    // 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 rank_features() function
        from the dlib C++ Library.

        This example creates a simple set of data and then shows
        you how to use the rank_features() function to find a good
        set of features (where "good" means the feature set will probably
        work well with a classification algorithm).

        The data used in this example will be 4 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.  Note that this data is conceptually 2 dimensional but we
        will add two extra features for the purpose of showing what
        the rank_features() function does.
    */

    #include <iostream>
    #include <dlib/svm.h>
    #include <dlib/rand.h>
    #include <vector>

    using namespace std;
    using namespace dlib;

    int main()
    {

        // This first typedef declares a matrix with 4 rows and 1 column.  It will be the
        // object that contains each of our 4 dimensional samples.
        typedef matrix<double, 4, 1> sample_type;

        // Now lets make some vector objects that can hold our samples
        std::vector<sample_type> samples;
        std::vector<double> labels;

        dlib::rand rnd;

        for (int x = -30; x <= 30; ++x)
        {
            for (int y = -30; y <= 30; ++y)
            {
                sample_type samp;

                // the first two features are just the (x,y) position of our points and so
                // we expect them to be good features since our two classes here are points
                // close to the origin and points far away from the origin.
                samp(0) = x;
                samp(1) = y;

                // This is a worthless feature since it is just random noise.  It should
                // be indicated as worthless by the rank_features() function below.
                samp(2) = rnd.get_random_double();

                // This is a version of the y feature that is corrupted by random noise.  It
                // should be ranked as less useful than features 0, and 1, but more useful
                // than the above feature.
                samp(3) = y*0.2 + (rnd.get_random_double()-0.5)*10;

                // add this sample into our vector of samples.
                samples.push_back(samp);

                // if this point is less than 15 from the origin then label it as a +1 class point.
                // otherwise it is a -1 class point
                if (sqrt((double)x*x + y*y) <= 15)
                    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.
        const sample_type m(mean(mat(samples)));  // compute a mean vector
        const sample_type sd(reciprocal(stddev(mat(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);

        // This is another thing that is often good to do from a numerical stability point of view.
        // However, in our case it doesn't really matter.   It's just here to show you how to do it.
        randomize_samples(samples,labels);

        // 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
        // 4D sample_type objects.  In general, I would suggest using the same kernel for
        // classification and feature ranking.
        typedef radial_basis_kernel<sample_type> kernel_type;

        // The radial_basis_kernel has a parameter called gamma that we need to set.  Generally,
        // you should try the same gamma that you are using for training.  But if you don't
        // have a particular gamma in mind then you can use the following function to
        // find a reasonable default gamma for your data.  Another reasonable way to pick a gamma
        // is often to use 1.0/compute_mean_squared_distance(randomly_subsample(samples, 2000)).
        // It computes the mean squared distance between 2000 randomly selected samples and often
        // works quite well.
        const double gamma = verbose_find_gamma_with_big_centroid_gap(samples, labels);

        // Next we declare an instance of the kcentroid object.  It is used by rank_features()
        // two represent the centroids of the two classes.  The kcentroid has 3 parameters
        // you need to set.  The first argument to the constructor is the kernel we wish to
        // use.  The second is a parameter that determines the numerical accuracy with which
        // the object will perform part of the ranking algorithm.  Generally, smaller values
        // give better results but cause the algorithm to attempt to use more dictionary vectors
        // (and thus run slower and use more memory).  The third argument, however, is the
        // maximum number of dictionary vectors a kcentroid is allowed to use.  So you can use
        // it to put an upper limit on the runtime complexity.
        kcentroid<kernel_type> kc(kernel_type(gamma), 0.001, 25);

        // And finally we get to the feature ranking. Here we call rank_features() with the kcentroid we just made,
        // the samples and labels we made above, and the number of features we want it to rank.
        cout << rank_features(kc, samples, labels) << endl;

        // The output is:
        /*
            0 0.749265
            1        1
            3 0.933378
            2 0.825179
        */

        // The first column is a list of the features in order of decreasing goodness.  So the rank_features() function
        // is telling us that the samples[i](0) and samples[i](1) (i.e. the x and y) features are the best two.  Then
        // after that the next best feature is the samples[i](3) (i.e. the y corrupted by noise) and finally the worst
        // feature is the one that is just random noise.  So in this case rank_features did exactly what we would
        // intuitively expect.

        // The second column of the matrix is a number that indicates how much the features up to that point
        // contribute to the separation of the two classes.  So bigger numbers are better since they
        // indicate a larger separation.  The max value is always 1.  In the case below we see that the bad
        // features actually make the class separation go down.

        // So to break it down a little more.
        //    0 0.749265   <-- class separation of feature 0 all by itself
        //    1        1   <-- class separation of feature 0 and 1
        //    3 0.933378   <-- class separation of feature 0, 1, and 3
        //    2 0.825179   <-- class separation of feature 0, 1, 3, and 2

    }