// 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 machine utilities from the dlib C++ Library. This example creates a simple set of data to train on and then shows you how to use the cross validation and svm training functions to find a good decision function that can classify examples in our data set. The data used in this example will be 2 dimensional data and will come from a distribution where points with a distance less than 10 from the origin are labeled +1 and all other points are labeled as -1. */ #include <iostream> #include <dlib/svm.h> using namespace std; using namespace dlib;intmain(){// 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 objects typedef 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; // 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 (intr = -20; r <= 20; ++r){for (intc = -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 origin if (sqrt((double)r*r + c*c) <= 10) labels.push_back(+1); else labels.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 samples normalizer.train(samples); // now normalize each sample for (unsignedlongi = 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. constdoublemax_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 << "doing cross validation" << endl; for (doublegamma = 0.00001; gamma <= 1; gamma *= 5){for (doublenu = 0.00001; nu < max_nu; nu *= 5){// tell the trainer the parameters we want to use trainer.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. cout << " cross validation accuracy: " << 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); 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 information learned_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 function cout << "\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);}