OpenCV机器学习（1）：贝叶斯分类器实现代码分析

OpenCV的机器学习类定义在ml.hpp文件中，基础类是CvStatModel，其他各种分类器从这里继承而来。

今天研究CvNormalBayesClassifier分类器。

1.类定义

在ml.hpp中有以下类定义：

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

此类使用方法如下：（引用别人的代码，忘记出处了，非常抱歉这个。。。）

//openCV中贝叶斯分类器的API函数用法举例
//运行环境：win7 + VS2005 + openCV2.4.5

#include "global_include.h"

using namespace std;
using namespace cv;

//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("normalBayes.txt");
}
else
{
cout<<"train error..."<<endl;
system("pause");
exit(-1);
}

CvNormalBayesClassifier testNbc;
testNbc.load("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;

system("pause");
return 0;
}

3.步骤

两步走：

1.调用train函数训练分类器；

2.调用predict函数，判定测试样本的类别。

以上示例代码还延时了怎样使用save和load函数，使得训练好的分类器可以保存在文本中。

4.初始化

接下来，看CvNormalBayesClassifier类的无参数初始化：

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";
}

还有另一种带参数的初始化形式：

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 );
}

可见，带参数形式糅合了类的初始化和train函数。

另外，以Mat参数形式的对应函数版本，功能是一致的，只不过为了体现2.0以后版本的C++特性罢了。如下：

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.训练

下面开始分析train函数，分析CvMat格式参数的train函数，即：

bool train( const CvMat* trainData, const CvMat* responses,const CvMat* varIdx = 0, const CvMat* sampleIdx=0, bool update=false );

在进入该函数之前，还要先回头看看CvNormalBayesClassifier类有哪些数据成员：

protected:
int     var_count, var_all;	//每个样本的特征维数、即变量数目，或者说trainData的列数目(在varIdx=0时)
CvMat*  var_idx;		//特征子集的索引，可能特征数目为100，但是只用其中一部分训练
CvMat*  cls_labels;		//类别数目
CvMat** count;		//count[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数目
CvMat** sum;		//sum[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累加和
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;

这些数据成员，怎样使用呢？在train函数中见分晓：

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;

//1.整理训练数据
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 )	//如果是初始训练数据
{
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 );			//count[cls]存储第cls类每个属性变量个数

sum             = count      + nclasses;//sum[cls]存储第cls类每个属性取值的累加和
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++ )	//对所有类别
{
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	//如果是更新训练数据
{
// check that the new training data has the same dimensionality etc.
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 ));

//2.处理训练数据，计算每一类的
// 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;
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;
}
}

//计算每一类的每个属性平均值、协方差矩阵
// calculate avg, covariance matrix, c
for( cls = 0; cls < nclasses; cls++ )	//对每一类
{
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++ )	//计算当前类别cls的每个变量属性值的平均值
{
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++ )//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。
{
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;
}

训练部分就此完成。

6.预测

下面看用于预测的predict函数的实现代码：

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;
}

可以发现，预测部分核心代码是：

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，可能会调用tbb模块。predict_body则是一个结构体，内部的()符号被重载，实现预测功能。其完整定义如下：

//predict函数调用predict_body结构体的(）符号重载函数，实现基于贝叶斯的分类
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);
}
// allocate memory and initializing headers for calculating
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 )//对于每个输入测试样本
{
int ival;
double opt = FLT_MAX;

for(int 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(int 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];

cvGEMM( &diff, u, 1, 0, 0, &diff, CV_GEMM_B_T );
for(int 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 )

}//for(int i = 0; i < nclasses; i++ )

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;

}//for(int k = range.begin()...

}//void operator()...
};

好啦，预测部分至此完成。

但有一个小小疑问：好像在predict部分实现代码中没有看到先验概率参与到计算当中，而贝叶斯估计是应该p(w|x)=p(w)*p(x|w)/...的呀，但是这里只看到了计算p(x|w)的部分。没有p(w)的身影，不知道为何，盼高人指点。

贝叶斯代码分析完成。