/**
* Obtains no more than maxNumSamples distinct samples. Each sample belongs to
* [loInclusive, hiExclusive).
*
* @param loInclusive The lower bound (inclusive).
* @param hiExclusive The high bound (exclusive).
* @param maxNumSamples The maximum number of samples to obtain.
* @param distinctSamples The samples that will be obtained.
*/
inline void ObtainDistinctSamples(const size_t loInclusive,
const size_t hiExclusive,
const size_t maxNumSamples,
arma::uvec& distinctSamples)
{
const size_t samplesRangeSize = hiExclusive - loInclusive;
if (samplesRangeSize > maxNumSamples)
{
arma::Col<size_t> samples;
samples.zeros(samplesRangeSize);
for (size_t i = 0; i < maxNumSamples; i++)
samples [ (size_t) math::RandInt(samplesRangeSize) ]++;
distinctSamples = arma::find(samples > 0);
if (loInclusive > 0)
distinctSamples += loInclusive;
}
else
{
distinctSamples.set_size(samplesRangeSize);
for (size_t i = 0; i < samplesRangeSize; i++)
distinctSamples[i] = loInclusive + i;
}
}
///
/// \brief Vespucci::Math::DimensionReduction::VCA
/// Vertex Component Analysis
/// \param R The dataset
/// \param endmembers Number of endmembers to compute
/// \param indices Row indices of pure components.
/// \param endmember_spectra Spectra of pure components (note that these are in
/// columns, not rows as in spectra_)
/// \param projected_data Projected data
/// \param fractional_abundances Purity of a given spectrum relative to endmember
/// \return Convergeance (no actual test implemented...)
///
bool Vespucci::Math::DimensionReduction::VCA(const arma::mat &R, arma::uword p,
arma::uvec &indices, arma::mat &endmember_spectra,
arma::mat &projected_data, arma::mat &fractional_abundances)
{
//Initializations
arma::uword L = R.n_rows;
arma::uword N = R.n_cols;
if (L == 0 || N == 0){
std::cerr << "No data!" << std::endl;
return false;
}
if (p > L){
std::cerr << "wrong number of endmembers (" << p << ")!"<< std::endl;
std::cerr << "set to 5 or one less than number of spectra" << std::endl;
p = (L < 5? 5: L-1);
}
//mat of SNR
arma::mat r_m = mean(R, 1);
arma::mat R_m = arma::repmat(r_m, 1, N); //the mean of each spectral band
arma::mat R_o = R - R_m; //mean-center the data
arma::mat Ud;
arma::vec Sd;
arma::mat Vd;
//arma::svds(Ud, Sd, Vd, arma::sp_mat(R_o * R_o.t()/N), p);
Vespucci::Math::DimensionReduction::svds(R_o*R_o.t()/N, p, Ud, Sd, Vd);
arma::mat x_p;
try{
x_p = Ud.t() * R_o;
}catch(std::exception e){
std::cout << "Ud.t() * R_o" << std::endl;
}
double SNR = Vespucci::Math::DimensionReduction::estimate_snr(R, r_m, x_p);
double SNR_th = 15 + 10*log10(p);
//Choose projective projection or projection to p-1 subspace
arma::mat y;
if (SNR < SNR_th){
arma::uword d = p - 1;
Ud = Ud.cols(0, d-1);
projected_data = Ud * x_p.rows(0, d-1) + R_m; //in dimension L
arma::mat x = x_p.rows(0, d-1);//x_p = trans(Ud)*R_o, p-dimensional subspace
//following three lines are one in arma::matlab...
arma::mat sum_squares = sum(pow(x, 2));
double c = sum_squares.max();
c = std::sqrt(c);
y = arma::join_vert(x, c*arma::ones(1, N));
}
else{
arma::uword d = p;
Vespucci::Math::DimensionReduction::svds(R*R.t()/N, p, Ud, Sd, Vd);
arma::svds(Ud, Sd, Vd, arma::sp_mat(R*R.t()/N), d);//R_o is a mean centered version...
x_p = Ud.t() * R;
projected_data = Ud * x_p.rows(0, d-1);
arma::mat x = Ud.t() * R;
arma::mat u = arma::mean(x, 1);
y = x / arma::repmat(sum(x % arma::repmat(u, 1, N)), d, 1);
}
// The VCA algorithm
arma::vec w;
w.set_size(p);
arma::vec f;
arma::rowvec v;
indices.set_size(p);
//there are no fill functions for arma::uvecs
for (arma::uword i = 0; i < p; ++i)
indices(i) = 0;
arma::mat A = arma::zeros(p, p);
double v_max;
double sum_squares;
arma::uvec q1;
A(p-1, 0) = 1;
for (arma::uword i = 0; i < p; ++i){
w.randu();
f = w - A*arma::pinv(A)*w;
sum_squares = sqrt(sum(square(f)));
f /= sum_squares;
v = f.t() * y;
v_max = arma::max(abs(v));
q1 = arma::find(abs(v) == v_max, 1);
indices(i) = q1(0);
A.col(i) = y.col(indices(i)); //same as x.col(indices(i));
}
endmember_spectra = projected_data.cols(indices);
fractional_abundances = arma::trans(pinv(endmember_spectra) * projected_data);
return true;
}