OpenCV（1）ML库->Normal Bayes分类器

       贝叶斯分类算法是统计学的一种分类方法，它是一类利用概率统计知识进行分类的算法。在许多场合，朴素贝叶斯(Naïve Bayes，NB)分类算法可以与决策树和神经网络分类算法相媲美，该算法能运用到大型数据库中，而且方法简单、分类准确率高、速度快。

       由于贝叶斯定理假设一个属性值对给定类的影响独立于其它属性的值，而此假设在实际情况中经常是不成立的，因此其分类准确率可能会下降。为此，就衍生出许多降低独立性假设的贝叶斯分类算法，如TAN(tree augmented Bayes network)算法。

       

                                                                                                     朴素贝叶斯算法

设每个数据样本用一个n维特征向量来描述n个属性的值，即：X={x1，x2，…，xn}，假定有m个类，分别用C1, C2,…，Cm表示。给定一个未知的数据样本X（即没有类标号），若朴素贝叶斯分类法将未知的样本X分配给类Ci，则一定是

P(Ci|X)>P(Cj|X) 1≤j≤m，j≠i

根据贝叶斯定理

由于P(X)对于所有类为常数，最大化后验概率P(Ci|X)可转化为最大化先验概率P(X|Ci)P(Ci)。如果训练数据集有许多属性和元组，计算P(X|Ci)的开销可能非常大，为此，通常假设各属性的取值互相独立，这样

先验概率P(x1|Ci)，P(x2|Ci)，…，P(xn|Ci)可以从训练数据集求得。

根据此方法，对一个未知类别的样本X，可以先分别计算出X属于每一个类别Ci的概率P(X|Ci)P(Ci)，然后选择其中概率最大的类别作为其类别。

朴素贝叶斯算法成立的前提是各属性之间互相独立。当数据集满足这种独立性假设时,分类的准确度较高，否则可能较低。另外，该算法没有分类规则输出。

贝叶斯分类器库源码：

/****************************************************************************************\
*                                 Normal Bayes Classifier                                *
\****************************************************************************************/

/* The structure, representing the grid range of statmodel parameters.
   It is used for optimizing statmodel accuracy by varying model parameters,
   the accuracy estimate being computed by cross-validation.
   The grid is logarithmic, so <step> must be greater then 1. */

class CvMLData;

struct CV_EXPORTS CvParamGrid
{
    // SVM params type
    enum { SVM_C=0, SVM_GAMMA=1, SVM_P=2, SVM_NU=3, SVM_COEF=4, SVM_DEGREE=5 };

    CvParamGrid()
    {
        min_val = max_val = step = 0;
    }

    CvParamGrid( double _min_val, double _max_val, double log_step )
    {
        min_val = _min_val;
        max_val = _max_val;
        step = log_step;
    }
    //CvParamGrid( int param_id );
    bool check() const;

    double min_val;
    double max_val;
    double step;
};

class CV_EXPORTS CvNormalBayesClassifier : public CvStatModel
{
public:
    CvNormalBayesClassifier();
    virtual ~CvNormalBayesClassifier();

    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;
    virtual void clear();

#ifndef SWIG
    CvNormalBayesClassifier( const cv::Mat& _train_data, const cv::Mat& _responses,
                            const cv::Mat& _var_idx=cv::Mat(), const cv::Mat& _sample_idx=cv::Mat() );
    virtual bool train( const cv::Mat& _train_data, const cv::Mat& _responses,
                       const cv::Mat& _var_idx = cv::Mat(), const cv::Mat& _sample_idx=cv::Mat(),
                       bool update=false );
    virtual float predict( const cv::Mat& _samples, cv::Mat* results=0 ) const;
#endif
    
    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;
};

测试源码：

//源码引用自：http://blog.csdn.net/carson2005/article/details/6854024#
#include "stdafx.h"
#include <ml.h>   
#include <iostream>
#include <highgui.h>
#include <cv.h>
#include <cxcore.h> 
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("c:/normalBayes.txt");
	}
	else
	{
		cout<<"train error..."<<endl;
		system("pause");
		exit(-1);
	}
	

	CvNormalBayesClassifier testNbc;
	testNbc.load("c:/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;
}

参考： http://blog.chinaunix.net/uid-7451264-id-2054393.html

          http://blog.csdn.net/carson2005/article/details/6854024

          http://blog.csdn.net/godenlove007/article/details/8913007