// 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 creates a simple set of data to train on and then shows you how to use the kernel ridge regression tool 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 13 from the origin are labeled +1 and all other points are labeled as -1. All together, the dataset will contain 10201 sample points. */ #include <iostream> #include <dlib/svm.h> using namespace std; using namespace dlib;intmain(){// 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 (doubler = -20; r <= 20; r += 0.4){for (doublec = -20; c <= 20; c += 0.4){sample_type samp; samp(0) = r; samp(1) = c; samples.push_back(samp); // if this point is less than 13 from the origin if (sqrt((double)r*r + c*c) <= 13) labels.push_back(+1); else labels.push_back(-1);}}cout << "samples generated: " << samples.size() << endl; cout << " number of +1 samples: " << sum(mat(labels) > 0) << endl; cout << " number of -1 samples: " << sum(mat(labels) < 0) << endl; // 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]); // here we make an instance of the krr_trainer object that uses our kernel type. krr_trainer<kernel_type> trainer; // The krr_trainer has the ability to perform leave-one-out cross-validation. // It does this to automatically determine the regularization parameter. Since // we are performing classification instead of regression we should be sure to // call use_classification_loss_for_loo_cv(). This function tells it to measure // errors in terms of the number of classification mistakes instead of mean squared // error between decision function output values and labels. trainer.use_classification_loss_for_loo_cv(); // Now we loop over some different gamma values to see how good they are. cout << "\ndoing leave-one-out 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)); // loo_values will contain the LOO predictions for each sample. In the case // of perfect prediction it will end up being a copy of labels. std::vector<double> loo_values; trainer.train(samples, labels, loo_values); // Print gamma and the fraction of samples correctly classified during LOO cross-validation. constdoubleclassification_accuracy = mean_sign_agreement(labels, loo_values); cout << "gamma: " << gamma << " LOO accuracy: " << classification_accuracy << endl;}// From looking at the output of the above loop it turns out that a good value for // gamma for this problem is 0.000625. So that is what we will use. trainer.set_kernel(kernel_type(0.000625)); 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 training and save the results // print out the number of basis vectors in the resulting decision function cout << "\nnumber of basis 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. // 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. 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; // The train_probabilistic_decision_function() is going to perform 3-fold cross-validation. // So it is important that the +1 and -1 samples be distributed uniformly across all the folds. // calling randomize_samples() will make sure that is the case. randomize_samples(samples, labels); 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 basis vectors in the resulting decision function. // (it should be the same as in the one above) cout << "\nnumber of basis 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;}