/*M/////////////////////////////////////////////////////////////////////////////////////// // // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. // // By downloading, copying, installing or using the software you agree to this license. // If you do not agree to this license, do not download, install, // copy or use the software. // // // Intel License Agreement // For Open Source Computer Vision Library // // Copyright( C) 2000, Intel Corporation, all rights reserved. // Third party copyrights are property of their respective owners. // // Redistribution and use in source and binary forms, with or without modification, // are permitted provided that the following conditions are met: // // * Redistribution's of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // // * Redistribution's in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // // * The name of Intel Corporation may not be used to endorse or promote products // derived from this software without specific prior written permission. // // This software is provided by the copyright holders and contributors "as is" and // any express or implied warranties, including, but not limited to, the implied // warranties of merchantability and fitness for a particular purpose are disclaimed. // In no event shall the Intel Corporation or contributors be liable for any direct, // indirect, incidental, special, exemplary, or consequential damages //(including, but not limited to, procurement of substitute goods or services; // loss of use, data, or profits; or business interruption) however caused // and on any theory of liability, whether in contract, strict liability, // or tort(including negligence or otherwise) arising in any way out of // the use of this software, even ifadvised of the possibility of such damage. // //M*/ #include "precomp.hpp" namespace cv { namespace ml { const double minEigenValue = DBL_EPSILON; class CV_EXPORTS EMImpl : public EM { public: int nclusters; int covMatType; TermCriteria termCrit; CV_IMPL_PROPERTY_S(TermCriteria, TermCriteria, termCrit) void setClustersNumber(int val) { nclusters = val; CV_Assert(nclusters > 1); } int getClustersNumber() const { return nclusters; } void setCovarianceMatrixType(int val) { covMatType = val; CV_Assert(covMatType == COV_MAT_SPHERICAL || covMatType == COV_MAT_DIAGONAL || covMatType == COV_MAT_GENERIC); } int getCovarianceMatrixType() const { return covMatType; } EMImpl() { nclusters = DEFAULT_NCLUSTERS; covMatType=EM::COV_MAT_DIAGONAL; termCrit = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, EM::DEFAULT_MAX_ITERS, 1e-6); } virtual ~EMImpl() {} void clear() { trainSamples.release(); trainProbs.release(); trainLogLikelihoods.release(); trainLabels.release(); weights.release(); means.release(); covs.clear(); covsEigenValues.clear(); invCovsEigenValues.clear(); covsRotateMats.clear(); logWeightDivDet.release(); } bool train(const Ptr& data, int) { Mat samples = data->getTrainSamples(), labels; return trainEM(samples, labels, noArray(), noArray()); } bool trainEM(InputArray samples, OutputArray logLikelihoods, OutputArray labels, OutputArray probs) { Mat samplesMat = samples.getMat(); setTrainData(START_AUTO_STEP, samplesMat, 0, 0, 0, 0); return doTrain(START_AUTO_STEP, logLikelihoods, labels, probs); } bool trainE(InputArray samples, InputArray _means0, InputArray _covs0, InputArray _weights0, OutputArray logLikelihoods, OutputArray labels, OutputArray probs) { Mat samplesMat = samples.getMat(); std::vector covs0; _covs0.getMatVector(covs0); Mat means0 = _means0.getMat(), weights0 = _weights0.getMat(); setTrainData(START_E_STEP, samplesMat, 0, !_means0.empty() ? &means0 : 0, !_covs0.empty() ? &covs0 : 0, !_weights0.empty() ? &weights0 : 0); return doTrain(START_E_STEP, logLikelihoods, labels, probs); } bool trainM(InputArray samples, InputArray _probs0, OutputArray logLikelihoods, OutputArray labels, OutputArray probs) { Mat samplesMat = samples.getMat(); Mat probs0 = _probs0.getMat(); setTrainData(START_M_STEP, samplesMat, !_probs0.empty() ? &probs0 : 0, 0, 0, 0); return doTrain(START_M_STEP, logLikelihoods, labels, probs); } float predict(InputArray _inputs, OutputArray _outputs, int) const { bool needprobs = _outputs.needed(); Mat samples = _inputs.getMat(), probs, probsrow; int ptype = CV_32F; float firstres = 0.f; int i, nsamples = samples.rows; if( needprobs ) { if( _outputs.fixedType() ) ptype = _outputs.type(); _outputs.create(samples.rows, nclusters, ptype); } else nsamples = std::min(nsamples, 1); for( i = 0; i < nsamples; i++ ) { if( needprobs ) probsrow = probs.row(i); Vec2d res = computeProbabilities(samples.row(i), needprobs ? &probsrow : 0, ptype); if( i == 0 ) firstres = (float)res[1]; } return firstres; } Vec2d predict2(InputArray _sample, OutputArray _probs) const { int ptype = CV_32F; Mat sample = _sample.getMat(); CV_Assert(isTrained()); CV_Assert(!sample.empty()); if(sample.type() != CV_64FC1) { Mat tmp; sample.convertTo(tmp, CV_64FC1); sample = tmp; } sample.reshape(1, 1); Mat probs; if( _probs.needed() ) { if( _probs.fixedType() ) ptype = _probs.type(); _probs.create(1, nclusters, ptype); probs = _probs.getMat(); } return computeProbabilities(sample, !probs.empty() ? &probs : 0, ptype); } bool isTrained() const { return !means.empty(); } bool isClassifier() const { return true; } int getVarCount() const { return means.cols; } String getDefaultModelName() const { return "opencv_ml_em"; } static void checkTrainData(int startStep, const Mat& samples, int nclusters, int covMatType, const Mat* probs, const Mat* means, const std::vector* covs, const Mat* weights) { // Check samples. CV_Assert(!samples.empty()); CV_Assert(samples.channels() == 1); int nsamples = samples.rows; int dim = samples.cols; // Check training params. CV_Assert(nclusters > 0); CV_Assert(nclusters <= nsamples); CV_Assert(startStep == START_AUTO_STEP || startStep == START_E_STEP || startStep == START_M_STEP); CV_Assert(covMatType == COV_MAT_GENERIC || covMatType == COV_MAT_DIAGONAL || covMatType == COV_MAT_SPHERICAL); CV_Assert(!probs || (!probs->empty() && probs->rows == nsamples && probs->cols == nclusters && (probs->type() == CV_32FC1 || probs->type() == CV_64FC1))); CV_Assert(!weights || (!weights->empty() && (weights->cols == 1 || weights->rows == 1) && static_cast(weights->total()) == nclusters && (weights->type() == CV_32FC1 || weights->type() == CV_64FC1))); CV_Assert(!means || (!means->empty() && means->rows == nclusters && means->cols == dim && means->channels() == 1)); CV_Assert(!covs || (!covs->empty() && static_cast(covs->size()) == nclusters)); if(covs) { const Size covSize(dim, dim); for(size_t i = 0; i < covs->size(); i++) { const Mat& m = (*covs)[i]; CV_Assert(!m.empty() && m.size() == covSize && (m.channels() == 1)); } } if(startStep == START_E_STEP) { CV_Assert(means); } else if(startStep == START_M_STEP) { CV_Assert(probs); } } static void preprocessSampleData(const Mat& src, Mat& dst, int dstType, bool isAlwaysClone) { if(src.type() == dstType && !isAlwaysClone) dst = src; else src.convertTo(dst, dstType); } static void preprocessProbability(Mat& probs) { max(probs, 0., probs); const double uniformProbability = (double)(1./probs.cols); for(int y = 0; y < probs.rows; y++) { Mat sampleProbs = probs.row(y); double maxVal = 0; minMaxLoc(sampleProbs, 0, &maxVal); if(maxVal < FLT_EPSILON) sampleProbs.setTo(uniformProbability); else normalize(sampleProbs, sampleProbs, 1, 0, NORM_L1); } } void setTrainData(int startStep, const Mat& samples, const Mat* probs0, const Mat* means0, const std::vector* covs0, const Mat* weights0) { clear(); checkTrainData(startStep, samples, nclusters, covMatType, probs0, means0, covs0, weights0); bool isKMeansInit = (startStep == START_AUTO_STEP) || (startStep == START_E_STEP && (covs0 == 0 || weights0 == 0)); // Set checked data preprocessSampleData(samples, trainSamples, isKMeansInit ? CV_32FC1 : CV_64FC1, false); // set probs if(probs0 && startStep == START_M_STEP) { preprocessSampleData(*probs0, trainProbs, CV_64FC1, true); preprocessProbability(trainProbs); } // set weights if(weights0 && (startStep == START_E_STEP && covs0)) { weights0->convertTo(weights, CV_64FC1); weights.reshape(1,1); preprocessProbability(weights); } // set means if(means0 && (startStep == START_E_STEP/* || startStep == START_AUTO_STEP*/)) means0->convertTo(means, isKMeansInit ? CV_32FC1 : CV_64FC1); // set covs if(covs0 && (startStep == START_E_STEP && weights0)) { covs.resize(nclusters); for(size_t i = 0; i < covs0->size(); i++) (*covs0)[i].convertTo(covs[i], CV_64FC1); } } void decomposeCovs() { CV_Assert(!covs.empty()); covsEigenValues.resize(nclusters); if(covMatType == COV_MAT_GENERIC) covsRotateMats.resize(nclusters); invCovsEigenValues.resize(nclusters); for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { CV_Assert(!covs[clusterIndex].empty()); SVD svd(covs[clusterIndex], SVD::MODIFY_A + SVD::FULL_UV); if(covMatType == COV_MAT_SPHERICAL) { double maxSingularVal = svd.w.at(0); covsEigenValues[clusterIndex] = Mat(1, 1, CV_64FC1, Scalar(maxSingularVal)); } else if(covMatType == COV_MAT_DIAGONAL) { covsEigenValues[clusterIndex] = svd.w; } else //COV_MAT_GENERIC { covsEigenValues[clusterIndex] = svd.w; covsRotateMats[clusterIndex] = svd.u; } max(covsEigenValues[clusterIndex], minEigenValue, covsEigenValues[clusterIndex]); invCovsEigenValues[clusterIndex] = 1./covsEigenValues[clusterIndex]; } } void clusterTrainSamples() { int nsamples = trainSamples.rows; // Cluster samples, compute/update means // Convert samples and means to 32F, because kmeans requires this type. Mat trainSamplesFlt, meansFlt; if(trainSamples.type() != CV_32FC1) trainSamples.convertTo(trainSamplesFlt, CV_32FC1); else trainSamplesFlt = trainSamples; if(!means.empty()) { if(means.type() != CV_32FC1) means.convertTo(meansFlt, CV_32FC1); else meansFlt = means; } Mat labels; kmeans(trainSamplesFlt, nclusters, labels, TermCriteria(TermCriteria::COUNT, means.empty() ? 10 : 1, 0.5), 10, KMEANS_PP_CENTERS, meansFlt); // Convert samples and means back to 64F. CV_Assert(meansFlt.type() == CV_32FC1); if(trainSamples.type() != CV_64FC1) { Mat trainSamplesBuffer; trainSamplesFlt.convertTo(trainSamplesBuffer, CV_64FC1); trainSamples = trainSamplesBuffer; } meansFlt.convertTo(means, CV_64FC1); // Compute weights and covs weights = Mat(1, nclusters, CV_64FC1, Scalar(0)); covs.resize(nclusters); for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { Mat clusterSamples; for(int sampleIndex = 0; sampleIndex < nsamples; sampleIndex++) { if(labels.at(sampleIndex) == clusterIndex) { const Mat sample = trainSamples.row(sampleIndex); clusterSamples.push_back(sample); } } CV_Assert(!clusterSamples.empty()); calcCovarMatrix(clusterSamples, covs[clusterIndex], means.row(clusterIndex), CV_COVAR_NORMAL + CV_COVAR_ROWS + CV_COVAR_USE_AVG + CV_COVAR_SCALE, CV_64FC1); weights.at(clusterIndex) = static_cast(clusterSamples.rows)/static_cast(nsamples); } decomposeCovs(); } void computeLogWeightDivDet() { CV_Assert(!covsEigenValues.empty()); Mat logWeights; cv::max(weights, DBL_MIN, weights); log(weights, logWeights); logWeightDivDet.create(1, nclusters, CV_64FC1); // note: logWeightDivDet = log(weight_k) - 0.5 * log(|det(cov_k)|) for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { double logDetCov = 0.; const int evalCount = static_cast(covsEigenValues[clusterIndex].total()); for(int di = 0; di < evalCount; di++) logDetCov += std::log(covsEigenValues[clusterIndex].at(covMatType != COV_MAT_SPHERICAL ? di : 0)); logWeightDivDet.at(clusterIndex) = logWeights.at(clusterIndex) - 0.5 * logDetCov; } } bool doTrain(int startStep, OutputArray logLikelihoods, OutputArray labels, OutputArray probs) { int dim = trainSamples.cols; // Precompute the empty initial train data in the cases of START_E_STEP and START_AUTO_STEP if(startStep != START_M_STEP) { if(covs.empty()) { CV_Assert(weights.empty()); clusterTrainSamples(); } } if(!covs.empty() && covsEigenValues.empty() ) { CV_Assert(invCovsEigenValues.empty()); decomposeCovs(); } if(startStep == START_M_STEP) mStep(); double trainLogLikelihood, prevTrainLogLikelihood = 0.; int maxIters = (termCrit.type & TermCriteria::MAX_ITER) ? termCrit.maxCount : DEFAULT_MAX_ITERS; double epsilon = (termCrit.type & TermCriteria::EPS) ? termCrit.epsilon : 0.; for(int iter = 0; ; iter++) { eStep(); trainLogLikelihood = sum(trainLogLikelihoods)[0]; if(iter >= maxIters - 1) break; double trainLogLikelihoodDelta = trainLogLikelihood - prevTrainLogLikelihood; if( iter != 0 && (trainLogLikelihoodDelta < -DBL_EPSILON || trainLogLikelihoodDelta < epsilon * std::fabs(trainLogLikelihood))) break; mStep(); prevTrainLogLikelihood = trainLogLikelihood; } if( trainLogLikelihood <= -DBL_MAX/10000. ) { clear(); return false; } // postprocess covs covs.resize(nclusters); for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { if(covMatType == COV_MAT_SPHERICAL) { covs[clusterIndex].create(dim, dim, CV_64FC1); setIdentity(covs[clusterIndex], Scalar(covsEigenValues[clusterIndex].at(0))); } else if(covMatType == COV_MAT_DIAGONAL) { covs[clusterIndex] = Mat::diag(covsEigenValues[clusterIndex]); } } if(labels.needed()) trainLabels.copyTo(labels); if(probs.needed()) trainProbs.copyTo(probs); if(logLikelihoods.needed()) trainLogLikelihoods.copyTo(logLikelihoods); trainSamples.release(); trainProbs.release(); trainLabels.release(); trainLogLikelihoods.release(); return true; } Vec2d computeProbabilities(const Mat& sample, Mat* probs, int ptype) const { // L_ik = log(weight_k) - 0.5 * log(|det(cov_k)|) - 0.5 *(x_i - mean_k)' cov_k^(-1) (x_i - mean_k)] // q = arg(max_k(L_ik)) // probs_ik = exp(L_ik - L_iq) / (1 + sum_j!=q (exp(L_ij - L_iq)) // see Alex Smola's blog http://blog.smola.org/page/2 for // details on the log-sum-exp trick int stype = sample.type(); CV_Assert(!means.empty()); CV_Assert((stype == CV_32F || stype == CV_64F) && (ptype == CV_32F || ptype == CV_64F)); CV_Assert(sample.size() == Size(means.cols, 1)); int dim = sample.cols; Mat L(1, nclusters, CV_64FC1), centeredSample(1, dim, CV_64F); int i, label = 0; for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { const double* mptr = means.ptr(clusterIndex); double* dptr = centeredSample.ptr(); if( stype == CV_32F ) { const float* sptr = sample.ptr(); for( i = 0; i < dim; i++ ) dptr[i] = sptr[i] - mptr[i]; } else { const double* sptr = sample.ptr(); for( i = 0; i < dim; i++ ) dptr[i] = sptr[i] - mptr[i]; } Mat rotatedCenteredSample = covMatType != COV_MAT_GENERIC ? centeredSample : centeredSample * covsRotateMats[clusterIndex]; double Lval = 0; for(int di = 0; di < dim; di++) { double w = invCovsEigenValues[clusterIndex].at(covMatType != COV_MAT_SPHERICAL ? di : 0); double val = rotatedCenteredSample.at(di); Lval += w * val * val; } CV_DbgAssert(!logWeightDivDet.empty()); L.at(clusterIndex) = logWeightDivDet.at(clusterIndex) - 0.5 * Lval; if(L.at(clusterIndex) > L.at(label)) label = clusterIndex; } double maxLVal = L.at(label); double expDiffSum = 0; for( i = 0; i < L.cols; i++ ) { double v = std::exp(L.at(i) - maxLVal); L.at(i) = v; expDiffSum += v; // sum_j(exp(L_ij - L_iq)) } if(probs) L.convertTo(*probs, ptype, 1./expDiffSum); Vec2d res; res[0] = std::log(expDiffSum) + maxLVal - 0.5 * dim * CV_LOG2PI; res[1] = label; return res; } void eStep() { // Compute probs_ik from means_k, covs_k and weights_k. trainProbs.create(trainSamples.rows, nclusters, CV_64FC1); trainLabels.create(trainSamples.rows, 1, CV_32SC1); trainLogLikelihoods.create(trainSamples.rows, 1, CV_64FC1); computeLogWeightDivDet(); CV_DbgAssert(trainSamples.type() == CV_64FC1); CV_DbgAssert(means.type() == CV_64FC1); for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++) { Mat sampleProbs = trainProbs.row(sampleIndex); Vec2d res = computeProbabilities(trainSamples.row(sampleIndex), &sampleProbs, CV_64F); trainLogLikelihoods.at(sampleIndex) = res[0]; trainLabels.at(sampleIndex) = static_cast(res[1]); } } void mStep() { // Update means_k, covs_k and weights_k from probs_ik int dim = trainSamples.cols; // Update weights // not normalized first reduce(trainProbs, weights, 0, CV_REDUCE_SUM); // Update means means.create(nclusters, dim, CV_64FC1); means = Scalar(0); const double minPosWeight = trainSamples.rows * DBL_EPSILON; double minWeight = DBL_MAX; int minWeightClusterIndex = -1; for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { if(weights.at(clusterIndex) <= minPosWeight) continue; if(weights.at(clusterIndex) < minWeight) { minWeight = weights.at(clusterIndex); minWeightClusterIndex = clusterIndex; } Mat clusterMean = means.row(clusterIndex); for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++) clusterMean += trainProbs.at(sampleIndex, clusterIndex) * trainSamples.row(sampleIndex); clusterMean /= weights.at(clusterIndex); } // Update covsEigenValues and invCovsEigenValues covs.resize(nclusters); covsEigenValues.resize(nclusters); if(covMatType == COV_MAT_GENERIC) covsRotateMats.resize(nclusters); invCovsEigenValues.resize(nclusters); for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { if(weights.at(clusterIndex) <= minPosWeight) continue; if(covMatType != COV_MAT_SPHERICAL) covsEigenValues[clusterIndex].create(1, dim, CV_64FC1); else covsEigenValues[clusterIndex].create(1, 1, CV_64FC1); if(covMatType == COV_MAT_GENERIC) covs[clusterIndex].create(dim, dim, CV_64FC1); Mat clusterCov = covMatType != COV_MAT_GENERIC ? covsEigenValues[clusterIndex] : covs[clusterIndex]; clusterCov = Scalar(0); Mat centeredSample; for(int sampleIndex = 0; sampleIndex < trainSamples.rows; sampleIndex++) { centeredSample = trainSamples.row(sampleIndex) - means.row(clusterIndex); if(covMatType == COV_MAT_GENERIC) clusterCov += trainProbs.at(sampleIndex, clusterIndex) * centeredSample.t() * centeredSample; else { double p = trainProbs.at(sampleIndex, clusterIndex); for(int di = 0; di < dim; di++ ) { double val = centeredSample.at(di); clusterCov.at(covMatType != COV_MAT_SPHERICAL ? di : 0) += p*val*val; } } } if(covMatType == COV_MAT_SPHERICAL) clusterCov /= dim; clusterCov /= weights.at(clusterIndex); // Update covsRotateMats for COV_MAT_GENERIC only if(covMatType == COV_MAT_GENERIC) { SVD svd(covs[clusterIndex], SVD::MODIFY_A + SVD::FULL_UV); covsEigenValues[clusterIndex] = svd.w; covsRotateMats[clusterIndex] = svd.u; } max(covsEigenValues[clusterIndex], minEigenValue, covsEigenValues[clusterIndex]); // update invCovsEigenValues invCovsEigenValues[clusterIndex] = 1./covsEigenValues[clusterIndex]; } for(int clusterIndex = 0; clusterIndex < nclusters; clusterIndex++) { if(weights.at(clusterIndex) <= minPosWeight) { Mat clusterMean = means.row(clusterIndex); means.row(minWeightClusterIndex).copyTo(clusterMean); covs[minWeightClusterIndex].copyTo(covs[clusterIndex]); covsEigenValues[minWeightClusterIndex].copyTo(covsEigenValues[clusterIndex]); if(covMatType == COV_MAT_GENERIC) covsRotateMats[minWeightClusterIndex].copyTo(covsRotateMats[clusterIndex]); invCovsEigenValues[minWeightClusterIndex].copyTo(invCovsEigenValues[clusterIndex]); } } // Normalize weights weights /= trainSamples.rows; } void write_params(FileStorage& fs) const { fs << "nclusters" << nclusters; fs << "cov_mat_type" << (covMatType == COV_MAT_SPHERICAL ? String("spherical") : covMatType == COV_MAT_DIAGONAL ? String("diagonal") : covMatType == COV_MAT_GENERIC ? String("generic") : format("unknown_%d", covMatType)); writeTermCrit(fs, termCrit); } void write(FileStorage& fs) const { fs << "training_params" << "{"; write_params(fs); fs << "}"; fs << "weights" << weights; fs << "means" << means; size_t i, n = covs.size(); fs << "covs" << "["; for( i = 0; i < n; i++ ) fs << covs[i]; fs << "]"; } void read_params(const FileNode& fn) { nclusters = (int)fn["nclusters"]; String s = (String)fn["cov_mat_type"]; covMatType = s == "spherical" ? COV_MAT_SPHERICAL : s == "diagonal" ? COV_MAT_DIAGONAL : s == "generic" ? COV_MAT_GENERIC : -1; CV_Assert(covMatType >= 0); termCrit = readTermCrit(fn); } void read(const FileNode& fn) { clear(); read_params(fn["training_params"]); fn["weights"] >> weights; fn["means"] >> means; FileNode cfn = fn["covs"]; FileNodeIterator cfn_it = cfn.begin(); int i, n = (int)cfn.size(); covs.resize(n); for( i = 0; i < n; i++, ++cfn_it ) (*cfn_it) >> covs[i]; decomposeCovs(); computeLogWeightDivDet(); } Mat getWeights() const { return weights; } Mat getMeans() const { return means; } void getCovs(std::vector& _covs) const { _covs.resize(covs.size()); std::copy(covs.begin(), covs.end(), _covs.begin()); } // all inner matrices have type CV_64FC1 Mat trainSamples; Mat trainProbs; Mat trainLogLikelihoods; Mat trainLabels; Mat weights; Mat means; std::vector covs; std::vector covsEigenValues; std::vector covsRotateMats; std::vector invCovsEigenValues; Mat logWeightDivDet; }; Ptr EM::create() { return makePtr(); } } } // namespace cv /* End of file. */