// 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. In particular, we show how to use the C parametrization of the SVM in this example. 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. You can use your own custom // kernels with these tools as well, see custom_trainer_ex.cpp for an // example. 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 it. 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 C 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 are 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); // here we make an instance of the svm_c_trainer object that uses our kernel // type. svm_c_trainer<kernel_type> trainer; // Now we loop over some different C 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 (doubleC = 1; C < 100000; C *= 5){// tell the trainer the parameters we want to use trainer.set_kernel(kernel_type(gamma)); trainer.set_c(C); cout << "gamma: " << gamma << " C: " << C; // Print out the cross validation accuracy for 3-fold cross validation using // the current gamma and C. 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 good // values for C and gamma for this problem are 5 and 0.15625 respectively. // So that is what we will use. // Now we train on the full set of data and obtain the resulting decision // function. 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_c(5); 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);}