dlib/examples/rvm_ex.cpp

/*

    This is an example illustrating the use of the relevance 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 rvm 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 rvm functions use column vectors to contain a lot of the data on which they 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 lets 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 is a parameter to the 
    // training.  This is the gamma parameter of the RBF kernel.  Our choice for this parameter will 
    // influence how good the resulting decision function is.  To test how good a particular choice of
    // kernel 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.  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 do.  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 rvm_trainer object that uses our kernel type.
    rvm_trainer<kernel_type> trainer;

    // Now we loop over some different gamma values to see how good they are.  Note
    // that this is just a simple brute force way to try out a few possible parameter 
    // choices.  You may want to investigate more sophisticated strategies for determining 
    // good parameter choices.
    cout << "doing cross validation" << endl;
    for (double gamma = 0.00001; gamma <= 1; gamma += 0.1)
    {
        // tell the trainer the parameters we want to use
        trainer.set_kernel(kernel_type(gamma));

        cout << "gamma: " << gamma;
        // Print out the cross validation accuracy for 3-fold cross validation using the current gamma.  
        // 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 
    // gamma for this problem is 0.1.  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 0.1 for 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(0.1));
    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 RVM 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.support_vectors.nr() << endl;

    // now lets try this decision_function on some samples we haven't seen before 
    sample_type sample;

    sample(0) = 3.123;
    sample(1) = 2;
    cout << "This sample should be >= 0 and it is classified as a " << learned_function(sample) << endl;

    sample(0) = 3.123;
    sample(1) = 9.3545;
    cout << "This sample should be >= 0 and it is classified as a " << learned_function(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 9.3545;
    cout << "This sample should be < 0 and it is classified as a " << learned_function(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 0;
    cout << "This sample should be < 0 and it is classified as a " << 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.support_vectors.nr() << endl;

    sample(0) = 3.123;
    sample(1) = 2;
    cout << "This +1 example should have high probability.  It's probability is: " << learned_pfunct(sample) << endl;

    sample(0) = 3.123;
    sample(1) = 9.3545;
    cout << "This +1 example should have high probability.  It's probability is: " << learned_pfunct(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 9.3545;
    cout << "This -1 example should have low probability.  It's probability is: " << learned_pfunct(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 0;
    cout << "This -1 example should have low probability.  It's 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:
    ofstream fout("saved_function.dat",ios::binary);
    serialize(learned_pfunct,fout);
    fout.close();

    // now lets open that file back up and load the function object it contains
    ifstream fin("saved_function.dat",ios::binary);
    deserialize(learned_pfunct, fin);


}