// 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);
}