1、Opencv中的朴素贝叶斯
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#include "iostream" using namespace cv; using namespace std; //10个样本特征向量维数为12的训练样本集,第一列为该样本的类别标签 double inputArr[10][13] = { 1,0.708333,1,1,-0.320755,-0.105023,-1,1,-0.419847,-1,-0.225806,0,1, -1,0.583333,-1,0.333333,-0.603774,1,-1,1,0.358779,-1,-0.483871,0,-1, 1,0.166667,1,-0.333333,-0.433962,-0.383562,-1,-1,0.0687023,-1,-0.903226,-1,-1, -1,0.458333,1,1,-0.358491,-0.374429,-1,-1,-0.480916,1,-0.935484,0,-0.333333, -1,0.875,-1,-0.333333,-0.509434,-0.347032,-1,1,-0.236641,1,-0.935484,-1,-0.333333, -1,0.5,1,1,-0.509434,-0.767123,-1,-1,0.0534351,-1,-0.870968,-1,-1, 1,0.125,1,0.333333,-0.320755,-0.406393,1,1,0.0839695,1,-0.806452,0,-0.333333, 1,0.25,1,1,-0.698113,-0.484018,-1,1,0.0839695,1,-0.612903,0,-0.333333, 1,0.291667,1,1,-0.132075,-0.237443,-1,1,0.51145,-1,-0.612903,0,0.333333, 1,0.416667,-1,1,0.0566038,0.283105,-1,1,0.267176,-1,0.290323,0,1 }; //一个测试样本的特征向量 double testArr[]={ 0.25,1,1,-0.226415,-0.506849,-1,-1,0.374046,-1,-0.83871,0,-1 }; int _tmain(int argc, _TCHAR* argv[]){ Mat trainData(10, 12, CV_32FC1);//构建训练样本的特征向量 for (int i=0; i<10; i++){ for (int j=0; j<12; j++){ trainData.at<float>(i, j) = inputArr[i][j+1]; } } Mat trainResponse(10, 1, CV_32FC1);//构建训练样本的类别标签 for (int i=0; i<10; i++){ trainResponse.at<float>(i, 0) = inputArr[i][0]; } CvNormalBayesClassifier nbc; bool trainFlag = nbc.train(trainData, trainResponse);//进行贝叶斯分类器训练 if (trainFlag){ cout<<"train over..."<<endl; nbc.save("d:\\normalBayes.txt"); } else{ cout<<"train error..."<<endl; system("pause"); exit(-1); } CvNormalBayesClassifier testNbc; testNbc.load("d:\\normalBayes.txt"); Mat testSample(1, 12, CV_32FC1);//构建测试样本 for (int i=0; i<12; i++){ testSample.at<float>(0, i) = testArr[i]; } float flag = testNbc.predict(testSample);//进行测试 cout<<"flag = "<<flag<<endl; return 0; } |
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CvNormalBayesClassifier Bayes classifier for normally distributed data class CV_EXPORTS CvNormalBayesClassifiejur : public CvStatModel { public: CvNormalBayesClassifier(); virtual ~CvNormalBayesClassifier();//析构函数为虚函数 CvNormalBayesClassifier( const CvMat* _train_data, const CvMat* _responses, const CvMat* _var_idx=0, const CvMat* _sample_idx=0 ); virtual bool train( const CvMat* _train_data, const CvMat* _responses, const CvMat* _var_idx = 0, const CvMat* _sample_idx=0, bool update=false ); virtual float predict( const CvMat* _samples, CvMat* results=0 ) const;//虚函数 virtual void clear(); virtual void write( CvFileStorage* storage, const char* name ); virtual void read( CvFileStorage* storage, CvFileNode* node ); protected: int var_count, var_all;//特征维数 CvMat* var_idx; CvMat* cls_labels; //<span class="comment">类别数目</span> CvMat** count; //正负类样本数,对应于每一维 CvMat** sum; //正负类每一维特征的求和,double型 CvMat** productsum;//productsum[0...(classNum-1)],每个元素是一个CvMat(rows=cols=var_count)指针,存储类内特征相关矩阵 CvMat** avg;//avg[0...(classNum-1)],每个元素是一个CvMat(rows=1,cols=var_count)指针,代表训练数据中每一类的某个特征的平均值 CvMat** inv_eigen_values;//inv_eigen_values[0...(classNum-1)],每个元素是一个CvMat(rows=1,cols=var_count)指针,代表训练数据中每一类的某个特征的特征值的倒数 CvMat** cov_rotate_mats;//特征变量的协方差矩阵经过SVD奇异值分解后得到的特征向量矩阵 CvMat* c; }; |
CvNormalBayesClassifier::train(Trains the model)
The method trains the Normal Bayes classifier. It follows the conventions of generic train "method" with the following limitations: only CV_ROW_SAMPLE data layout is supported; the input variables are all ordered; the output variable is categorical (i.e. elements of _responses
must be integer numbers, though the vector may have 32fC1
type), missing measurements are not supported.
In addition, there is update
flag that identifies, whether the model should be trained from scratch (update=false
) or should be updated using new training data (update=true
).
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bool CvNormalBayesClassifier::train( const CvMat* _train_data, const CvMat* _responses, const CvMat* _var_idx, const CvMat* _sample_idx, bool update ){ const float min_variation = FLT_EPSILON; bool result = false; CvMat* responses = 0; const float** train_data = 0; //二级指针,用于存放数据 CvMat* __cls_labels = 0; CvMat* __var_idx = 0; CvMat* cov = 0; CV_FUNCNAME( "CvNormalBayesClassifier::train" ); __BEGIN__; int cls, nsamples = 0, _var_count = 0, _var_all = 0, nclasses = 0; int s, c1, c2; const int* responses_data; //分配内存 CV_CALL( cvPrepareTrainData( 0, _train_data, CV_ROW_SAMPLE, _responses, CV_VAR_CATEGORICAL, _var_idx, _sample_idx, false, &train_data, &nsamples, &_var_count, &_var_all, &responses, &__cls_labels, &__var_idx )); if( !update ){ const size_t mat_size = sizeof(CvMat*); size_t data_size; clear(); var_idx = __var_idx; cls_labels = __cls_labels; __var_idx = __cls_labels = 0; var_count = _var_count; var_all = _var_all; nclasses = cls_labels->cols; data_size = nclasses*6*mat_size; CV_CALL( count = (CvMat**)cvAlloc( data_size )); memset( count, 0, data_size ); sum = count + nclasses; productsum = sum + nclasses; //productsum[cls]存储第cls类的协方差矩阵的乘积项sum(XiXj),cov(Xi,Xj)=sum(XiXj)-sum(Xi)E(Xj) avg = productsum + nclasses; //avg[cls]存储第cls类的每个变量均值 inv_eigen_values= avg + nclasses; //inv_eigen_values[cls]存储第cls类的协方差矩阵的特征值 cov_rotate_mats = inv_eigen_values + nclasses; //存储第cls类的矩阵的特征值对应的特征向量 CV_CALL( c = cvCreateMat( 1, nclasses, CV_64FC1 )); for( cls = 0; cls < nclasses; cls++ ){ CV_CALL(count[cls] = cvCreateMat( 1, var_count, CV_32SC1 )); CV_CALL(sum[cls] = cvCreateMat( 1, var_count, CV_64FC1 )); CV_CALL(productsum[cls] = cvCreateMat( var_count, var_count, CV_64FC1 )); CV_CALL(avg[cls] = cvCreateMat( 1, var_count, CV_64FC1 )); CV_CALL(inv_eigen_values[cls] = cvCreateMat( 1, var_count, CV_64FC1 )); CV_CALL(cov_rotate_mats[cls] = cvCreateMat( var_count, var_count, CV_64FC1 )); CV_CALL(cvZero( count[cls] )); CV_CALL(cvZero( sum[cls] )); CV_CALL(cvZero( productsum[cls] )); CV_CALL(cvZero( avg[cls] )); CV_CALL(cvZero( inv_eigen_values[cls] )); CV_CALL(cvZero( cov_rotate_mats[cls] )); } } else { // check that the new training data has the same dimensionality etc. .... } responses_data = responses->data.i; CV_CALL( cov = cvCreateMat( _var_count, _var_count, CV_64FC1 )); /* process train data (count, sum , productsum) */ for( s = 0; s < nsamples; s++ ) { cls = responses_data[s]; int* count_data = count[cls]->data.i; double* sum_data = sum[cls]->data.db; //求和 double* prod_data = productsum[cls]->data.db; //乘积求和 const float* train_vec = train_data[s]; //取样本的特征向量 for( c1 = 0; c1 < _var_count; c1++, prod_data += _var_count ) { double val1 = train_vec[c1]; //取样本向量的每一维 sum_data[c1] += val1; //取每一维特征 count_data[c1]++; for( c2 = c1; c2 < _var_count; c2++ ) prod_data[c2] += train_vec[c2]*val1; //协方差矩阵的乘积项sum(XiXj) } } /* calculate avg, covariance matrix, c */ //cov(Xi,Xj)=sum(XiXj)-sum(Xi)E(Xj) for( cls = 0; cls < nclasses; cls++ ){ double det = 1; int i, j; CvMat* w = inv_eigen_values[cls]; int* count_data = count[cls]->data.i; double* avg_data = avg[cls]->data.db; double* sum1 = sum[cls]->data.db; cvCompleteSymm( productsum[cls], 0 ); for( j = 0; j < _var_count; j++ ){ int n = count_data[j]; avg_data[j] = n ? sum1[j] / n : 0.; } count_data = count[cls]->data.i; avg_data = avg[cls]->data.db; sum1 = sum[cls]->data.db; //计算当前类别cls的变量协方差矩阵,矩阵大小为_var_count * _var_count,注意协方差矩阵对称。 for( i = 0; i < _var_count; i++ ){ double* avg2_data = avg[cls]->data.db; double* sum2 = sum[cls]->data.db; double* prod_data = productsum[cls]->data.db + i*_var_count; double* cov_data = cov->data.db + i*_var_count; double s1val = sum1[j]; double avg1 = avg_data[i]; int count = count_data[i]; for( j = 0; j <= i; j++ ){ double avg2 = avg2_data[j]; double cov_val = prod_data[j] - avg1 * sum2[j] - avg2 * s1val + avg1 * avg2 * count; cov_val = (count > 1) ? cov_val / (count - 1) : cov_val; cov_data[j] = cov_val; } } CV_CALL( cvCompleteSymm( cov, 1 )); CV_CALL( cvSVD( cov, w, cov_rotate_mats[cls], 0, CV_SVD_U_T )); CV_CALL( cvMaxS( w, min_variation, w )); for( j = 0; j < _var_count; j++ ) det *= w->data.db[j]; CV_CALL( cvDiv( NULL, w, w )); c->data.db[cls] = log( det ); } result = true; __END__; if( !result || cvGetErrStatus() < 0 ) clear(); cvReleaseMat( &cov ); cvReleaseMat( &__cls_labels ); cvReleaseMat( &__var_idx ); cvFree( &train_data ); return result; } |
CvNormalBayesClassifier::predict(Predicts the response for sample(s))
The method predict
estimates the most probable classes for the input vectors. The input vectors (one or more) are stored as rows of the matrixsamples
. In case of multiple input vectors, there should be output vector results
. The predicted class for a single input vector is returned by the method.
先对输入的训练样本计算得到每一类的特征均值、协方差矩阵、特征值,然后分类的时候就将输入样本放入predict函数,函数内部先使用训练获得的以上参数计算样本属于每一类的后验概率,取后验概率最大的就是那一类。
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float CvNormalBayesClassifier::predict( const CvMat* samples, CvMat* results ) const{ float value = 0; void* buffer = 0; int allocated_buffer = 0; CV_FUNCNAME( "CvNormalBayesClassifier::predict" ); __BEGIN__; int i, j, k, cls = -1, _var_count, nclasses; double opt = FLT_MAX; CvMat diff; int rtype = 0, rstep = 0, size; const int* vidx = 0; nclasses = cls_labels->cols; _var_count = avg[0]->cols; if( !CV_IS_MAT(samples) || CV_MAT_TYPE(samples->type) != CV_32FC1 || samples->cols != var_all ) CV_ERROR( CV_StsBadArg, "The input samples must be 32f matrix with the number of columns = var_all" ); if( samples->rows > 1 && !results ) CV_ERROR( CV_StsNullPtr, "When the number of input samples is >1, the output vector of results must be passed" ); if( results ){ if( !CV_IS_MAT(results) || CV_MAT_TYPE(results->type) != CV_32FC1 && CV_MAT_TYPE(results->type) != CV_32SC1 || results->cols != 1 && results->rows != 1 || results->cols + results->rows - 1 != samples->rows ) CV_ERROR( CV_StsBadArg, "The output array must be integer or floating-point vector " "with the number of elements = number of rows in the input matrix" ); rtype = CV_MAT_TYPE(results->type); rstep = CV_IS_MAT_CONT(results->type) ? 1 : results->step/CV_ELEM_SIZE(rtype); } if( var_idx ) vidx = var_idx->data.i; // allocate memory and initializing headers for calculating size = sizeof(double) * (nclasses + var_count); if( size <= CV_MAX_LOCAL_SIZE ) buffer = cvStackAlloc( size ); else { CV_CALL( buffer = cvAlloc( size )); allocated_buffer = 1; } diff = cvMat( 1, var_count, CV_64FC1, buffer ); for( k = 0; k < samples->rows; k++ )//对于每个输入测试样本 { int ival; for( i = 0; i < nclasses; i++ )//对于每一类别,计算其似然概率 { double cur = c->data.db[i]; CvMat* u = cov_rotate_mats[i]; CvMat* w = inv_eigen_values[i]; const double* avg_data = avg[i]->data.db; const float* x = (const float*)(samples->data.ptr + samples->step*k); // cov = u w u' --> cov^(-1) = u w^(-1) u' for( j = 0; j < _var_count; j++ )//计算特征相对于均值的偏移 diff.data.db[j] = avg_data[j] - x[vidx ? vidx[j] : j]; CV_CALL(cvGEMM( &diff, u, 1, 0, 0, &diff, CV_GEMM_B_T )); for( j = 0; j < _var_count; j++ )//计算特征的联合概率 { double d = diff.data.db[j]; cur += d*d*w->data.db[j]; } if( cur < opt )//找到分类概率最大的 { cls = i; opt = cur; } /* probability = exp( -0.5 * cur ) */ } ival = cls_labels->data.i[cls]; if( results ){ if( rtype == CV_32SC1 ) results->data.i[k*rstep] = ival; else results->data.fl[k*rstep] = (float)ival; } if( k == 0 ) value = (float)ival; /*if( _probs ){ CV_CALL( cvConvertScale( &expo, &expo, -0.5 )); CV_CALL( cvExp( &expo, &expo )); if( _probs->cols == 1 ) CV_CALL( cvReshape( &expo, &expo, 1, nclasses )); CV_CALL( cvConvertScale( &expo, _probs, 1./cvSum( &expo ).val[0] )); }*/ } __END__; if( allocated_buffer ) cvFree( &buffer ); return value; } |
讨论:predict函数中没有计算的先验概率。只有同时考虑类间距和类内距来计算相似度的时候才要用到先验概率,如果不考虑类间距,就只需要计算p(x|w)。在"Bayesian face recognition"它是用高维高斯分布计算的。用主成分分析优化计算的。
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void CvNormalBayesClassifier::write( CvFileStorage* fs, const char* name ){ CV_FUNCNAME( "CvNormalBayesClassifier::write" ); __BEGIN__; int nclasses, i; nclasses = cls_labels->cols; cvStartWriteStruct( fs, name, CV_NODE_MAP, CV_TYPE_NAME_ML_NBAYES ); CV_CALL( cvWriteInt( fs, "var_count", var_count )); CV_CALL( cvWriteInt( fs, "var_all", var_all )); if( var_idx ) CV_CALL( cvWrite( fs, "var_idx", var_idx )); CV_CALL( cvWrite( fs, "cls_labels", cls_labels )); CV_CALL( cvStartWriteStruct( fs, "count", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, count[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvStartWriteStruct( fs, "sum", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, sum[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvStartWriteStruct( fs, "productsum", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, productsum[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvStartWriteStruct( fs, "avg", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, avg[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvStartWriteStruct( fs, "inv_eigen_values", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, inv_eigen_values[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvStartWriteStruct( fs, "cov_rotate_mats", CV_NODE_SEQ )); for( i = 0; i < nclasses; i++ ) CV_CALL( cvWrite( fs, NULL, cov_rotate_mats[i] )); CV_CALL( cvEndWriteStruct( fs )); CV_CALL( cvWrite( fs, "c", c )); cvEndWriteStruct( fs ); __END__; } |
参考资料:
1)opencv2.3.1 源码
2)http://blog.csdn.net/godenlove007/article/details/8913007
附录:
训练模型形式
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%YAML:1.0 my_nb: !!opencv-ml-bayesian var_count: 12 var_all: 12 cls_labels: !!opencv-matrix rows: 1 cols: 2 dt: i data: [ -1, 1 ] count: - !!opencv-matrix rows: 1 cols: 12 dt: i data: [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ] //4个负样本 - !!opencv-matrix rows: 1 cols: 12 dt: i data: [ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 ] //6个正样本 sum: - !!opencv-matrix //负类每一维特征的求和 rows: 1 cols: 12 dt: d data: [ 2.4166660010814667e+000, 0., 2., -1.9811329841613770e+000, -4.8858398199081421e-001, -4., 0., -3.0534288659691811e-001, 0., -3.2258069813251495e+000, -2., -2.6666659712791443e+000 ] - !!opencv-matrix //正类每一维的求和 rows: 1 cols: 12 dt: d data: [ 1.9583340436220169e+000, 4., 4., -1.8490562178194523e+000, -1.3333339989185333e+000, -4., 4., 5.9542029350996017e-001, -2., -2.8709670007228851e+000, -1., 6.6666701436042786e-001 ] productsum: - !!opencv-matrix rows: 12 cols: 12 dt: d data: [ 1.5659715326298178e+000, -5.0000002980232239e-001, 8.6111075886432786e-001, -1.2169812955662263e+000, -2.7549464151248770e-001, -2.4166660010814667e+000, 5.0000002980232239e-001, -1.9147534940509647e-001, 2.4999997019767761e-001, -1.9650535933592703e+000, -1.3750000000000000e+000, -1.5277768803968579e+000, -5.0000002980232239e-001, 4., 2., 2.4528300762176514e-001, -1.7945199608802795e+000, 0., -4., -5.4961890354752541e-001, 0., -3.8709697127342224e-001, 0., 0., 8.6111075886432786e-001, 2., 2.2222217586307824e+000, -8.9937163092791117e-001, -6.9254176960508396e-001, -2., -2., -2.2900776281655455e-001, -6.6666597127914429e-001, -1.6559144735977478e+000, -6.6666701436042786e-001, -1.5555550919637531e+000, -1.2169812955662263e+000, 2.4528300762176514e-001, -8.9937163092791117e-001, 1.0121048257718783e+000, 9.8043830817573507e-002, 1.9811329841613770e+000, -2.4528300762176514e-001, 4.9113928091631287e-002, 2.4528300762176514e-001, 1.5477793660022474e+000, 1.0188679695129395e+000, 1.4025160235427361e+000, -2.7549464151248770e-001, -1.7945199608802795e+000, -6.9254176960508396e-001, 9.8043830817573507e-002, 1.8491059555100868e+000, 4.8858398199081421e-001, 1.7945199608802795e+000, 5.7997861317776689e-001, -9.5433801412582397e-001, 8.5918376063058233e-001, 1.1141549944877625e+000, 7.6097324377801812e-003, -2.4166660010814667e+000, 0., -2., 1.9811329841613770e+000, 4.8858398199081421e-001, 4., 0., 3.0534288659691811e-001, 0., 3.2258069813251495e+000, 2., 2.6666659712791443e+000, 5.0000002980232239e-001, -4., -2., -2.4528300762176514e-001, 1.7945199608802795e+000, 0., 4., 5.4961890354752541e-001, 0., 3.8709697127342224e-001, 0., 0., -1.9147534940509647e-001, -5.4961890354752541e-001, -2.2900776281655455e-001, 4.9113928091631287e-002, 5.7997861317776689e-001, 3.0534288659691811e-001, 5.4961890354752541e-001, 4.1885684787540123e-001, -1.1297711096704006e+000, 4.5112006073894362e-001, 1.8320590630173683e-001, -1.7302869498227968e-001, 2.4999997019767761e-001, 0., -6.6666597127914429e-001, 2.4528300762176514e-001, -9.5433801412582397e-001, 0., 0., -1.1297711096704006e+000, 4., -5.1612898707389832e-001, 0., 1.3333340287208557e+000, -1.9650535933592703e+000, -3.8709697127342224e-001, -1.6559144735977478e+000, 1.5477793660022474e+000, 8.5918376063058233e-001, 3.2258069813251495e+000, 3.8709697127342224e-001, 4.5112006073894362e-001, -5.1612898707389832e-001, 2.7429769856005288e+000, 1.8064519762992859e+000, 1.9784943413349048e+000, -1.3750000000000000e+000, 0., -6.6666701436042786e-001, 1.0188679695129395e+000, 1.1141549944877625e+000, 2., 0., 1.8320590630173683e-001, 0., 1.8064519762992859e+000, 2., 1.3333329856395721e+000, -1.5277768803968579e+000, 0., -1.5555550919637531e+000, 1.4025160235427361e+000, 7.6097324377801812e-003, 2.6666659712791443e+000, 0., -1.7302869498227968e-001, 1.3333340287208557e+000, 1.9784943413349048e+000, 1.3333329856395721e+000, 2.2222217586307824e+000 ] - !!opencv-matrix rows: 12 cols: 12 dt: d data: [ 8.6631959759572141e-001, 1.1250000149011612e+000, 1.6527780588303504e+000, -5.2908811726975735e-001, -2.6141578843615010e-001, -1.7083340436220169e+000, 1.6250000447034836e+000, 6.0439903392527361e-003, -1.2083340436220169e+000, -6.2231163504302511e-001, -1.6666699945926666e-001, 9.3055539743755755e-001, 1.1250000149011612e+000, 6., 2., -1.9622638188302517e+000, -1.8995439708232880e+000, -2., 2., 6.1068288981914520e-002, 0., -3.4516129791736603e+000, -1., -1.3333329856395721e+000, 1.6527780588303504e+000, 2., 4.2222217586307824e+000, -1.0566036039317090e+000, -5.5098933181082455e-001, -3.3333340287208557e+000, 4.6666659712791443e+000, 4.4783754861005121e-001, -1.3333340287208557e+000, -1.1290310262351380e+000, 3.3333298563957214e-001, 2.2222221063241809e+000, -5.2908811726975735e-001, -1.9622638188302517e+000, -1.0566036039317090e+000, 9.0210014253098636e-001, 7.1577493502039558e-001, 1.2075462080538273e+000, -9.8113224282860756e-001, -3.3126579362578457e-002, -1.8867984041571617e-001, 1.2483257817913533e+000, 4.3396198749542236e-001, 4.6540815221512188e-001, -2.6141578843615010e-001, -1.8995439708232880e+000, -5.5098933181082455e-001, 7.1577493502039558e-001, 6.9410593390375031e-001, 5.2054801583290100e-001, -5.6621000170707703e-001, -1.0282673240917339e-001, -4.4748798012733459e-001, 1.2222719254841339e+000, 3.8356199860572815e-001, 7.7929975734273960e-001, -1.7083340436220169e+000, -2., -3.3333340287208557e+000, 1.2075462080538273e+000, 5.2054801583290100e-001, 6., -2., -4.2748128622770309e-001, 4., 1.2580630481243134e+000, 1., -1.3333329856395721e+000, 1.6250000447034836e+000, 2., 4.6666659712791443e+000, -9.8113224282860756e-001, -5.6621000170707703e-001, -2., 6., 4.5801568776369095e-001, 0., -1.0645149648189545e+000, 1., 2.6666670143604279e+000, 6.0439903392527361e-003, 6.1068288981914520e-002, 4.4783754861005121e-001, -3.3126579362578457e-002, -1.0282673240917339e-001, -4.2748128622770309e-001, 4.5801568776369095e-001, 5.2805738579891548e-001, -2.5954227894544601e-001, -3.2233416549041038e-001, -6.8702302873134613e-002, -1.0686976982041685e-001, -1.2083340436220169e+000, 0., -1.3333340287208557e+000, -1.8867984041571617e-001, -4.4748798012733459e-001, 4., 0., -2.5954227894544601e-001, 6., 3.2257050275802612e-002, 1., -1.9999989569187164e+000, -6.2231163504302511e-001, -3.4516129791736603e+000, -1.1290310262351380e+000, 1.2483257817913533e+000, 1.2222719254841339e+000, 1.2580630481243134e+000, -1.0645149648189545e+000, -3.2233416549041038e-001, 3.2257050275802612e-002, 2.3527579885002057e+000, 9.0322601795196533e-001, 1.2365600543636166e+000, -1.6666699945926666e-001, -1., 3.3333298563957214e-001, 4.3396198749542236e-001, 3.8356199860572815e-001, 1., 1., -6.8702302873134613e-002, 1., 9.0322601795196533e-001, 1., 1., 9.3055539743755755e-001, -1.3333329856395721e+000, 2.2222221063241809e+000, 4.6540815221512188e-001, 7.7929975734273960e-001, -1.3333329856395721e+000, 2.6666670143604279e+000, -1.0686976982041685e-001, -1.9999989569187164e+000, 1.2365600543636166e+000, 1., 3.3333326379461736e+000 ] avg: - !!opencv-matrix //负类每一维的平均值 rows: 1 cols: 12 dt: d data: [ 6.0416650027036667e-001, 0., 5.0000000000000000e-001, -4.9528324604034424e-001, -1.2214599549770355e-001, -1., 0., -7.6335721649229527e-002, 0., -8.0645174533128738e-001, -5.0000000000000000e-001, -6.6666649281978607e-001 ] - !!opencv-matrix //正类每一维的平均值 rows: 1 cols: 12 dt: d data: [ 3.2638900727033615e-001, 6.6666666666666663e-001, 6.6666666666666663e-001, -3.0817603630324203e-001, -2.2222233315308890e-001, -6.6666666666666663e-001, 6.6666666666666663e-001, 9.9236715584993362e-002, -3.3333333333333331e-001, -4.7849450012048084e-001, -1.6666666666666666e-001, 1.1111116906007130e-001 ] inv_eigen_values: - !!opencv-matrix rows: 1 cols: 12 dt: d data: [ 2.9876414443477345e-001, 5.6785719912200472e-001, 1.6615312007953884e+000, 8388608., 8388608., 8388608., 8388608., 8388608., 8388608., 8388608., 8388608., 8388608. ] - !!opencv-matrix rows: 1 cols: 12 dt: d data: [ 4.7581101410665855e-001, 6.4277674465846990e-001, 1.8305143244848343e+000, 2.9750070399310831e+000, 7.2736135168211442e+000, 8388608., 8388608., 8388608., 8388608., 8388608., 8388608., 8388608. ] cov_rotate_mats: - !!opencv-matrix rows: 12 cols: 12 dt: d data: [ -7.2822795234056423e-002, 6.2863810953042876e-001, 3.0107086657362325e-001, 4.0565036943532626e-002, -3.0842583309004801e-001, 0., -6.2863810953042876e-001, -9.8711921458055837e-002, 4.1622425044189004e-002, -6.9871141717708030e-002, -1.8933393509533603e-002, 1.3874148917325085e-002, 7.3896560588951818e-002, -6.5483667090597622e-002, -1.9979267464743827e-001, 4.6336215406475985e-002, -2.3866173960603801e-001, 0., 6.5483667090597622e-002, -2.3476444086263926e-001, 8.5509235608547995e-001, -1.1824385343582010e-001, -7.3606868007040901e-002, 2.8503093401696544e-001, -1.1481772619646893e-001, 7.1148689279798311e-002, 2.3669136431758517e-001, 4.0875065071777163e-002, 5.4347978651861062e-001, 0., -7.1148689279798311e-002, -6.0159773689547516e-002, 2.5753340229060168e-001, 1.0158493155094871e-001, 7.3211838952321173e-001, 8.5844512201579196e-002, 2.7222697680699531e-001, 2.3439198726380414e-001, -2.6274577931606413e-001, -1.7773453055739136e-001, 5.1790572959362724e-001, 0., -2.3439198726380414e-001, 5.4372219454034798e-001, 1.8702350838782372e-001, -1.5059943007954968e-001, -2.9997776878840593e-001, 6.2318098749766231e-002, -1.0073664459788399e-001, 1.1155100313710881e-002, -2.8660695735789388e-001, 1.6006629903753910e-002, -1.3101387269764123e-002, 0., -1.1155100313710881e-002, -1.1358472566907701e-001, -1.5853298919734374e-001, -8.8799356423973086e-001, 2.6502753753328784e-001, -1.0112114023595761e-001, -6.1514995016844709e-001, -1.4621795959162093e-001, 5.0803673293704366e-001, -1.2721073070070282e-001, 1.4531540788252417e-002, 0., 1.4621795959162093e-001, 3.5147292455379053e-001, 2.2910813990840159e-001, -2.4942368104540683e-001, -2.4336725677111484e-001, -8.2900825664345229e-002, 4.3127887212578270e-001, -9.4096296127127457e-002, 2.1714577971373331e-001, 1.5217538623209076e-001, -4.4497785724359473e-001, 0., 9.4096296127127457e-002, 6.1056779084558910e-001, 4.8446931324894187e-002, -8.7446240526810187e-002, 3.8054281941470358e-001, 1.9379436150877869e-002, 2.2565216666674645e-001, -4.6117009326889086e-002, 2.1639741177242056e-001, -8.8236995576279009e-001, -8.2705001846677215e-002, 0., 4.6117009326889086e-002, -1.5570412268162212e-001, -8.4835800070551623e-002, -8.1126937638573274e-002, 8.2847106586930008e-002, 2.6018596564937407e-001, -5.2510733455850511e-001, 7.9475219075679504e-002, -5.1587121566555783e-001, -1.9150539365590283e-001, -2.5004959264894100e-001, 0., -7.9475219075679504e-002, 3.1892656094220034e-001, -9.3049481373702309e-002, 2.4043304561743387e-001, 2.5109390078662269e-001, 3.3923279155720204e-001, -2.7020182259065550e-002, 4.1508396732401108e-002, -2.0984032816897225e-001, -3.2878551307683390e-001, -1.2870289372494284e-001, 0., -4.1508396732401108e-002, 2.6512860089234043e-002, 2.6449521312133978e-001, 1.5923413831849509e-001, 1.5507324958760463e-001, -8.4087028185431667e-001, 1.1507450386868655e-017, -5.7735026918962562e-001, 5.0071420166376901e-019, -5.9418957692149693e-018, 1.7905853646285833e-017, -5.7735026918962562e-001, -5.7735026918962573e-001, 2.4778451259378389e-017, 1.3082185095152320e-017, -1.2285937208894122e-017, -1.7344818049930933e-017, 1.7739590268386996e-018, 5.7115447004617324e-018, 4.0824829046386296e-001, -4.2035923022410986e-018, -2.1571214999777572e-018, 7.7987638586082717e-018, -8.1649658092772615e-001, 4.0824829046386296e-001, 9.6813638733537024e-018, -3.3724976894451128e-018, -2.6623091301948213e-019, -9.2979652540915047e-019, -1.1438034213708074e-018 ] - 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