dlib C++ Library - svm_ex.cpp

// 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;
int main()
{
 // 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 (int r = -20; r <= 20; ++r)
 {
 for (int c = -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 (unsigned long i = 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.
 const double max_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 (double gamma = 0.00001; gamma <= 1; gamma *= 5)
 {
 for (double nu = 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);
}