, (const float***)&train_data.data.fl, 324 &train_data.count, &train_data.dims, &train_data.dims, 325 0, 0, 0, &sample_idx )); 326 327 CV_CALL( set_params( _params, train_data )); 328 nsamples = train_data.count; 329 nclusters = params.nclusters; 330 dims = train_data.dims; 331 332 if( labels && (!CV_IS_MAT(labels) || CV_MAT_TYPE(labels->type) != CV_32SC1 || 333 labels->cols != 1 && labels->rows != 1 || labels->cols + labels->rows - 1 != nsamples )) 334 CV_ERROR( CV_StsBadArg, 335 "labels array (when passed) must be a valid 1d integer vector of <sample_count> elements" ); 336 337 if( nsamples <= nclusters ) 338 CV_ERROR( CV_StsOutOfRange, 339 "The number of samples should be greater than the number of clusters" ); 340 341 CV_CALL( log_weight_div_det = cvCreateMat( 1, nclusters, CV_64FC1 )); 342 CV_CALL( probs = cvCreateMat( nsamples, nclusters, CV_64FC1 )); 343 CV_CALL( means = cvCreateMat( nclusters, dims, CV_64FC1 )); 344 CV_CALL( weights = cvCreateMat( 1, nclusters, CV_64FC1 )); 345 CV_CALL( inv_eigen_values = cvCreateMat( nclusters, 346 params.cov_mat_type == COV_MAT_SPHERICAL ? 1 : dims, CV_64FC1 )); 347 CV_CALL( covs = (CvMat**)cvAlloc( nclusters * sizeof(*covs) )); 348 CV_CALL( cov_rotate_mats = (CvMat**)cvAlloc( nclusters * sizeof(cov_rotate_mats[0]) )); 349 350 for( i = 0; i < nclusters; i++ ) 351 { 352 CV_CALL( covs[i] = cvCreateMat( dims, dims, CV_64FC1 )); 353 CV_CALL( cov_rotate_mats[i] = cvCreateMat( dims, dims, CV_64FC1 )); 354 cvZero( cov_rotate_mats[i] ); 355 } 356 357 init_em( train_data ); 358 log_likelihood = run_em( train_data ); 359 if( log_likelihood <= -DBL_MAX/10000. ) 360 EXIT; 361 362 if( labels ) 363 { 364 if( nclusters == 1 ) 365 cvZero( labels ); 366 else 367 { 368 CvMat sample = cvMat( 1, dims, CV_32F ); 369 CvMat prob = cvMat( 1, nclusters, CV_64F ); 370 int lstep = CV_IS_MAT_CONT(labels->type) ? 1 : labels->step/sizeof(int); 371 372 for( i = 0; i < nsamples; i++ ) 373 { 374 int idx = sample_idx ? sample_idx->data.i[i] : i; 375 sample.data.ptr = _samples->data.ptr + _samples->step*idx; 376 prob.data.ptr = probs->data.ptr + probs->step*i; 377 378 labels->data.i[i*lstep] = cvRound(predict(&sample, &prob)); 379 } 380 } 381 } 382 383 result = true; 384 385 __END__; 386 387 if( sample_idx != _sample_idx ) 388 cvReleaseMat( &sample_idx ); 389 390 cvFree( &train_data.data.ptr ); 391 392 return result; 393 } 394 395 396 void CvEM::init_em( const CvVectors& train_data ) 397 { 398 CvMat *w = 0, *u = 0, *tcov = 0; 399 400 CV_FUNCNAME( "CvEM::init_em" ); 401 402 __BEGIN__; 403 404 double maxval = 0; 405 int i, force_symm_plus = 0; 406 int nclusters = params.nclusters, nsamples = train_data.count, dims = train_data.dims; 407 408 if( params.start_step == START_AUTO_STEP || nclusters == 1 || nclusters == nsamples ) 409 init_auto( train_data ); 410 else if( params.start_step == START_M_STEP ) 411 { 412 for( i = 0; i < nsamples; i++ ) 413 { 414 CvMat prob; 415 cvGetRow( params.probs, &prob, i ); 416 cvMaxS( &prob, 0., &prob ); 417 cvMinMaxLoc( &prob, 0, &maxval ); 418 if( maxval < FLT_EPSILON ) 419 cvSet( &prob, cvScalar(1./nclusters) ); 420 else 421 cvNormalize( &prob, &prob, 1., 0, CV_L1 ); 422 } 423 EXIT; // do not preprocess covariation matrices, 424 // as in this case they are initialized at the first iteration of EM 425 } 426 else 427 { 428 CV_ASSERT( params.start_step == START_E_STEP && params.means ); 429 if( params.weights && params.covs ) 430 { 431 cvConvert( params.means, means ); 432 cvReshape( weights, weights, 1, params.weights->rows ); 433 cvConvert( params.weights, weights ); 434 cvReshape( weights, weights, 1, 1 ); 435 cvMaxS( weights, 0., weights ); 436 cvMinMaxLoc( weights, 0, &maxval ); 437 if( maxval < FLT_EPSILON ) 438 cvSet( &weights, cvScalar(1./nclusters) ); 439 cvNormalize( weights, weights, 1., 0, CV_L1 ); 440 for( i = 0; i < nclusters; i++ ) 441 CV_CALL( cvConvert( params.covs[i], covs[i] )); 442 force_symm_plus = 1; 443 } 444 else 445 init_auto( train_data ); 446 } 447 448 CV_CALL( tcov = cvCreateMat( dims, dims, CV_64FC1 )); 449 CV_CALL( w = cvCreateMat( dims, dims, CV_64FC1 )); 450 if( params.cov_mat_type == COV_MAT_GENERIC ) 451 CV_CALL( u = cvCreateMat( dims, dims, CV_64FC1 )); 452 453 for( i = 0; i < nclusters; i++ ) 454 { 455 if( force_symm_plus ) 456 { 457 cvTranspose( covs[i], tcov ); 458 cvAddWeighted( covs[i], 0.5, tcov, 0.5, 0, tcov ); 459 } 460 else 461 cvCopy( covs[i], tcov ); 462 cvSVD( tcov, w, u, 0, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T ); 463 if( params.cov_mat_type == COV_MAT_SPHERICAL ) 464 cvSetIdentity( covs[i], cvScalar(cvTrace(w).val[0]/dims) ); 465 else if( params.cov_mat_type == COV_MAT_DIAGONAL ) 466 cvCopy( w, covs[i] ); 467 else 468 { 469 // generic case: covs[i] = (u')'*max(w,0)*u' 470 cvGEMM( u, w, 1, 0, 0, tcov, CV_GEMM_A_T ); 471 cvGEMM( tcov, u, 1, 0, 0, covs[i], 0 ); 472 } 473 } 474 475 __END__; 476 477 cvReleaseMat( &w ); 478 cvReleaseMat( &u ); 479 cvReleaseMat( &tcov ); 480 } 481 482 483 void CvEM::init_auto( const CvVectors& train_data ) 484 { 485 CvMat* hdr = 0; 486 const void** vec = 0; 487 CvMat* class_ranges = 0; 488 CvMat* labels = 0; 489 490 CV_FUNCNAME( "CvEM::init_auto" ); 491 492 __BEGIN__; 493 494 int nclusters = params.nclusters, nsamples = train_data.count, dims = train_data.dims; 495 int i, j; 496 497 if( nclusters == nsamples ) 498 { 499 CvMat src = cvMat( 1, dims, CV_32F ); 500 CvMat dst = cvMat( 1, dims, CV_64F ); 501 for( i = 0; i < nsamples; i++ ) 502 { 503 src.data.ptr = train_data.data.ptr[i]; 504 dst.data.ptr = means->data.ptr + means->step*i; 505 cvConvert( &src, &dst ); 506 cvZero( covs[i] ); 507 cvSetIdentity( cov_rotate_mats[i] ); 508 } 509 cvSetIdentity( probs ); 510 cvSet( weights, cvScalar(1./nclusters) ); 511 } 512 else 513 { 514 int max_count = 0; 515 516 CV_CALL( class_ranges = cvCreateMat( 1, nclusters+1, CV_32SC1 )); 517 if( nclusters > 1 ) 518 { 519 CV_CALL( labels = cvCreateMat( 1, nsamples, CV_32SC1 )); 520 kmeans( train_data, nclusters, labels, cvTermCriteria( CV_TERMCRIT_ITER, 521 params.means ? 1 : 10, 0.5 ), params.means ); 522 CV_CALL( cvSortSamplesByClasses( (const float**)train_data.data.fl, 523 labels, class_ranges->data.i )); 524 } 525 else 526 { 527 class_ranges->data.i[0] = 0; 528 class_ranges->data.i[1] = nsamples; 529 } 530 531 for( i = 0; i < nclusters; i++ ) 532 { 533 int left = class_ranges->data.i[i], right = class_ranges->data.i[i+1]; 534 max_count = MAX( max_count, right - left ); 535 } 536 CV_CALL( hdr = (CvMat*)cvAlloc( max_count*sizeof(hdr[0]) )); 537 CV_CALL( vec = (const void**)cvAlloc( max_count*sizeof(vec[0]) )); 538 hdr[0] = cvMat( 1, dims, CV_32F ); 539 for( i = 0; i < max_count; i++ ) 540 { 541 vec[i] = hdr + i; 542 hdr[i] = hdr[0]; 543 } 544 545 for( i = 0; i < nclusters; i++ ) 546 { 547 int left = class_ranges->data.i[i], right = class_ranges->data.i[i+1]; 548 int cluster_size = right - left; 549 CvMat avg; 550 551 if( cluster_size <= 0 ) 552 continue; 553 554 for( j = left; j < right; j++ ) 555 hdr[j - left].data.fl = train_data.data.fl[j]; 556 557 CV_CALL( cvGetRow( means, &avg, i )); 558 CV_CALL( cvCalcCovarMatrix( vec, cluster_size, covs[i], 559 &avg, CV_COVAR_NORMAL | CV_COVAR_SCALE )); 560 weights->data.db[i] = (double)cluster_size/(double)nsamples; 561 } 562 } 563 564 __END__; 565 566 cvReleaseMat( &class_ranges ); 567 cvReleaseMat( &labels ); 568 cvFree( &hdr ); 569 cvFree( &vec ); 570 } 571 572 573 void CvEM::kmeans( const CvVectors& train_data, int nclusters, CvMat* labels, 574 CvTermCriteria termcrit, const CvMat* centers0 ) 575 { 576 CvMat* centers = 0; 577 CvMat* old_centers = 0; 578 CvMat* counters = 0; 579 580 CV_FUNCNAME( "CvEM::kmeans" ); 581 582 __BEGIN__; 583 584 CvRNG rng = cvRNG(-1); 585 int i, j, k, nsamples, dims; 586 int iter = 0; 587 double max_dist = DBL_MAX; 588 589 termcrit = cvCheckTermCriteria( termcrit, 1e-6, 100 ); 590 termcrit.epsilon *= termcrit.epsilon; 591 nsamples = train_data.count; 592 dims = train_data.dims; 593 nclusters = MIN( nclusters, nsamples ); 594 595 CV_CALL( centers = cvCreateMat( nclusters, dims, CV_64FC1 )); 596 CV_CALL( old_centers = cvCreateMat( nclusters, dims, CV_64FC1 )); 597 CV_CALL( counters = cvCreateMat( 1, nclusters, CV_32SC1 )); 598 cvZero( old_centers ); 599 600 if( centers0 ) 601 { 602 CV_CALL( cvConvert( centers0, centers )); 603 } 604 else 605 { 606 for( i = 0; i < nsamples; i++ ) 607 labels->data.i[i] = i*nclusters/nsamples; 608 cvRandShuffle( labels, &rng ); 609 } 610 611 for( ;; ) 612 { 613 CvMat* temp; 614 615 if( iter > 0 || centers0 ) 616 { 617 for( i = 0; i < nsamples; i++ ) 618 { 619 const float* s = train_data.data.fl[i]; 620 int k_best = 0; 621 double min_dist = DBL_MAX; 622 623 for( k = 0; k < nclusters; k++ ) 624 { 625 const double* c = (double*)(centers->data.ptr + k*centers->step); 626 double dist = 0; 627 628 for( j = 0; j <= dims - 4; j += 4 ) 629 { 630 double t0 = c[j] - s[j]; 631 double t1 = c[j+1] - s[j+1]; 632 dist += t0*t0 + t1*t1; 633 t0 = c[j+2] - s[j+2]; 634 t1 = c[j+3] - s[j+3]; 635 dist += t0*t0 + t1*t1; 636 } 637 638 for( ; j < dims; j++ ) 639 { 640 double t = c[j] - s[j]; 641 dist += t*t; 642 } 643 644 if( min_dist > dist ) 645 { 646 min_dist = dist; 647 k_best = k; 648 } 649 } 650 651 labels->data.i[i] = k_best; 652 } 653 } 654 655 if( ++iter > termcrit.max_iter ) 656 break; 657 658 CV_SWAP( centers, old_centers, temp ); 659 cvZero( centers ); 660 cvZero( counters ); 661 662 // update centers 663 for( i = 0; i < nsamples; i++ ) 664 { 665 const float* s = train_data.data.fl[i]; 666 k = labels->data.i[i]; 667 double* c = (double*)(centers->data.ptr + k*centers->step); 668 669 for( j = 0; j <= dims - 4; j += 4 ) 670 { 671 double t0 = c[j] + s[j]; 672 double t1 = c[j+1] + s[j+1]; 673 674 c[j] = t0; 675 c[j+1] = t1; 676 677 t0 = c[j+2] + s[j+2]; 678 t1 = c[j+3] + s[j+3]; 679 680 c[j+2] = t0; 681 c[j+3] = t1; 682 } 683 for( ; j < dims; j++ ) 684 c[j] += s[j]; 685 counters->data.i[k]++; 686 } 687 688 if( iter > 1 ) 689 max_dist = 0; 690 691 for( k = 0; k < nclusters; k++ ) 692 { 693 double* c = (double*)(centers->data.ptr + k*centers->step); 694 if( counters->data.i[k] != 0 ) 695 { 696 double scale = 1./counters->data.i[k]; 697 for( j = 0; j < dims; j++ ) 698 c[j] *= scale; 699 } 700 else 701 { 702 const float* s; 703 for( j = 0; j < 10; j++ ) 704 { 705 i = cvRandInt( &rng ) % nsamples; 706 if( counters->data.i[labels->data.i[i]] > 1 ) 707 break; 708 } 709 s = train_data.data.fl[i]; 710 for( j = 0; j < dims; j++ ) 711 c[j] = s[j]; 712 } 713 714 if( iter > 1 ) 715 { 716 double dist = 0; 717 const double* c_o = (double*)(old_centers->data.ptr + k*old_centers->step); 718 for( j = 0; j < dims; j++ ) 719 { 720 double t = c[j] - c_o[j]; 721 dist += t*t; 722 } 723 if( max_dist < dist ) 724 max_dist = dist; 725 } 726 } 727 728 if( max_dist < termcrit.epsilon ) 729 break; 730 } 731 732 cvZero( counters ); 733 for( i = 0; i < nsamples; i++ ) 734 counters->data.i[labels->data.i[i]]++; 735 736 // ensure that we do not have empty clusters 737 for( k = 0; k < nclusters; k++ ) 738 if( counters->data.i[k] == 0 ) 739 for(;;) 740 { 741 i = cvRandInt(&rng) % nsamples; 742 j = labels->data.i[i]; 743 if( counters->data.i[j] > 1 ) 744 { 745 labels->data.i[i] = k; 746 counters->data.i[j]--; 747 counters->data.i[k]++; 748 break; 749 } 750 } 751 752 __END__; 753 754 cvReleaseMat( ¢ers ); 755 cvReleaseMat( &old_centers ); 756 cvReleaseMat( &counters ); 757 } 758 759 760 /****************************************************************************************/ 761 /* log_weight_div_det[k] = -2*log(weights_k) + log(det(Sigma_k))) 762 763 covs[k] = cov_rotate_mats[k] * cov_eigen_values[k] * (cov_rotate_mats[k])' 764 cov_rotate_mats[k] are orthogonal matrices of eigenvectors and 765 cov_eigen_values[k] are diagonal matrices (represented by 1D vectors) of eigen values. 766 767 The <alpha_ik> is the probability of the vector x_i to belong to the k-th cluster: 768 <alpha_ik> ~ weights_k * exp{ -0.5[ln(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)] } 769 We calculate these probabilities here by the equivalent formulae: 770 Denote 771 S_ik = -0.5(log(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)) + log(weights_k), 772 M_i = max_k S_ik = S_qi, so that the q-th class is the one where maximum reaches. Then 773 alpha_ik = exp{ S_ik - M_i } / ( 1 + sum_j!=q exp{ S_ji - M_i }) 774 */ 775 double CvEM::run_em( const CvVectors& train_data ) 776 { 777 CvMat* centered_sample = 0; 778 CvMat* covs_item = 0; 779 CvMat* log_det = 0; 780 CvMat* log_weights = 0; 781 CvMat* cov_eigen_values = 0; 782 CvMat* samples = 0; 783 CvMat* sum_probs = 0; 784 log_likelihood = -DBL_MAX; 785 786 CV_FUNCNAME( "CvEM::run_em" ); 787 __BEGIN__; 788 789 int nsamples = train_data.count, dims = train_data.dims, nclusters = params.nclusters; 790 double min_variation = FLT_EPSILON; 791 double min_det_value = MAX( DBL_MIN, pow( min_variation, dims )); 792 double likelihood_bias = -CV_LOG2PI * (double)nsamples * (double)dims / 2., _log_likelihood = -DBL_MAX; 793 int start_step = params.start_step; 794 795 int i, j, k, n; 796 int is_general = 0, is_diagonal = 0, is_spherical = 0; 797 double prev_log_likelihood = -DBL_MAX / 1000., det, d; 798 CvMat whdr, iwhdr, diag, *w, *iw; 799 double* w_data; 800 double* sp_data; 801 802 if( nclusters == 1 ) 803 { 804 double log_weight; 805 CV_CALL( cvSet( probs, cvScalar(1.)) ); 806 807 if( params.cov_mat_type == COV_MAT_SPHERICAL ) 808 { 809 d = cvTrace(*covs).val[0]/dims; 810 d = MAX( d, FLT_EPSILON ); 811 inv_eigen_values->data.db[0] = 1./d; 812 log_weight = pow( d, dims*0.5 ); 813 } 814 else 815 { 816 w_data = inv_eigen_values->data.db; 817 818 if( params.cov_mat_type == COV_MAT_GENERIC ) 819 cvSVD( *covs, inv_eigen_values, *cov_rotate_mats, 0, CV_SVD_U_T ); 820 else 821 cvTranspose( cvGetDiag(*covs, &diag), inv_eigen_values ); 822 823 cvMaxS( inv_eigen_values, FLT_EPSILON, inv_eigen_values ); 824 for( j = 0, det = 1.; j < dims; j++ ) 825 det *= w_data[j]; 826 log_weight = sqrt(det); 827 cvDiv( 0, inv_eigen_values, inv_eigen_values ); 828 } 829 830 log_weight_div_det->data.db[0] = -2*log(weights->data.db[0]/log_weight); 831 log_likelihood = DBL_MAX/1000.; 832 EXIT; 833 } 834 835 if( params.cov_mat_type == COV_MAT_GENERIC ) 836 is_general = 1; 837 else if( params.cov_mat_type == COV_MAT_DIAGONAL ) 838 is_diagonal = 1; 839 else if( params.cov_mat_type == COV_MAT_SPHERICAL ) 840 is_spherical = 1; 841 /* In the case of <cov_mat_type> == COV_MAT_DIAGONAL, the k-th row of cov_eigen_values 842 contains the diagonal elements (variations). In the case of 843 <cov_mat_type> == COV_MAT_SPHERICAL - the 0-ths elements of the vectors cov_eigen_values[k] 844 are to be equal to the mean of the variations over all the dimensions. */ 845 846 CV_CALL( log_det = cvCreateMat( 1, nclusters, CV_64FC1 )); 847 CV_CALL( log_weights = cvCreateMat( 1, nclusters, CV_64FC1 )); 848 CV_CALL( covs_item = cvCreateMat( dims, dims, CV_64FC1 )); 849 CV_CALL( centered_sample = cvCreateMat( 1, dims, CV_64FC1 )); 850 CV_CALL( cov_eigen_values = cvCreateMat( inv_eigen_values->rows, inv_eigen_values->cols, CV_64FC1 )); 851 CV_CALL( samples = cvCreateMat( nsamples, dims, CV_64FC1 )); 852 CV_CALL( sum_probs = cvCreateMat( 1, nclusters, CV_64FC1 )); 853 sp_data = sum_probs->data.db; 854 855 // copy the training data into double-precision matrix 856 for( i = 0; i < nsamples; i++ ) 857 { 858 const float* src = train_data.data.fl[i]; 859 double* dst = (double*)(samples->data.ptr + samples->step*i); 860 861 for( j = 0; j < dims; j++ ) 862 dst[j] = src[j]; 863 } 864 865 if( start_step != START_M_STEP ) 866 { 867 for( k = 0; k < nclusters; k++ ) 868 { 869 if( is_general || is_diagonal ) 870 { 871 w = cvGetRow( cov_eigen_values, &whdr, k ); 872 if( is_general ) 873 cvSVD( covs[k], w, cov_rotate_mats[k], 0, CV_SVD_U_T ); 874 else 875 cvTranspose( cvGetDiag( covs[k], &diag ), w ); 876 w_data = w->data.db; 877 for( j = 0, det = 1.; j < dims; j++ ) 878 det *= w_data[j]; 879 if( det < min_det_value ) 880 { 881 if( start_step == START_AUTO_STEP ) 882 det = min_det_value; 883 else 884 EXIT; 885 } 886 log_det->data.db[k] = det; 887 } 888 else 889 { 890 d = cvTrace(covs[k]).val[0]/(double)dims; 891 if( d < min_variation ) 892 { 893 if( start_step == START_AUTO_STEP ) 894 d = min_variation; 895 else 896 EXIT; 897 } 898 cov_eigen_values->data.db[k] = d; 899 log_det->data.db[k] = d; 900 } 901 } 902 903 cvLog( log_det, log_det ); 904 if( is_spherical ) 905 cvScale( log_det, log_det, dims ); 906 } 907 908 for( n = 0; n < params.term_crit.max_iter; n++ ) 909 { 910 if( n > 0 || start_step != START_M_STEP ) 911 { 912 // e-step: compute probs_ik from means_k, covs_k and weights_k. 913 CV_CALL(cvLog( weights, log_weights )); 914 915 // S_ik = -0.5[log(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)] + log(weights_k) 916 for( k = 0; k < nclusters; k++ ) 917 { 918 CvMat* u = cov_rotate_mats[k]; 919 const double* mean = (double*)(means->data.ptr + means->step*k); 920 w = cvGetRow( cov_eigen_values, &whdr, k ); 921 iw = cvGetRow( inv_eigen_values, &iwhdr, k ); 922 cvDiv( 0, w, iw ); 923 924 w_data = (double*)(inv_eigen_values->data.ptr + inv_eigen_values->step*k); 925 926 for( i = 0; i < nsamples; i++ ) 927 { 928 double *csample = centered_sample->data.db, p = log_det->data.db[k]; 929 const double* sample = (double*)(samples->data.ptr + samples->step*i); 930 double* pp = (double*)(probs->data.ptr + probs->step*i); 931 for( j = 0; j < dims; j++ ) 932 csample[j] = sample[j] - mean[j]; 933 if( is_general ) 934 cvGEMM( centered_sample, u, 1, 0, 0, centered_sample, CV_GEMM_B_T ); 935 for( j = 0; j < dims; j++ ) 936 p += csample[j]*csample[j]*w_data[is_spherical ? 0 : j]; 937 pp[k] = -0.5*p + log_weights->data.db[k]; 938 939 // S_ik <- S_ik - max_j S_ij 940 if( k == nclusters - 1 ) 941 { 942 double max_val = 0; 943 for( j = 0; j < nclusters; j++ ) 944 max_val = MAX( max_val, pp[j] ); 945 for( j = 0; j < nclusters; j++ ) 946 pp[j] -= max_val; 947 } 948 } 949 } 950 951 CV_CALL(cvExp( probs, probs )); // exp( S_ik ) 952 cvZero( sum_probs ); 953 954 // alpha_ik = exp( S_ik ) / sum_j exp( S_ij ), 955 // log_likelihood = sum_i log (sum_j exp(S_ij)) 956 for( i = 0, _log_likelihood = likelihood_bias; i < nsamples; i++ ) 957 { 958 double* pp = (double*)(probs->data.ptr + probs->step*i), sum = 0; 959 for( j = 0; j < nclusters; j++ ) 960 sum += pp[j]; 961 sum = 1./MAX( sum, DBL_EPSILON ); 962 for( j = 0; j < nclusters; j++ ) 963 { 964 double p = pp[j] *= sum; 965 sp_data[j] += p; 966 } 967 _log_likelihood -= log( sum ); 968 } 969 970 // check termination criteria 971 if( fabs( (_log_likelihood - prev_log_likelihood) / prev_log_likelihood ) < params.term_crit.epsilon ) 972 break; 973 prev_log_likelihood = _log_likelihood; 974 } 975 976 // m-step: update means_k, covs_k and weights_k from probs_ik 977 cvGEMM( probs, samples, 1, 0, 0, means, CV_GEMM_A_T ); 978 979 for( k = 0; k < nclusters; k++ ) 980 { 981 double sum = sp_data[k], inv_sum = 1./sum; 982 CvMat* cov = covs[k], _mean, _sample; 983 984 w = cvGetRow( cov_eigen_values, &whdr, k ); 985 w_data = w->data.db; 986 cvGetRow( means, &_mean, k ); 987 cvGetRow( samples, &_sample, k ); 988 989 // update weights_k 990 weights->data.db[k] = sum; 991 992 // update means_k 993 cvScale( &_mean, &_mean, inv_sum ); 994 995 // compute covs_k 996 cvZero( cov ); 997 cvZero( w ); 998 999 for( i = 0; i < nsamples; i++ ) 1000 { 1001 double p = probs->data.db[i*nclusters + k]*inv_sum; 1002 _sample.data.db = (double*)(samples->data.ptr + samples->step*i); 1003 1004 if( is_general ) 1005 { 1006 cvMulTransposed( &_sample, covs_item, 1, &_mean ); 1007 cvScaleAdd( covs_item, cvRealScalar(p), cov, cov ); 1008 } 1009 else 1010 for( j = 0; j < dims; j++ ) 1011 { 1012 double val = _sample.data.db[j] - _mean.data.db[j]; 1013 w_data[is_spherical ? 0 : j] += p*val*val; 1014 } 1015 } 1016 1017 if( is_spherical ) 1018 { 1019 d = w_data[0]/(double)dims; 1020 d = MAX( d, min_variation ); 1021 w->data.db[0] = d; 1022 log_det->data.db[k] = d; 1023 } 1024 else 1025 { 1026 if( is_general ) 1027 cvSVD( cov, w, cov_rotate_mats[k], 0, CV_SVD_U_T ); 1028 cvMaxS( w, min_variation, w ); 1029 for( j = 0, det = 1.; j < dims; j++ ) 1030 det *= w_data[j]; 1031 log_det->data.db[k] = det; 1032 } 1033 } 1034 1035 cvConvertScale( weights, weights, 1./(double)nsamples, 0 ); 1036 cvMaxS( weights, DBL_MIN, weights ); 1037 1038 cvLog( log_det, log_det ); 1039 if( is_spherical ) 1040 cvScale( log_det, log_det, dims ); 1041 } // end of iteration process 1042 1043 //log_weight_div_det[k] = -2*log(weights_k/det(Sigma_k))^0.5) = -2*log(weights_k) + log(det(Sigma_k))) 1044 if( log_weight_div_det ) 1045 { 1046 cvScale( log_weights, log_weight_div_det, -2 ); 1047 cvAdd( log_weight_div_det, log_det, log_weight_div_det ); 1048 } 1049 1050 /* Now finalize all the covariation matrices: 1051 1) if <cov_mat_type> == COV_MAT_DIAGONAL we used array of <w> as diagonals. 1052 Now w[k] should be copied back to the diagonals of covs[k]; 1053 2) if <cov_mat_type> == COV_MAT_SPHERICAL we used the 0-th element of w[k] 1054 as an average variation in each cluster. The value of the 0-th element of w[k] 1055 should be copied to the all of the diagonal elements of covs[k]. */ 1056 if( is_spherical ) 1057 { 1058 for( k = 0; k < nclusters; k++ ) 1059 cvSetIdentity( covs[k], cvScalar(cov_eigen_values->data.db[k])); 1060 } 1061 else if( is_diagonal ) 1062 { 1063 for( k = 0; k < nclusters; k++ ) 1064 cvTranspose( cvGetRow( cov_eigen_values, &whdr, k ), 1065 cvGetDiag( covs[k], &diag )); 1066 } 1067 cvDiv( 0, cov_eigen_values, inv_eigen_values ); 1068 1069 log_likelihood = _log_likelihood; 1070 1071 __END__; 1072 1073 cvReleaseMat( &log_det ); 1074 cvReleaseMat( &log_weights ); 1075 cvReleaseMat( &covs_item ); 1076 cvReleaseMat( ¢ered_sample ); 1077 cvReleaseMat( &cov_eigen_values ); 1078 cvReleaseMat( &samples ); 1079 cvReleaseMat( &sum_probs ); 1080 1081 return log_likelihood; 1082 } 1083 1084 1085 int CvEM::get_nclusters() const 1086 { 1087 return params.nclusters; 1088 } 1089 1090 const CvMat* CvEM::get_means() const 1091 { 1092 return means; 1093 } 1094 1095 const CvMat** CvEM::get_covs() const 1096 { 1097 return (const CvMat**)covs; 1098 } 1099 1100 const CvMat* CvEM::get_weights() const 1101 { 1102 return weights; 1103 } 1104 1105 const CvMat* CvEM::get_probs() const 1106 { 1107 return probs; 1108 } 1109 1110 /* End of file. */ 1111
