dlib C++ Library - spectral_cluster.h

    // Copyright (C) 2015  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_SPECTRAL_CLUSTEr_H_
    #define DLIB_SPECTRAL_CLUSTEr_H_

    #include "spectral_cluster_abstract.h"
    #include <vector>
    #include "../matrix.h"
    #include "../svm/kkmeans.h"

    namespace dlib
    {
        template <
            typename kernel_type,
            typename vector_type
            >
        std::vector<unsigned long> spectral_cluster (
            const kernel_type& k,
            const vector_type& samples,
            const unsigned long num_clusters
        )
        {
            DLIB_CASSERT(num_clusters > 0,
                "\t std::vector<unsigned long> spectral_cluster(k,samples,num_clusters)"
                << "\n\t num_clusters can't be 0."
                );

            if (num_clusters == 1)
            {
                // nothing to do, just assign everything to the 0 cluster.
                return std::vector<unsigned long>(samples.size(), 0);
            }

            // compute the similarity matrix.
            matrix<double> K(samples.size(), samples.size());
            for (long r = 0; r < K.nr(); ++r)
                for (long c = r+1; c < K.nc(); ++c)
                    K(r,c) = K(c,r) = (double)k(samples[r], samples[c]);
            for (long r = 0; r < K.nr(); ++r)
                K(r,r) = 0;

            matrix<double,0,1> D(K.nr());
            for (long r = 0; r < K.nr(); ++r)
                D(r) = sum(rowm(K,r));
            D = sqrt(reciprocal(D));
            K = diagm(D)*K*diagm(D);
            matrix<double> u,w,v;
            // Use the normal SVD routine unless the matrix is really big, then use the fast
            // approximate version.
            if (K.nr() < 1000)
                svd3(K,u,w,v);
            else
                svd_fast(K,u,w,v, num_clusters+100, 5);
            // Pick out the eigenvectors associated with the largest eigenvalues.
            rsort_columns(v,w);
            v = colm(v, range(0,num_clusters-1));
            // Now build the normalized spectral vectors, one for each input vector.
            std::vector<matrix<double,0,1> > spec_samps, centers;
            for (long r = 0; r < v.nr(); ++r)
            {
                spec_samps.push_back(trans(rowm(v,r)));
                const double len = length(spec_samps.back());
                if (len != 0)
                    spec_samps.back() /= len;
            }
            // Finally do the K-means clustering
            pick_initial_centers(num_clusters, centers, spec_samps);
            find_clusters_using_kmeans(spec_samps, centers);
            // And then compute the cluster assignments based on the output of K-means.
            std::vector<unsigned long> assignments;
            for (unsigned long i = 0; i < spec_samps.size(); ++i)
                assignments.push_back(nearest_center(centers, spec_samps[i]));

            return assignments;
        }

    }

    #endif // DLIB_SPECTRAL_CLUSTEr_H_