// 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 kernel ridge regression object from the dlib C++ Library. This example will train on data from the sinc function. */ #include <iostream> #include <vector> #include <dlib/svm.h> using namespace std; using namespace dlib; // Here is the sinc function we will be trying to learn with kernel ridge regressiondoublesinc(doublex){if (x == 0) return 1; return sin(x)/x;}intmain(){// Here we declare that our samples will be 1 dimensional column vectors. typedef matrix<double,1,1> sample_type; // Now sample some points from the sinc() function sample_type m; std::vector<sample_type> samples; std::vector<double> labels; for (doublex = -10; x <= 4; x += 1){m(0) = x; samples.push_back(m); labels.push_back(sinc(x));}// Now we are making a typedef for the kind of kernel we want to use. I picked the // radial basis kernel because it only has one parameter and generally gives good // results without much fiddling. typedef radial_basis_kernel<sample_type> kernel_type; // Here we declare an instance of the krr_trainer object. This is the // object that we will later use to do the training. krr_trainer<kernel_type> trainer; // Here we set the kernel we want to use for training. The radial_basis_kernel // has a parameter called gamma that we need to determine. As a rule of thumb, a good // gamma to try is 1.0/(mean squared distance between your sample points). So // below we are using a similar value computed from at most 2000 randomly selected // samples. constdoublegamma = 3.0/compute_mean_squared_distance(randomly_subsample(samples, 2000)); cout << "using gamma of " << gamma << endl; trainer.set_kernel(kernel_type(gamma)); // now train a function based on our sample points decision_function<kernel_type> test = trainer.train(samples, labels); // now we output the value of the sinc function for a few test points as well as the // value predicted by our regression. m(0) = 2.5; cout << sinc(m(0)) << " " << test(m) << endl; m(0) = 0.1; cout << sinc(m(0)) << " " << test(m) << endl; m(0) = -4; cout << sinc(m(0)) << " " << test(m) << endl; m(0) = 5.0; cout << sinc(m(0)) << " " << test(m) << endl; // The output is as follows: //using gamma of 0.075 // 0.239389 0.239389 // 0.998334 0.998362 // -0.189201 -0.189254 // -0.191785 -0.186618 // The first column is the true value of the sinc function and the second // column is the output from the krr estimate. // Note that the krr_trainer has the ability to tell us the leave-one-out predictions // for each sample. std::vector<double> loo_values; trainer.train(samples, labels, loo_values); cout << "mean squared LOO error: " << mean_squared_error(labels,loo_values) << endl; cout << "R^2 LOO value: " << r_squared(labels,loo_values) << endl; // Which outputs the following: // mean squared LOO error: 8.29575e-07 // R^2 LOO value: 0.999995 // Another thing that is worth knowing is that just about everything in dlib is serializable. // So for example, you can save the test object to disk and recall it later like so: serialize("saved_function.dat") << test; // Now let's open that file back up and load the function object it contains. deserialize("saved_function.dat") >> test;}