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:
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 )
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;
}
分类结果:
KNN的思想很好理解,也非常容易实现,同时分类结果较高,对异常值不敏感。但计算复杂度较高,不适于大数据的分类问题。