svm_ex.cpp

/*

    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 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.  
    const sample_type m(mean(vector_to_matrix(samples)));  // compute a mean vector
    const sample_type sd(reciprocal(sqrt(variance(vector_to_matrix(samples))))); // compute a standard deviation vector
    // now normalize each sample
    for (unsigned long i = 0; i < samples.size(); ++i)
        samples[i] = pointwise_multiply(samples[i] - m, sd); 



    // 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 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 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);


    // 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 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)
    {
        for (double nu = 0.00001; nu < max_nu; nu += 0.1)
        {
            // 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 0.1 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 0.1 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(0.1));
    trainer.set_nu(0.1);
    decision_function<kernel_type> learned_decision_function = trainer.train(samples, labels);

    // print out the number of support vectors in the resulting decision function
    cout << "\nnumber of support vectors in our learned_decision_function is " 
         << learned_decision_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;
    // don't forget that we have to normalize each new sample the same way we did for the training samples.
    sample = pointwise_multiply(sample-m, sd);

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

    sample(0) = 3.123;
    sample(1) = 9.3545;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This sample should be >= 0 and it is classified as a " << learned_decision_function(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 9.3545;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This sample should be < 0 and it is classified as a " << learned_decision_function(sample) << endl;

    sample(0) = 13.123;
    sample(1) = 0;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This sample should be < 0 and it is classified as a " << learned_decision_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:
    probabilistic_decision_function<kernel_type> learned_probabilistic_decision_function;  
    learned_probabilistic_decision_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_probabilistic_decision_function is " 
         << learned_probabilistic_decision_function.decision_funct.support_vectors.nr() << endl;

    sample(0) = 3.123;
    sample(1) = 2;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This +1 example should have high probability.  It's probability is: " 
         << learned_probabilistic_decision_function(sample) << endl;

    sample(0) = 3.123;
    sample(1) = 9.3545;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This +1 example should have high probability.  It's probability is: " 
         << learned_probabilistic_decision_function(sample) << endl;

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

    sample(0) = 13.123;
    sample(1) = 0;
    sample = pointwise_multiply(sample-m, sd);
    cout << "This -1 example should have low probability.  It's probability is: " 
         << learned_probabilistic_decision_function(sample) << endl;




    // Lastly, note that the decision functions we trained above involved well over 100 
    // support vectors.  Support vector machines in general tend to find decision functions
    // that involve a lot of support vectors.  This is significant because the more 
    // support 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
    // support vector machine using fewer support vectors.  

    // Here we determine the cross validation accuracy when we approximate the output
    // using only 10 support vectors.  To do this we use the reduced2() function.  It
    // takes a trainer object and the number of support 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);

    // Lets 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 support vectors down to 10 without hurting the cross validation
    // accuracy. 


    // To get the reduced decision function out we would just do this:
    learned_decision_function = reduced2(trainer,10).train(samples, labels);
    // And similarly for the probabilistic_decision_function: 
    learned_probabilistic_decision_function = train_probabilistic_decision_function(reduced2(trainer,10), samples, labels, 3);
}