```// Copyright (C) 2015  Davis E. King (davis@dlib.net)
#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_

```