使用SVM进行非线性回归(Do non-linear regression with OpenCV's SVM tool)

OpenCV集成的东西越来越多了，不用费劲去配置很多环境，这点还是挺方便的，原来一直用SVM进行分类，最近了研究一下使用SVM进行回归，发现还是很好用的。

下面就用OpenCV的SVM工具对Sinc函数的样本进行回归，代码比较简单，效果还不错。

本文为原创，转载请注明，本文地址：http://blog.youkuaiyun.com/houston11235/article/details/9023229。

从Sinc函数获得的样本点如下图所示，这是没有噪声时候的情形（Data without noise）

加入噪声之后的样本如下图（Add noise to data）

使用SVM进行回归之后的结果如下图（Result）

最后附上源代码，其中的参数设置参考了以下链接：http://dlib.net/svr_ex.cpp.html

// draw some samples from sinc function and do a non-linear regression

#include <opencv2/opencv.hpp>
#include <iostream>


using namespace std;
using namespace cv;

// the sinc function
float sinc(float x)
{
	return static_cast<float>( x==0 ? 1.0 : sin(x) / x );
}

int main(int argc, char* argv[])
{
	RNG rng;
	int ndata = 10;
	Mat traindata(ndata, 1, CV_32FC1); // train data
	Mat label(ndata, 1, CV_32FC1); // train response
	for (int i = 0; i < ndata; ++i)
	{
		traindata.at<float>(i, 0) = static_cast<float>(i);
		float noise = static_cast<float>(rng.gaussian(0.1));
		//noise = 0.0;    // uncomment to eliminate the noise
		label.at<float>(i, 0) = static_cast<float>(sinc(i) + noise);
	}

	// show the train data
	int width = 500;
	int height = 500;
	Mat canvas(height, width, CV_8UC3, Scalar(0,0,0));
	double minV;
	double maxV;
	Point minId;
	Point maxId;

	minMaxLoc(traindata, &minV, &maxV, &minId, &maxId);
	float X_shift = static_cast<float>(minV);
	float X_ratio = static_cast<float>(width) / static_cast<float>(maxV - minV);

	minMaxLoc(label, &minV, &maxV, &minId, &maxId);
	float Y_shift = static_cast<float>(minV);
	float Y_ratio = static_cast<float>(height) / static_cast<float>(maxV - minV);

	for (int idx = 0; idx < traindata.rows; ++idx)
	{
		float x = (traindata.at<float>(idx, 0) - X_shift) * X_ratio;
		float y = static_cast<float>(height) - (label.at<float>(idx, 0) - Y_shift) * Y_ratio;
		circle(canvas, Point2f(x, y), 3, Scalar(0,0,255), -1);
	}

	imshow("train", canvas);
	//imwrite("train_noise.png", canvas);

	CvSVMParams param;
	param.svm_type = CvSVM::EPS_SVR;
	param.kernel_type = CvSVM::RBF;
	param.C = 5;
	param.p = 1e-3;
	param.gamma = 0.1;

	CvSVM regresser;
	regresser.train(traindata, label, Mat(), Mat(), param);

	// predict the responses of the samples and show them
	for (float i = 0; i < 10; i+=0.23f)
	{
		Mat sample(1,1, CV_32FC1);
		sample.at<float>(0, 0) = static_cast<float>(i);

		float response = regresser.predict(sample);
		//cout<<response<<endl;
		float x = (sample.at<float>(0, 0) - X_shift) * X_ratio;
		float y = static_cast<float>(height) - (response - Y_shift) * Y_ratio;
		circle(canvas, Point2f(x, y), 3, Scalar(0,255,0), -1);
	}

	imshow("predict", canvas);
	//imwrite("regress.png", canvas);

	waitKey(0);
	return 0;
}