【模式识别】K-近邻分类算法KNN-蒲公英云

K-近邻（K-Nearest Neighbors, KNN）是一种很好理解的分类算法，简单说来就是从训练样本中找出K个与其最相近的样本，然后看这K个样本中哪个类别的样本多，则待判定的值（或说抽样）就属于这个类别。

KNN算法的步骤

计算已知类别数据集中每个点与当前点的距离；
选取与当前点距离最小的K个点；
统计前K个点中每个类别的样本出现的频率；
返回前K个点出现频率最高的类别作为当前点的预测分类。

OpenCV中使用CvKNearest

OpenCV中实现CvKNearest类可以实现简单的KNN训练和预测。

int main()
{
    float labels[10] = {0,0,0,0,0,1,1,1,1,1};
    Mat labelsMat(10, 1, CV_32FC1, labels);
    cout<<labelsMat<<endl;
    float trainingData[10][2];
    srand(time(0)); 
    for(int i=0;i<5;i++){
        trainingData[i][0] = rand()%255+1;
        trainingData[i][1] = rand()%255+1;
        trainingData[i+5][0] = rand()%255+255;
        trainingData[i+5][1] = rand()%255+255;
    }
    Mat trainingDataMat(10, 2, CV_32FC1, trainingData);
    cout<<trainingDataMat<<endl;
    CvKNearest knn;
    knn.train(trainingDataMat,labelsMat,Mat(), false, 2 );
    // Data for visual representation
    int width = 512, height = 512;
    Mat image = Mat::zeros(height, width, CV_8UC3);
    Vec3b green(0,255,0), blue (255,0,0);
    for (int i = 0; i < image.rows; ++i){
        for (int j = 0; j < image.cols; ++j){
            const Mat sampleMat = (Mat_<float>(1,2) << i,j);
            Mat response;
            float result = knn.find_nearest(sampleMat,1);
            if (result !=0){
                image.at<Vec3b>(j, i)  = green;
            }
            else  
                image.at<Vec3b>(j, i)  = blue;
        }
    }
        // Show the training data
        for(int i=0;i<5;i++){
            circle(    image, Point(trainingData[i][0],  trainingData[i][1]), 
                5, Scalar(  0,   0,   0), -1, 8);
            circle(    image, Point(trainingData[i+5][0],  trainingData[i+5][1]), 
                5, Scalar(255, 255, 255), -1, 8);
        }
        imshow("KNN Simple Example", image); // show it to the user
        waitKey(10000);
}

使用的是之前BP神经网络中的例子，分类结果如下：

20140415201435109

预测函数find_nearest()除了输入sample参数外还有些其他的参数：

float CvKNearest::find_nearest(const Mat& samples, int k, Mat* results=0, 
const float** neighbors=0, Mat* neighborResponses=0, Mat* dist=0 )

20140415201848234

即，samples为样本数*特征数的浮点矩阵；K为寻找最近点的个数；results与预测结果；neibhbors为k*样本数的指针数组（输入为const，实在不知为何如此设计）；neighborResponse为样本数*k的每个样本K个近邻的输出值；dist为样本数*k的每个样本K个近邻的距离。

另一个例子

OpenCV refman也提供了一个类似的示例，使用CvMat格式的输入参数：

int main( int argc, char** argv )
{
    const int K = 10;
    int i, j, k, accuracy;
    float response;
    int train_sample_count = 100;
    CvRNG rng_state = cvRNG(-1);
    CvMat* trainData = cvCreateMat( train_sample_count, 2, CV_32FC1 );
    CvMat* trainClasses = cvCreateMat( train_sample_count, 1, CV_32FC1 );
    IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );
    float _sample[2];
    CvMat sample = cvMat( 1, 2, CV_32FC1, _sample );
    cvZero( img );
    CvMat trainData1, trainData2, trainClasses1, trainClasses2;
    // form the training samples
    cvGetRows( trainData, &trainData1, 0, train_sample_count/2 );
    cvRandArr( &rng_state, &trainData1, CV_RAND_NORMAL, cvScalar(200,200), cvScalar(50,50) );
    cvGetRows( trainData, &trainData2, train_sample_count/2, train_sample_count );
    cvRandArr( &rng_state, &trainData2, CV_RAND_NORMAL, cvScalar(300,300), cvScalar(50,50) );
    cvGetRows( trainClasses, &trainClasses1, 0, train_sample_count/2 );
    cvSet( &trainClasses1, cvScalar(1) );
    cvGetRows( trainClasses, &trainClasses2, train_sample_count/2, train_sample_count );
    cvSet( &trainClasses2, cvScalar(2) );
    // learn classifier
    CvKNearest knn( trainData, trainClasses, 0, false, K );
    CvMat* nearests = cvCreateMat( 1, K, CV_32FC1);
    for( i = 0; i < img->height; i++ )
    {
        for( j = 0; j < img->width; j++ )
        {
            sample.data.fl[0] = (float)j;
            sample.data.fl[1] = (float)i;
            // estimate the response and get the neighbors’ labels
            response = knn.find_nearest(&sample,K,0,0,nearests,0);
            // compute the number of neighbors representing the majority
            for( k = 0, accuracy = 0; k < K; k++ )
            {
                if( nearests->data.fl[k] == response)
                    accuracy++;
            }
            // highlight the pixel depending on the accuracy (or confidence)
            cvSet2D( img, i, j, response == 1 ?
                (accuracy > 5 ? CV_RGB(180,0,0) : CV_RGB(180,120,0)) :
                (accuracy > 5 ? CV_RGB(0,180,0) : CV_RGB(120,120,0)) );
        }
    }
    // display the original training samples
    for( i = 0; i < train_sample_count/2; i++ )
    {
        CvPoint pt;
        pt.x = cvRound(trainData1.data.fl[i*2]);
        pt.y = cvRound(trainData1.data.fl[i*2+1]);
        cvCircle( img, pt, 2, CV_RGB(255,0,0), CV_FILLED );
        pt.x = cvRound(trainData2.data.fl[i*2]);
        pt.y = cvRound(trainData2.data.fl[i*2+1]);
        cvCircle( img, pt, 2, CV_RGB(0,255,0), CV_FILLED );
    }
    cvNamedWindow( "classifier result", 1 );
    cvShowImage( "classifier result", img );
    cvWaitKey(0);
    cvReleaseMat( &trainClasses );
    cvReleaseMat( &trainData );
    return 0;
}