Optimal Sub-sampled Population with Max Expansion and Min Projection Error

A subsample of an input population that has max pair-distance and min projection error

% 150525: Reza Farrahi Moghaddam ([e-mail]) (May 25th, 2015)
% Optimal Sub-sampled Population with Max Expansion and Min Projection Error
%
% This function searches for a subsample of an input population that has
% maximum pair-distance in all neighborhoods. Also, it minimizes the
% projection error of the input population on the output subsampled
% population. The size of a neighborhood should be higher than 1.
%
% Syntax:
% [spectra_2D_Sampled, spectra_2D_Sampled_index, spectra_2D_Sampled_allProjected_global] = Subsample_MaxNeighborDistance_R(spectra_2D, subsample_size, neighborhood_size)
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% spectra_2D: Input population
% subsample_size: The size of subsampled required
% neighborhood_size: Size of neighborhood (including the center) used in calculations
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% spectra_2D_Sampled: Output subsampled population
% spectra_2D_Sampled_index: Indices of the output subsampled population in the input population
% spectra_2D_Sampled_allProjected_global: 1-NN projection of the input population onto the output subsampled population
%