// 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 relevance 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 rvm 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 rvm 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 is a parameter to the // training. This is the gamma parameter of the RBF kernel. Our choice for this parameter will // influence how good the resulting decision function is. To test how good a particular choice of // kernel 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. 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 rvm_trainer object that uses our kernel type. rvm_trainer<kernel_type> trainer; // One thing you can do to reduce the RVM training time is to make its // stopping epsilon bigger. However, this might make the outputs less // reliable. But sometimes it works out well. 0.001 is the default. trainer.set_epsilon(0.001); // You can also set an explicit limit on the number of iterations used by the numeric // solver. The default is 2000. trainer.set_max_iterations(2000); // Now we loop over some different 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 = 0.000001; gamma <= 1; gamma *= 5){// tell the trainer the parameters we want to use trainer.set_kernel(kernel_type(gamma)); cout << "gamma: " << gamma; // Print out the cross validation accuracy for 3-fold cross validation using the current gamma. // 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 // gamma for this problem is 0.08. 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 0.08 for 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(0.08)); 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 RVM training and save the results // Print out the number of relevance vectors in the resulting decision function. cout << "\nnumber of relevance 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 relevance vectors in the resulting decision function. // (it should be the same as in the one above) cout << "\nnumber of relevance 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;}