I've been trying to use the OpenCV EM code and have had a problem. By setting the maxiter parameter to 1 and using the trainE function I allow only the first expectation step to be completed. I then check the loglikelihood output.
Now my problem lies in the fact that if I change the model from GENERIC to SPHERICAL, I get different values for loglikelihood for the same initialization. However the equations for the expectation step remain the same and the loglikelihoods in the first E-Step should be the same values for both models.
#include <opencv2/opencv.hpp>
#define NumObs 100
#define Dim 2
#define numClusters 2
#define maxiter 1
int main(int argc, char** argv)
{
cv::Mat X = cv::Mat(NumObs, Dim, CV_64F);
cv::Mat mean = cv::Mat(numClusters,Dim,CV_64F);
std::vector<cv::Mat> covar;
cv::Mat mixfrac = cv::Mat(numClusters, 1, CV_64F);
cv::Mat logLikelihoods = cv::Mat(NumObs, 1, CV_64F);
cv::Mat labels = cv::Mat(NumObs, 1, CV_32SC1);
cv::Mat probs = cv::Mat(NumObs, numClusters, CV_64F);
int i;
mean = (cv::Mat_<double>(numClusters, Dim) << 2, 3, 4, 5);
mixfrac = (cv::Mat_<double>(numClusters, 1) << 0.5, 0.5);
cv::Mat temp(2, 2, CV_64F);
temp = (cv::Mat_<double>(Dim, Dim) << 2, 0, 0, 2);
covar.push_back(temp);
temp = (cv::Mat_<double>(Dim, Dim) << 3, 0, 0, 3);
covar.push_back(temp);
X = (cv::Mat_<double>(NumObs, Dim) << 1.497295712046560, 2.389842806384741
, -1.152388866819642, 2.324051537951996
, 0.173091890138541, 3.534436744900519
, 4.013635589903881, 2.635470732249428
, 0.343404593485856, 2.710797002553179
, 1.921946750771822, 2.230097059251492
, 2.923105482852674, 1.968687377364361
, 0.833763816549866, 1.621119740290876
, 1.000974973520235, 0.501003642054062
, 2.722581031828046, 2.179151938477484
, 2.061657164408961, 1.870114601526011
, 2.020337185029648, 1.822954976448330
, 1.076363394410326, 2.640385082400831
, 1.543478612011669, 2.241597508998520
, 1.485372235285237, 2.893724906106137
, -0.715927044291090, 1.369537907446789
, 1.864588596758692, 1.688875700397673
, -0.335577615523311, 2.183975485869516
, -1.456483320753825, 1.493965172927608
, -0.712160818106508, 1.912240385882839
, 0.233365021273562, 1.954626227148290
, 1.998344873833923, 0.343780671699337
, 0.880159284239810, 0.926396318575558
, 0.800239863676473, 2.841303191042556
, 2.509835594907550, 0.767610261936824
, -0.806015998003402, 2.440467562347095
, 2.672846813458981, 1.899891020249070
, 2.396696676145479, 3.621937374575406
, 0.151374345266610, 2.569943677660735
, 2.775466044119043, 1.781063533049695
, 1.191366838548084, 1.702684062103669
, -0.232621783623176, 1.631979353155736
, -1.174537262824991, 1.738099976739696
, -2.550748638571660, 1.816963733157464
, 0.039014544632652, 1.808195242782888
, -2.078943086646864, 2.084038835619226
, 1.081089945552743, 2.576115695603576
, -0.916439364072319, 0.708922705869511
, 0.903297610096863, 2.791378047921652
, -0.561947988394385, 2.656510856158910
, 1.216211768410659, 1.219031885881044
, 0.693337555617687, 1.359035671153648
, 1.417702588339615, 2.313005179476850
, 0.430424593609415, 1.132064410966174
, -0.261023655491497, 1.981218019474763
, 2.268819458983812, 0.391842019202139
, 0.806386480042758, 3.199864590240754
, -0.985989695126394, 0.893059534741550
, -2.442654072043812, 1.689554199357084
, 1.210751074224775, 1.499372753495019
, -0.672567018407857, 2.970910199573346
, -0.507381574772955, 1.967926272242394
, 0.247969979069518, 0.947965104732303
, 2.891713920836473, 0.861177994177589
, 3.354602636199656, 1.942017768571913
, -1.693061842976859, 1.760474923494942
, 3.997953758133590, 1.297952400955861
, 1.512000798331720, 0.853595479991537
, 1.423345018469304, 3.082589664236521
, -0.666695083234841, 1.125720158829322
, 3.464220247867981, 1.038778673164228
, 2.933373891043690, 1.628066445794965
, 2.438787742568557, 1.882463318993010
, 1.156530661730840, 2.009751864529454
, 1.471382343384891, 2.299778193525170
, 0.710205836898082, 2.982463815839716
, 0.574655988307198, 1.897536569003219
, -0.481180738023749, 3.243258184346350
, 2.057634665518593, 1.158138790043992
, 2.764066483839555, 1.749966682737925
, 1.188742536016829, 1.830731044279766
, 1.062643063683092, 2.464027653634071
, 2.274832425103863, 2.976150757847411
, -0.391925728913642, 2.459189741355192
, 0.214293806085435, 1.173608789474463
, 0.457619276357005, 2.215723842685201
, -3.276595636919820, 2.027190449572088
, 1.136813051985737, 2.411476105137650
, 2.754286393796612, 1.525510310208986
, 1.772550672306315, 1.678744622863505
, 1.151056973603011, 0.934580048074344
, 1.572929476032799, 1.934085057470423
, 2.070875710998629, 2.577539460790769
, -0.449497770648108, 1.397218305043158
, 0.271960009043126, 2.461090941688480
, 1.502451262202109, 2.258525296739507
, 1.867786756275275, 1.401950731642538
, -0.397193560292116, 1.959501415433482
, -0.799417427242084, 1.323993855920221
, 1.063400687978604, 1.690226733204147
, 1.270024853701466, 2.875733585500125
, -1.772562991551423, 0.986750552965217
, 0.532253741838827, 0.619813291703453
, 1.138823786767506, 2.845567676726764
, 1.285833310664554, 1.354502560988730
, 3.353413094595020, 2.320556360323725
, -1.158616580303092, 1.591324520299605
, 0.300520863016906, 0.893745059745460
, 1.133378827555012, 1.534905699580405
, 0.040235892761628, 2.368829212292840);
cv::EM emModel(numClusters, cv::EM::COV_MAT_SPHERICAL, cv::TermCriteria(cv::TermCriteria::COUNT + cv::TermCriteria::EPS, maxiter, FLT_EPSILON));
bool success = emModel.cv::EM::trainE(X, mean, covar, mixfrac, logLikelihoods,labels,probs);
if (success)
printf("Success\n");
else
printf("Failed\n");
cv::Mat newmean = emModel.cv::EM::get<cv::Mat>("means");
cv::Mat newweight = emModel.cv::EM::get<cv::Mat>("weights");
std::vector<cv::Mat> newvar = emModel.cv::EM::get<std::vector<cv::Mat>>("covs");
std::cout << "LLH\n" << logLikelihoods << "\n\n";
std::cout <<"NEWMEAN\n"<< newmean<<"\n\n";
std::cout << "NEWWEIGHTS\n" << newweight << "\n\n";
std::cout << "NEWSIGMA1\n" << newvar[0] << "\n";
std::cout << "NEWSIGMA2\n" << newvar[1] << "\n\n";
scanf("%d", &i);
}
Output for Spherical GMM
LLH
[-2.931318011752626;
-5.437115860016975;
-3.667420897566784;
-3.274239241308711;
-3.512773886210777;
-2.906378240768077;
-3.145533448424205;
-3.642481763141506;
-4.650852173801083;
-2.975512838378632;
-3.086635213907651;
-3.118147350422762;
-3.02853906103177;
-2.976176233676393;
-2.81071576186187;
-5.359239062666107;
-3.221342073874848;
-4.364890315806004;
-6.406040105709825;
-4.978136266645567;
-3.885209083574705;
-4.577679428989389;
-4.226199670930593;
-3.149979577537311;
-4.088024534030816;
-4.880127907834185;
-3.122802132137833;
-2.646131497925848;
-3.716520697504866;
-3.224961706370468;
-3.399575606628337;
-4.557644951387831;
-5.765981658468872;
-8.37554003304065;
-4.15407503628638;
-7.21426852540733;
-3.042169136121539;
-6.295443523476872;
-3.093842961677683;
-4.495265457885608;
-3.772140198103474;
-3.935028312978259;
-2.986138732258714;
-4.33067591541676;
-4.375573985871765;
-4.519102272986751;
-3.12565345021085;
-6.194705958136484;
-8.213811782800219;
-3.538572963594731;
-4.601005773126856;
-4.678804407509512;
-4.666930234789473;
-4.083218428518389;
-3.326859772310369;
-6.643334152388976;
-4.217625141712781;
-4.034734535109596;
-2.814646585841023;
-5.508686183211898;
-4.14839280421732;
-3.381874480419066;
-3.094404661798319;
-3.230164061642246;
-2.973679171864843;
-3.195153092832868;
-3.638373707120748;
-4.353325915681707;
-3.643177605071091;
-3.243476559240886;
-3.318103507338534;
-3.083978027938285;
-2.668655332006318;
-4.331983635797021;
-4.47589600534346;
-3.569193241927018;
-10.03869961506342;
-3.064692854541199;
-3.408620622130172;
-3.24166993975683;
-4.078595023654192;
-3.122174103654394;
-2.764010652665211;
-4.990765765921384;
-3.636211257765106;
-2.980988844038545;
-3.439623639120886;
-4.547175745026653;
-5.512926199458751;
-3.467745941915222;
-2.894697423739033;
-7.428294826501615;
-4.801229141025504;
-2.958713722999831;
-3.625296272969862;
-3.108524035685613;
-5.840522469845191;
-4.677873214788853;
-3.545697817254149;
-3.884322355072641]
NEWMEAN
[2, 3;
4, 5]
NEWWEIGHTS
[0.5, 0.5]
NEWSIGMA1
[2, 0;
0, 2]
NEWSIGMA2
[3, 0;
0, 3]
Output for Spherical GMM
LLH
[-3.295935746117501;
-5.790750393412513;
-4.03429419104581;
-3.71263347108744;
-3.872144489126807;
-3.274075193172064;
-3.527637461113017;
-3.998128057592525;
-5.004203357427852;
-3.356081006983058;
-3.452688438712195;
-3.483334605887541;
-3.391826118348322;
-3.33991303502579;
-3.180885949172912;
-5.710717495080189;
-3.583938119252925;
-4.719201739742172;
-6.757228800928109;
-5.330902409373262;
-4.240038592584679;
-4.935658714571719;
-4.579970929182056;
-3.513114639026275;
-4.4522906425319;
-5.234662136130952;
-3.498568777684983;
-3.050795422255073;
-4.074129455698702;
-3.60134679297809;
-3.757286012239146;
-4.910366860830981;
-6.117838563989898;
-8.727422737804261;
-4.507867855539753;
-7.566730910097011;
-3.404909140030045;
-6.645804917417026;
-3.457241856183214;
-4.851307959586312;
-4.128055700550207;
-4.289284804578601;
-3.349349646254201;
-4.683600556531062;
-4.729290711442341;
-4.879400262194479;
-3.492881334973137;
-6.545230968603729;
-8.565356892970549;
-3.895492494864605;
-4.958752084391844;
-5.032035254354657;
-5.01908185049789;
-4.453534794387545;
-3.72062903465443;
-6.99499565346089;
-4.624250701398458;
-4.391029813440906;
-3.186754423099298;
-5.859793331816577;
-4.532911965106766;
-3.759785100598588;
-3.465822699838461;
-3.589297731185657;
-3.337252862476405;
-3.55907539338088;
-3.994110028844047;
-4.713786842080629;
-4.004537247619449;
-3.619271902441214;
-3.67643636032134;
-3.4456342295298;
-3.053353732793124;
-4.687381509300202;
-4.828411093949869;
-3.925970540180974;
-10.3918013626343;
-3.426464016898089;
-3.781854557415382;
-3.603359371297283;
-4.433394247345532;
-3.483824967527195;
-3.138004621822025;
-5.342610735990292;
-3.993620083098697;
-3.344492754280415;
-3.800540886464314;
-4.900564570171441;
-5.864239423435192;
-3.824719561169336;
-3.262235974218792;
-7.778626718537899;
-5.153466442034869;
-3.324629479023928;
-3.982041010852076;
-3.50977175586426;
-6.192064850807197;
-5.030038737191805;
-3.902365100307677;
-4.240420295976542]
NEWMEAN
[2, 3;
4, 5]
NEWWEIGHTS
[0.5, 0.5]
NEWSIGMA1
[2, 0;
0, 2]
NEWSIGMA2
[3, 0;
0, 3]
Thank you for your time.
