    // 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 kkmeans object
        and spectral_cluster() routine from the dlib C++ Library.

        The kkmeans object is an implementation of a kernelized k-means clustering
        algorithm.  It is implemented by using the kcentroid object to represent
        each center found by the usual k-means clustering algorithm.

        So this object allows you to perform non-linear clustering in the same way
        a svm classifier finds non-linear decision surfaces.

        This example will make points from 3 classes and perform kernelized k-means
        clustering on those points.  It will also do the same thing using spectral
        clustering.

        The classes are as follows:
            - points very close to the origin
            - points on the circle of radius 10 around the origin
            - points that are on a circle of radius 4 but not around the origin at all
    */

    #include <iostream>
    #include <vector>

    #include <dlib/clustering.h>
    #include <dlib/rand.h>

    using namespace std;
    using namespace dlib;

    int main()
    {
        // Here we declare that our samples will be 2 dimensional column vectors.
        // (Note that if you don't know the dimensionality of your vectors at compile time
        // you can change the 2 to a 0 and then set the size at runtime)
        typedef matrix<double,2,1> sample_type;

        // Now we are making a typedef for the kind of kernel we want to use.  I picked the
        // radial basis kernel because it only has one parameter and generally gives good
        // results without much fiddling.
        typedef radial_basis_kernel<sample_type> kernel_type;

        // Here we declare an instance of the kcentroid object.  It is the object used to
        // represent each of the centers used for clustering.  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 learning 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 control the runtime complexity.
        kcentroid<kernel_type> kc(kernel_type(0.1),0.01, 8);

        // Now we make an instance of the kkmeans object and tell it to use kcentroid objects
        // that are configured with the parameters from the kc object we defined above.
        kkmeans<kernel_type> test(kc);

        std::vector<sample_type> samples;
        std::vector<sample_type> initial_centers;

        sample_type m;

        dlib::rand rnd;

        // we will make 50 points from each class
        const long num = 50;

        // make some samples near the origin
        double radius = 0.5;
        for (long i = 0; i < num; ++i)
        {
            double sign = 1;
            if (rnd.get_random_double() < 0.5)
                sign = -1;
            m(0) = 2*radius*rnd.get_random_double()-radius;
            m(1) = sign*sqrt(radius*radius - m(0)*m(0));

            // add this sample to our set of samples we will run k-means
            samples.push_back(m);
        }

        // make some samples in a circle around the origin but far away
        radius = 10.0;
        for (long i = 0; i < num; ++i)
        {
            double sign = 1;
            if (rnd.get_random_double() < 0.5)
                sign = -1;
            m(0) = 2*radius*rnd.get_random_double()-radius;
            m(1) = sign*sqrt(radius*radius - m(0)*m(0));

            // add this sample to our set of samples we will run k-means
            samples.push_back(m);
        }

        // make some samples in a circle around the point (25,25)
        radius = 4.0;
        for (long i = 0; i < num; ++i)
        {
            double sign = 1;
            if (rnd.get_random_double() < 0.5)
                sign = -1;
            m(0) = 2*radius*rnd.get_random_double()-radius;
            m(1) = sign*sqrt(radius*radius - m(0)*m(0));

            // translate this point away from the origin
            m(0) += 25;
            m(1) += 25;

            // add this sample to our set of samples we will run k-means
            samples.push_back(m);
        }

        // tell the kkmeans object we made that we want to run k-means with k set to 3.
        // (i.e. we want 3 clusters)
        test.set_number_of_centers(3);

        // You need to pick some initial centers for the k-means algorithm.  So here
        // we will use the dlib::pick_initial_centers() function which tries to find
        // n points that are far apart (basically).
        pick_initial_centers(3, initial_centers, samples, test.get_kernel());

        // now run the k-means algorithm on our set of samples.
        test.train(samples,initial_centers);

        // now loop over all our samples and print out their predicted class.  In this example
        // all points are correctly identified.
        for (unsigned long i = 0; i < samples.size()/3; ++i)
        {
            cout << test(samples[i]) << " ";
            cout << test(samples[i+num]) << " ";
            cout << test(samples[i+2*num]) << "\n";
        }

        // Now print out how many dictionary vectors each center used.  Note that
        // the maximum number of 8 was reached.  If you went back to the kcentroid
        // constructor and changed the 8 to some bigger number you would see that these
        // numbers would go up.  However, 8 is all we need to correctly cluster this dataset.
        cout << "num dictionary vectors for center 0: " << test.get_kcentroid(0).dictionary_size() << endl;
        cout << "num dictionary vectors for center 1: " << test.get_kcentroid(1).dictionary_size() << endl;
        cout << "num dictionary vectors for center 2: " << test.get_kcentroid(2).dictionary_size() << endl;

        // Finally, we can also solve the same kind of non-linear clustering problem with
        // spectral_cluster().  The output is a vector that indicates which cluster each sample
        // belongs to.  Just like with kkmeans, it assigns each point to the correct cluster.
        std::vector<unsigned long> assignments = spectral_cluster(kernel_type(0.1), samples, 3);
        cout << mat(assignments) << endl;

    }