dlib C++ Library - svm_c_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. 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;
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. 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 (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 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 (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 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 (double gamma = 0.00001; gamma <= 1; gamma *= 5)
 {
 for (double C = 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);
}