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);
}