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Normal Bayes 分类器过程详解
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OpenCV的機器學習類定義在ml.hpp文件中，基礎類是CvStatModel，其他各種分類器從這里繼承而來。
今天研究CvNormalBayesClassifier分類器。
1.類定義
在ml.hpp中有以下類定義：
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class?CV_EXPORTS_W?CvNormalBayesClassifier?:?public?CvStatModel?? {?? public:?? ????CV_WRAP?CvNormalBayesClassifier();?? ????virtual?~CvNormalBayesClassifier();?? ?? ????CvNormalBayesClassifier(?const?CvMat*?trainData,?const?CvMat*?responses,?? ????????const?CvMat*?varIdx=0,?const?CvMat*?sampleIdx=0?);?? ?? ????virtual?bool?train(?const?CvMat*?trainData,?const?CvMat*?responses,?? ????????const?CvMat*?varIdx?=?0,?const?CvMat*?sampleIdx=0,?bool?update=false?);?? ?? ????virtual?float?predict(?const?CvMat*?samples,?CV_OUT?CvMat*?results=0?)?const;?? ????CV_WRAP?virtual?void?clear();?? ?? ????CV_WRAP?CvNormalBayesClassifier(?const?cv::Mat&?trainData,?const?cv::Mat&?responses,?? ????????????????????????????const?cv::Mat&?varIdx=cv::Mat(),?const?cv::Mat&?sampleIdx=cv::Mat()?);?? ????CV_WRAP?virtual?bool?train(?const?cv::Mat&?trainData,?const?cv::Mat&?responses,?? ???????????????????????const?cv::Mat&?varIdx?=?cv::Mat(),?const?cv::Mat&?sampleIdx=cv::Mat(),?? ???????????????????????bool?update=false?);?? ????CV_WRAP?virtual?float?predict(?const?cv::Mat&?samples,?CV_OUT?cv::Mat*?results=0?)?const;?? ?? ????virtual?void?write(?CvFileStorage*?storage,?const?char*?name?)?const;?? ????virtual?void?read(?CvFileStorage*?storage,?CvFileNode*?node?);?? ?? protected:?? ????int?????var_count,?var_all;?? ????CvMat*??var_idx;?? ????CvMat*??cls_labels;?? ????CvMat**?count;?? ????CvMat**?sum;?? ????CvMat**?productsum;?? ????CvMat**?avg;?? ????CvMat**?inv_eigen_values;?? ????CvMat**?cov_rotate_mats;?? ????CvMat*??c;?? };??
2.示例
此類使用方法如下：（引用別人的代碼，忘記出處了，非常抱歉這個。。。）
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?? ?? ?? #include?"global_include.h"?? ?? using?namespace?std;?? using?namespace?cv;?? ?? ?? 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?? };?? ?? ?? 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);?? ????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);?? ????for?(int?i=0;?i<10;?i++)?? ????{?? ????????trainResponse.at<float>(i,?0)?=?inputArr[i][0];?? ????}?? ?? ????CvNormalBayesClassifier?nbc;?? ????bool?trainFlag?=?nbc.train(trainData,?trainResponse);?? ????if?(trainFlag)?? ????{?? ????????cout<<"train?over..."<<endl;?? ????????nbc.save("normalBayes.txt");?? ????}?? ????else?? ????{?? ????????cout<<"train?error..."<<endl;?? ????????system("pause");?? ????????exit(-1);?? ????}?? ?? ?? ????CvNormalBayesClassifier?testNbc;?? ????testNbc.load("normalBayes.txt");?? ?? ????Mat?testSample(1,?12,?CV_32FC1);?? ????for?(int?i=0;?i<12;?i++)?? ????{?? ????????testSample.at<float>(0,?i)?=?testArr[i];?? ????}?? ?? ????float?flag?=?testNbc.predict(testSample);?? ????cout<<"flag?=?"<<flag<<endl;?? ?? ????system("pause");?? ????return?0;?? }??
3.步驟
兩步走：
1.調用train函數訓練分類器；
2.調用predict函數，判定測試樣本的類別。
以上示例代碼還延時了怎樣使用save和load函數，使得訓練好的分類器可以保存在文本中。
4.初始化
接下來，看CvNormalBayesClassifier類的無參數初始化：
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CvNormalBayesClassifier::CvNormalBayesClassifier()?? {?? ????var_count?=?var_all?=?0;?? ????var_idx?=?0;?? ????cls_labels?=?0;?? ????count?=?0;?? ????sum?=?0;?? ????productsum?=?0;?? ????avg?=?0;?? ????inv_eigen_values?=?0;?? ????cov_rotate_mats?=?0;?? ????c?=?0;?? ????default_model_name?=?"my_nb";?? }??
還有另一種帶參數的初始化形式：
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CvNormalBayesClassifier::CvNormalBayesClassifier(?? ????const?CvMat*?_train_data,?const?CvMat*?_responses,?? ????const?CvMat*?_var_idx,?const?CvMat*?_sample_idx?)?? {?? ????var_count?=?var_all?=?0;?? ????var_idx?=?0;?? ????cls_labels?=?0;?? ????count?=?0;?? ????sum?=?0;?? ????productsum?=?0;?? ????avg?=?0;?? ????inv_eigen_values?=?0;?? ????cov_rotate_mats?=?0;?? ????c?=?0;?? ????default_model_name?=?"my_nb";?? ?? ????train(?_train_data,?_responses,?_var_idx,?_sample_idx?);?? }??
可見，帶參數形式糅合了類的初始化和train函數。
另外，以Mat參數形式的對應函數版本，功能是一致的，只不過為了體現2.0以后版本的C++特性罷了。如下：
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CV_WRAP?CvNormalBayesClassifier(?const?cv::Mat&?trainData,?const?cv::Mat&?responses,?? ????????????????????????const?cv::Mat&?varIdx=cv::Mat(),?const?cv::Mat&?sampleIdx=cv::Mat()?);?? CV_WRAP?virtual?bool?train(?const?cv::Mat&?trainData,?const?cv::Mat&?responses,?? ???????????????????const?cv::Mat&?varIdx?=?cv::Mat(),?const?cv::Mat&?sampleIdx=cv::Mat(),?? ???????????????????bool?update=false?);?? CV_WRAP?virtual?float?predict(?const?cv::Mat&?samples,?CV_OUT?cv::Mat*?results=0?)?const;??
5.訓練
下面開始分析train函數，分析CvMat格式參數的train函數，即：
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bool?train(?const?CvMat*?trainData,?const?CvMat*?responses,const?CvMat*?varIdx?=?0,?const?CvMat*?sampleIdx=0,?bool?update=false?);??
在進入該函數之前，還要先回頭看看CvNormalBayesClassifier類有哪些數據成員：
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protected:?? ????int?????var_count,?var_all;??? ????CvMat*??var_idx;?????????? ????CvMat*??cls_labels;??????? ????CvMat**?count;???????? ????CvMat**?sum;?????????? ????CvMat**?productsum;??????? ????CvMat**?avg;?????????? ????CvMat**?inv_eigen_values;?? ????CvMat**?cov_rotate_mats;?????? ????CvMat*??c;??
這些數據成員，怎樣使用呢？在train函數中見分曉：
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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;?? ????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;?? ?? ?????? ????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;?? ????????avg?????????????=?productsum?+?nclasses;?? ????????inv_eigen_values=?avg????????+?nclasses;?? ????????cov_rotate_mats?=?inv_eigen_values?????????+?nclasses;?? ?? ????????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?????? ????{?? ?????????? ????????if(?_var_count?!=?var_count?||?_var_all?!=?var_all?||?!((!_var_idx?&&?!var_idx)?||?? ????????????(_var_idx?&&?var_idx?&&?cvNorm(_var_idx,var_idx,CV_C)?<?DBL_EPSILON))?)?? ????????????CV_ERROR(?CV_StsBadArg,?? ????????????"The?new?training?data?is?inconsistent?with?the?original?training?data"?);?? ?? ????????if(?cls_labels->cols?!=?__cls_labels->cols?||?? ????????????cvNorm(cls_labels,?__cls_labels,?CV_C)?>?DBL_EPSILON?)?? ????????????CV_ERROR(?CV_StsNotImplemented,?? ????????????"In?the?current?implementation?the?new?training?data?must?have?absolutely?"?? ????????????"the?same?set?of?class?labels?as?used?in?the?original?training?data"?);?? ?? ????????nclasses?=?cls_labels->cols;?? ????}?? ?? ????responses_data?=?responses->data.i;?? ????CV_CALL(?cov?=?cvCreateMat(?_var_count,?_var_count,?CV_64FC1?));?? ?? ?????? ?????? ????for(?s?=?0;?s?<?nsamples;?s++?)?? ????{?? ????????cls?=?responses_data[s];?? ????????int*?count_data?=?count[cls]->data.i;?? ????????double*?sum_data?=?sum[cls]->data.db;?? ????????double*?prod_data?=?productsum[cls]->data.db;?? ????????const?float*?train_vec?=?train_data[s];?? ?? ????????for(?c1?=?0;?c1?<?_var_count;?c1++,?prod_data?+=?_var_count?)?? ????????{?? ????????????double?val1?=?train_vec[c1];?? ????????????sum_data[c1]?+=?val1;?? ????????????count_data[c1]++;?? ????????????for(?c2?=?c1;?c2?<?_var_count;?c2++?)?? ????????????????prod_data[c2]?+=?train_vec[c2]*val1;?? ????????}?? ????}?? ?? ?????? ?????? ????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;?? ?? ????????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[i];?? ????????????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]?=?det?>?0???log(det)?:?-700;?? ????}?? ?? ????result?=?true;?? ?? ????__END__;?? ?? ????if(?!result?||?cvGetErrStatus()?<?0?)?? ????????clear();?? ?? ????cvReleaseMat(?&cov?);?? ????cvReleaseMat(?&__cls_labels?);?? ????cvReleaseMat(?&__var_idx?);?? ????cvFree(?&train_data?);?? ?? ????return?result;?? }??
訓練部分就此完成。
6.預測
下面看用于預測的predict函數的實現代碼：
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float?CvNormalBayesClassifier::predict(?const?CvMat*?samples,?CvMat*?results?)?const?? {?? ????float?value?=?0;?? ?? ????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"?);?? ????}?? ?? ????const?int*?vidx?=?var_idx???var_idx->data.i?:?0;?? ?? ????cv::parallel_for(cv::BlockedRange(0,?samples->rows),?predict_body(c,?cov_rotate_mats,?inv_eigen_values,?avg,?samples,?? ??????????????????????????????????????????????????????????????????????vidx,?cls_labels,?results,?&value,?var_count?? ????));?? ?? ????return?value;?? }??
可以發現，預測部分核心代碼是：
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cv::parallel_for(cv::BlockedRange(0,?samples->rows),?predict_body(c,?cov_rotate_mats,?inv_eigen_values,?avg,?samples,?? ??????????????????????????????????????????????????????????????????????vidx,?cls_labels,?results,?&value,?var_count));??
parallel_for是用于并行支持的，可能會調用tbb模塊。predict_body則是一個結構體，內部的()符號被重載，實現預測功能。其完整定義如下：
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?? struct?predict_body??? {?? ????predict_body(CvMat*?_c,?CvMat**?_cov_rotate_mats,?CvMat**?_inv_eigen_values,?CvMat**?_avg,?? ????????????????const?CvMat*?_samples,?const?int*?_vidx,?CvMat*?_cls_labels,?? ????????????????CvMat*?_results,?float*?_value,?int?_var_count1)?? ????{?? ????????c?=?_c;?? ????????cov_rotate_mats?=?_cov_rotate_mats;?? ????????inv_eigen_values?=?_inv_eigen_values;?? ????????avg?=?_avg;?? ????????samples?=?_samples;?? ????????vidx?=?_vidx;?? ????????cls_labels?=?_cls_labels;?? ????????results?=?_results;?? ????????value?=?_value;?? ????????var_count1?=?_var_count1;?? ????}?? ?? ????CvMat*?c;?? ????CvMat**?cov_rotate_mats;?? ????CvMat**?inv_eigen_values;?? ????CvMat**?avg;?? ????const?CvMat*?samples;?? ????const?int*?vidx;?? ????CvMat*?cls_labels;?? ?? ????CvMat*?results;?? ????float*?value;?? ????int?var_count1;?? ?? ????void?operator()(?const?cv::BlockedRange&?range?)?const?? ????{?? ?? ????????int?cls?=?-1;?? ????????int?rtype?=?0,?rstep?=?0;?? ????????int?nclasses?=?cls_labels->cols;?? ????????int?_var_count?=?avg[0]->cols;?? ?? ????????if?(results)?? ????????{?? ????????????rtype?=?CV_MAT_TYPE(results->type);?? ????????????rstep?=?CV_IS_MAT_CONT(results->type)???1?:?results->step/CV_ELEM_SIZE(rtype);?? ????????}?? ?????????? ????????cv::AutoBuffer<double>?buffer(nclasses?+?var_count1);?? ????????CvMat?diff?=?cvMat(?1,?var_count1,?CV_64FC1,?&buffer[0]?);?? ?? ????????for(int?k?=?range.begin();?k?<?range.end();?k?+=?1?)?? ????????{?? ????????????int?ival;?? ????????????double?opt?=?FLT_MAX;?? ?? ????????????for(int?i?=?0;?i?<?nclasses;?i++?)????? ????????????{?? ?? ????????????????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);?? ?? ?????????????????? ????????????????for(int?j?=?0;?j?<?_var_count;?j++?)??? ????????????????????diff.data.db[j]?=?avg_data[j]?-?x[vidx???vidx[j]?:?j];?? ?? ????????????????cvGEMM(?&diff,?u,?1,?0,?0,?&diff,?CV_GEMM_B_T?);?? ????????????????for(int?j?=?0;?j?<?_var_count;?j++?)?? ????????????????{?? ????????????????????double?d?=?diff.data.db[j];?? ????????????????????cur?+=?d*d*w->data.db[j];?? ????????????????}?? ?? ????????????????if(?cur?<?opt?)???? ????????????????{?? ????????????????????cls?=?i;?? ????????????????????opt?=?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;?? ?? ????????}?? ?? ????}?? }; ?
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