SVM分类器的实现（包括交叉验证选择参数，Dlib，可视化）

惯例先放结果图，左侧为训练样本，右侧为训练完后的分类演示图

Dlib的支持向量机用起来比Opencv的爽多了，

支持交叉验证，

降低支持向量的个数

以及两种方式判别类别（正负以及可能性两种）

然后就是简单粗暴的代码了：

//需要配置Opencv以及Dlib的环境

Dlib配置见： 地址

Opencv配置见：地址

// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt/*This is an example illustrating the use of the support vector machineutilities from the dlib C++ Library.This example creates a simple set of data to train on and then showsyou how to use the cross validation and svm training functionsto find a good decision function that can classify examples in ourdata set.The data used in this example will be 2 dimensional data and willcome from a distribution where points with a distance less than 10from the origin are labeled +1 and all other points are labeledas -1.*/#include <iostream>#include <dlib/svm.h>#include<opencv2/opencv.hpp>using namespace std;using namespace dlib;using namespace cv;int main(){// The svm functions use column vectors to contain a lot of the data on which they// operate. So the first thing we do here is declare a convenient typedef.  // This typedef declares a matrix with 2 rows and 1 column.  It will be the object that// contains each of our 2 dimensional samples.   (Note that if you wanted more than 2// features in this vector you can simply change the 2 to something else.  Or if you// don't know how many features you want until runtime then you can put a 0 here and// use the matrix.set_size() member function)typedef matrix<double, 2, 1> sample_type;// This is a typedef for the type of kernel we are going to use in this example.  In// this case I have selected the radial basis kernel that can operate on our 2D// sample_type objectstypedef radial_basis_kernel<sample_type> kernel_type;// Now we make objects to contain our samples and their respective labels.std::vector<sample_type> samples;std::vector<double> labels;int 宽 = 500, 高 = 500;Mat 演示图片 = Mat::zeros(高, 宽, CV_8UC3);for (int r = -20; r <= 20; ++r){for (int c = -20; c <= 20; ++c){// if this point is less than 10 from the originif (sqrt((double)r*r + c*c) <= 10){line(演示图片, Point(c * 10 + 250 - 2, r * 10 + 250 - 2), Point(c * 10 + 250 + 2, r * 10 + 250 + 2), Scalar(0, 0, 255));line(演示图片, Point(c * 10 + 250 - 2, r * 10 + 250 + 2), Point(c * 10 + 250 + 2, r * 10 + 250 - 2), Scalar(0, 0, 255));}elsecircle(演示图片, Point(c * 10 + 250, r * 10 + 250), 1, Scalar(100));}}imshow("训练样本", 演示图片);waitKey(1);// Now let's put some data into our samples and labels objects.  We do this by looping// over a bunch of points and labeling them according to their distance from the// origin.for (int r = -20; r <= 20; ++r){for (int c = -20; c <= 20; ++c){sample_type samp;samp(0) = r;samp(1) = c;samples.push_back(samp);// if this point is less than 10 from the originif (sqrt((double)r*r + c*c) <= 10)labels.push_back(+1);elselabels.push_back(-1);}}// Here we normalize all the samples by subtracting their mean and dividing by their// standard deviation.  This is generally a good idea since it often heads off// numerical stability problems and also prevents one large feature from smothering// others.  Doing this doesn't matter much in this example so I'm just doing this here// so you can see an easy way to accomplish this with the library.  vector_normalizer<sample_type> normalizer;// let the normalizer learn the mean and standard deviation of the samplesnormalizer.train(samples);// now normalize each samplefor (unsigned long i = 0; i < samples.size(); ++i)samples[i] = normalizer(samples[i]);// Now that we have some data we want to train on it.  However, there are two// parameters to the training.  These are the nu and gamma parameters.  Our choice for// these parameters will influence how good the resulting decision function is.  To// test how good a particular choice of these parameters is we can use the// cross_validate_trainer() function to perform n-fold cross validation on our training// data.  However, there is a problem with the way we have sampled our distribution// above.  The problem is that there is a definite ordering to the samples.  That is,// the first half of the samples look like they are from a different distribution than// the second half.  This would screw up the cross validation process but we can fix it// by randomizing the order of the samples with the following function call.randomize_samples(samples, labels);// The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1// labels in the training data.  This function finds that value.const double max_nu = maximum_nu(labels);// here we make an instance of the svm_nu_trainer object that uses our kernel type.svm_nu_trainer<kernel_type> trainer;// Now we loop over some different nu and gamma values to see how good they are.  Note// that this is a very simple way to try out a few possible parameter choices.  You// should look at the model_selection_ex.cpp program for examples of more sophisticated// strategies for determining good parameter choices.cout << "开始测试各参数效果" << endl;double Gamma=0.00001, Nu=0.00001;double OK = 0;for (double gamma = 0.00001; gamma <= 1; gamma *= 2){for (double nu = 0.00001; nu < max_nu; nu *= 5){// tell the trainer the parameters we want to usetrainer.set_kernel(kernel_type(gamma));trainer.set_nu(nu);cout << "gamma: " << gamma << "    nu: " << nu;// Print out the cross validation accuracy for 3-fold cross validation using// the current gamma and nu.  cross_validate_trainer() returns a row vector.// The first element of the vector is the fraction of +1 training examples// correctly classified and the second number is the fraction of -1 training// examples correctly classified.matrix<double>temp= cross_validate_trainer(trainer, samples, labels, 3);if (OK < (temp(0, 1) + temp(0, 0))) {OK = temp(0, 1) + temp(0, 0);Gamma = gamma;Nu = nu;}cout << "     交叉训练测试结果: " << cross_validate_trainer(trainer, samples, labels, 3) ;}}// From looking at the output of the above loop it turns out that a good value for nu// and gamma for this problem is 0.15625 for both.  So that is what we will use.// Now we train on the full set of data and obtain the resulting decision function.  We// use the value of 0.15625 for nu and gamma.  The decision function will return values// >= 0 for samples it predicts are in the +1 class and numbers < 0 for samples it// predicts to be in the -1 class.//trainer.set_kernel(kernel_type(0.15625));//trainer.set_nu(0.15625);trainer.set_kernel(kernel_type(Gamma));trainer.set_nu(Nu);cout << "设置参数Gamma:" << Gamma << " Nu:" << Nu << endl;typedef decision_function<kernel_type> dec_funct_type;typedef normalized_function<dec_funct_type> funct_type;// Here we are making an instance of the normalized_function object.  This object// provides a convenient way to store the vector normalization information along with// the decision function we are going to learn.  funct_type learned_function;learned_function.normalizer = normalizer;  // save normalization informationlearned_function.function = trainer.train(samples, labels); // perform the actual SVM training and save the results// print out the number of support vectors in the resulting decision functioncout << "\nnumber of support vectors in our learned_function is "<< learned_function.function.basis_vectors.size() << endl;// Now let's try this decision_function on some samples we haven't seen before.sample_type sample;sample(0) = 3.123;sample(1) = 2;cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;sample(0) = 3.123;sample(1) = 9.3545;cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;sample(0) = 13.123;sample(1) = 9.3545;cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;sample(0) = 13.123;sample(1) = 0;cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;// We can also train a decision function that reports a well conditioned probability// instead of just a number > 0 for the +1 class and < 0 for the -1 class.  An example// of doing that follows:typedef probabilistic_decision_function<kernel_type> probabilistic_funct_type;typedef normalized_function<probabilistic_funct_type> pfunct_type;pfunct_type learned_pfunct;learned_pfunct.normalizer = normalizer;learned_pfunct.function = train_probabilistic_decision_function(trainer, samples, labels, 3);// Now we have a function that returns the probability that a given sample is of the +1 class.  // print out the number of support vectors in the resulting decision function.  // (it should be the same as in the one above)cout << "\nnumber of support vectors in our learned_pfunct is "<< learned_pfunct.function.decision_funct.basis_vectors.size() << endl;sample(0) = 3.123;sample(1) = 2;cout << "This +1 class example should have high probability.  Its probability is: "<< learned_pfunct(sample) << endl;sample(0) = 3.123;sample(1) = 9.3545;cout << "This +1 class example should have high probability.  Its probability is: "<< learned_pfunct(sample) << endl;sample(0) = 13.123;sample(1) = 9.3545;cout << "This -1 class example should have low probability.  Its probability is: "<< learned_pfunct(sample) << endl;sample(0) = 13.123;sample(1) = 0;cout << "This -1 class example should have low probability.  Its probability is: "<< learned_pfunct(sample) << endl;// Another thing that is worth knowing is that just about everything in dlib is// serializable.  So for example, you can save the learned_pfunct object to disk and// recall it later like so:serialize("saved_function.dat") << learned_pfunct;// Now let's open that file back up and load the function object it contains.deserialize("saved_function.dat") >> learned_pfunct;// Note that there is also an example program that comes with dlib called the// file_to_code_ex.cpp example.  It is a simple program that takes a file and outputs a// piece of C++ code that is able to fully reproduce the file's contents in the form of// a std::string object.  So you can use that along with the std::istringstream to save// learned decision functions inside your actual C++ code files if you want.  // Lastly, note that the decision functions we trained above involved well over 200// basis vectors.  Support vector machines in general tend to find decision functions// that involve a lot of basis vectors.  This is significant because the more basis// vectors in a decision function, the longer it takes to classify new examples.  So// dlib provides the ability to find an approximation to the normal output of a trainer// using fewer basis vectors.  // Here we determine the cross validation accuracy when we approximate the output using// only 10 basis vectors.  To do this we use the reduced2() function.  It takes a// trainer object and the number of basis vectors to use and returns a new trainer// object that applies the necessary post processing during the creation of decision// function objects.cout << "\ncross validation accuracy with only 10 support vectors: "<< cross_validate_trainer(reduced2(trainer, 10), samples, labels, 3);// Let's print out the original cross validation score too for comparison.cout << "cross validation accuracy with all the original support vectors: "<< cross_validate_trainer(trainer, samples, labels, 3);// When you run this program you should see that, for this problem, you can reduce the// number of basis vectors down to 10 without hurting the cross validation accuracy. // To get the reduced decision function out we would just do this:learned_function.function = reduced2(trainer, 10).train(samples, labels);// And similarly for the probabilistic_decision_function: learned_pfunct.function = train_probabilistic_decision_function(reduced2(trainer, 10), samples, labels, 3);cout << "\nnumber of support vectors in our learned_function is "<< learned_function.function.basis_vectors.size() << endl;Vec3b green(0, 255, 0), blue(255, 0, 0), red(0, 0, 255), black(0, 0, 0);for (int i = 0; i < 演示图片.rows; ++i)for (int j = 0; j < 演示图片.cols; ++j){Mat sampleMat = (Mat_<float>(1, 2) << j, i);sample_type sample;sample(0) = (i - 250) / 10.0;sample(1) = (j - 250) / 10.0;float response = learned_function(sample);if (response <0)演示图片.at<Vec3b>(i, j) = green;else if (response >= 0)演示图片.at<Vec3b>(i, j) = blue;else if (response == 3)演示图片.at<Vec3b>(i, j) = red;else if (response == 4)演示图片.at<Vec3b>(i, j) = black;}for (int r = -20; r <= 20; ++r){for (int c = -20; c <= 20; ++c){// if this point is less than 10 from the originif (sqrt((double)r*r + c*c) <= 10){line(演示图片, Point(c * 10 + 250-2, r * 10 + 250-2), Point(c * 10 + 250+2, r * 10 + 250+2), Scalar(0, 0, 255));line(演示图片, Point(c * 10 + 250-2, r * 10 + 250+2), Point(c * 10 + 250+2, r * 10 + 250-2), Scalar(0, 0, 255));}elsecircle(演示图片, Point(c * 10 + 250, r * 10 + 250), 1, Scalar(0));}}imshow("分类结果", 演示图片);waitKey(-1);system("pause");}