OpenCV（3）ML库->Expectation - Maximization 算法

来源：互联网发布：苹果cms如何添加采集编辑：程序博客网时间：2024/06/06 20:30

最大期望算法（Expectation-maximization algorithm，又译期望最大化算法）在统计中被用于寻找，依赖于不可观察的隐性变量的概率模型中，参数的最大似然估计。

在统计计算中，最大期望（EM）算法是在概率（probabilistic）模型中寻找参数最大似然估计或者最大后验估计的算法，其中概率模型依赖于无法观测的隐藏变量（Latent Variable）。最大期望经常用在机器学习和计算机视觉的数据聚类（Data Clustering）领域。

最大期望算法经过两个步骤交替进行计算：

第一步是计算期望（E），利用对隐藏变量的现有估计值，计算其最大似然估计值；

第二步是最大化（M），最大化在 E 步上求得的最大似然值来计算参数的值。

M 步上找到的参数估计值被用于下一个 E 步计算中，这个过程不断交替进行。

总体来说，EM的算法流程如下：

1.初始化分布参数

2.重复直到收敛：

E步骤：估计未知参数的期望值，给出当前的参数估计。

M步骤：重新估计分布参数，以使得数据的似然性最大，给出未知变量的期望估计。

/****************************************************************************************\*                              Expectation - Maximization                                *\****************************************************************************************/struct CV_EXPORTS CvEMParams   //参数设定 EM算法估计混合高斯模型所需要的参数{    CvEMParams() : nclusters(10), cov_mat_type(1/*CvEM::COV_MAT_DIAGONAL*/),        start_step(0/*CvEM::START_AUTO_STEP*/), probs(0), weights(0), means(0), covs(0)    {        term_crit=cvTermCriteria( CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 100, FLT_EPSILON );    }    CvEMParams( int _nclusters, int _cov_mat_type=1/*CvEM::COV_MAT_DIAGONAL*/,                int _start_step=0/*CvEM::START_AUTO_STEP*/,                CvTermCriteria _term_crit=cvTermCriteria(CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 100, FLT_EPSILON),                const CvMat* _probs=0, const CvMat* _weights=0, const CvMat* _means=0, const CvMat** _covs=0 ) :                nclusters(_nclusters), cov_mat_type(_cov_mat_type), start_step(_start_step),                probs(_probs), weights(_weights), means(_means), covs(_covs), term_crit(_term_crit)    {}    int nclusters;    int cov_mat_type;    int start_step;      const CvMat* probs; //初始的后验概率     const CvMat* weights; //初始的各个成分的概率    const CvMat* means;   //初始的均值    const CvMat** covs;  //初始的协方差矩阵    CvTermCriteria term_crit; //E步和M步 迭代停止的准则。 EM算法会在一定的迭代次数之后（term_crit.num_iter)，或者当模型参数在两次迭代之间的变化小于预定值（term_crit.epsilon）时停止};class CV_EXPORTS CvEM : public CvStatModel //模型设置{public:    // Type of covariation matrices    enum { COV_MAT_SPHERICAL=0, COV_MAT_DIAGONAL=1, COV_MAT_GENERIC=2 };   //    // The initial step    enum { START_E_STEP=1, START_M_STEP=2, START_AUTO_STEP=0 };    CvEM();    CvEM( const CvMat* samples, const CvMat* sample_idx=0,          CvEMParams params=CvEMParams(), CvMat* labels=0 );    //CvEM (CvEMParams params, CvMat * means, CvMat ** covs, CvMat * weights, CvMat * probs, CvMat * log_weight_div_det, CvMat * inv_eigen_values, CvMat** cov_rotate_mats);    virtual ~CvEM();    virtual bool train( const CvMat* samples, const CvMat* sample_idx=0,                        CvEMParams params=CvEMParams(), CvMat* labels=0 );    virtual float predict( const CvMat* sample, CvMat* probs ) const;#ifndef SWIG    CvEM( const cv::Mat& samples, const cv::Mat& sample_idx=cv::Mat(),         CvEMParams params=CvEMParams(), cv::Mat* labels=0 );        virtual bool train( const cv::Mat& samples, const cv::Mat& sample_idx=cv::Mat(),                       CvEMParams params=CvEMParams(), cv::Mat* labels=0 );        virtual float predict( const cv::Mat& sample, cv::Mat* probs ) const;#endif        virtual void clear();    int           get_nclusters() const;    const CvMat*  get_means()     const;    const CvMat** get_covs()      const;    const CvMat*  get_weights()   const;    const CvMat*  get_probs()     const;    inline double         get_log_likelihood     () const { return log_likelihood;     };    //    inline const CvMat *  get_log_weight_div_det () const { return log_weight_div_det; };//    inline const CvMat *  get_inv_eigen_values   () const { return inv_eigen_values;   };//    inline const CvMat ** get_cov_rotate_mats    () const { return cov_rotate_mats;    };protected:    virtual void set_params( const CvEMParams& params,                             const CvVectors& train_data );    virtual void init_em( const CvVectors& train_data );    virtual double run_em( const CvVectors& train_data );    virtual void init_auto( const CvVectors& samples );    virtual void kmeans( const CvVectors& train_data, int nclusters,                         CvMat* labels, CvTermCriteria criteria,                         const CvMat* means );    CvEMParams params;    double log_likelihood;    CvMat* means;    CvMat** covs;    CvMat* weights;    CvMat* probs;    CvMat* log_weight_div_det;    CvMat* inv_eigen_values;    CvMat** cov_rotate_mats;};

循环重复直到收敛 {

（E步）对于每一个i，计算

（M步）计算

clip_image075

#include "stdafx.h"#include <ml.h>   #include <iostream>#include <highgui.h>#include <cv.h>#include <cxcore.h> using namespace cv; using namespace std; int main( int argc, char** argv ){    const int N = 4;    const int N1 = (int)sqrt((double)N);    const CvScalar colors[] = {{{0,0,255}},{{0,255,0}},{{0,255,255}},{{255,255,0}}};    int i, j;    int nsamples = 100;    CvRNG rng_state = cvRNG(-1);    CvMat* samples = cvCreateMat( nsamples, 2, CV_32FC1 );    CvMat* labels = cvCreateMat( nsamples, 1, CV_32SC1 );    IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );    float _sample[2];    CvMat sample = cvMat( 1, 2, CV_32FC1, _sample );//EM算法初始化    CvEM em_model;    CvEMParams params;    CvMat samples_part;    cvReshape( samples, samples, 2, 0 );    for( i = 0; i < N; i++ )    {        CvScalar mean, sigma;        // form the training samples        cvGetRows( samples, &samples_part, i*nsamples/N, (i+1)*nsamples/N );        mean = cvScalar(((i%N1)+1.)*img->width/(N1+1), ((i/N1)+1.)*img->height/(N1+1));        sigma = cvScalar(30,30);        cvRandArr( &rng_state, &samples_part, CV_RAND_NORMAL, mean, sigma );    }    cvReshape( samples, samples, 1, 0 );    // initialize model's parameters    params.covs      = NULL;    params.means     = NULL;    params.weights   = NULL;    params.probs     = NULL;    params.nclusters = N;    params.cov_mat_type       = CvEM::COV_MAT_SPHERICAL;    params.start_step         = CvEM::START_AUTO_STEP;    params.term_crit.max_iter = 10;    params.term_crit.epsilon  = 0.1;    params.term_crit.type     = CV_TERMCRIT_ITER|CV_TERMCRIT_EPS;    // cluster the data    em_model.train( samples, 0, params, labels );#if 0    // the piece of code shows how to repeatedly optimize the model    // with less-constrained parameters (COV_MAT_DIAGONAL instead of COV_MAT_SPHERICAL)    // when the output of the first stage is used as input for the second.    CvEM em_model2;    params.cov_mat_type = CvEM::COV_MAT_DIAGONAL;    params.start_step = CvEM::START_E_STEP;    params.means = em_model.get_means();    params.covs = (const CvMat**)em_model.get_covs();    params.weights = em_model.get_weights();    em_model2.train( samples, 0, params, labels );    // to use em_model2, replace em_model.predict() with em_model2.predict() below#endif    // classify every image pixel    cvZero( img );    for( i = 0; i < img->height; i++ )    {        for( j = 0; j < img->width; j++ )        {            CvPoint pt = cvPoint(j, i);            sample.data.fl[0] = (float)j;            sample.data.fl[1] = (float)i;            int response = cvRound(em_model.predict( &sample, NULL ));            CvScalar c = colors[response];            cvCircle( img, pt, 1, cvScalar(c.val[0]*0.75,c.val[1]*0.75,c.val[2]*0.75), CV_FILLED );        }    }    //draw the clustered samples    for( i = 0; i < nsamples; i++ )    {        CvPoint pt;        pt.x = cvRound(samples->data.fl[i*2]);        pt.y = cvRound(samples->data.fl[i*2+1]);        cvCircle( img, pt, 1, colors[labels->data.i[i]], CV_FILLED );    }    cvNamedWindow( "EM-clustering result", 1 );    cvShowImage( "EM-clustering result", img );    cvWaitKey(0);    cvReleaseMat( &samples );    cvReleaseMat( &labels );    return 0;}

参考：http://www.cnblogs.com/jerrylead/archive/2011/04/06/2006936.html

http://zhidao.baidu.com/link?url=12xrCFpWm1U-bYb4V8uxf3uu2ZDTFlwpDzbWe7HjOrNWXdsCQTlA466N78ZUDWP-jFAcVsTQo9JyKW28o86ng_

http://www.360doc.com/content/13/0624/13/10942270_295158557.shtml

http://fuliang.iteye.com/blog/1621633

http://wiki.opencv.org.cn/index.php/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E4%B8%AD%E6%96%87%E5%8F%82%E8%80%83%E6%89%8B%E5%86%8C#CvEMParams

http://www.seas.upenn.edu/~bensapp/opencvdocs/ref/opencvref_ml.htm#ch_em

http://hi.baidu.com/darkhorse/item/cc58043eb19800159dc65e70

0 0