function [rank_feat, ind_feat] = RfeRanking(alpha_Y, supp_vect, in_parameters)
% RfeRanking -- Feature ranking according to SVM's weights
%
% Usage:
%
% [rank_feat, ind_feat] = RfeRanking(alpha_Y, supp_vect, in_parameters)
%
% INPUTS:
%   
%   alpha_y         	: the AlphaY coefficients returned by SVMTrain()
%
%   supp_vect         	: the SVs returned by SVMTrain()
%
%   in_parameters   	: SVM's parameters (see SVMTrain() help)
%
% OUTPUTS:
%
%   rank_feat 	        : the features ranked according to their weights
%
%   ind_feat 	        : the index of each feature

% G. Palermo (giuseppe.palermo@bo.infn.it) and M. Masotti (matteo.masotti@bo.infn.it)
% Last Revision: 14 Oct 2004



% Checking the number of input arguments (min = 3)
if nargin < 3
    disp('Error: Incorrect number of input arguments');
    help RfeRanking;
    return
end



% Number of support vectors (N_sv) and number of features (N_feat)
[N_feat, N_sv] = size(supp_vect);

% Computation of the matrix H
H = ones(N_sv, N_sv);
gamma = in_parameters(3);
coefficient = in_parameters(4);
degree = in_parameters(2);
H = (gamma * (supp_vect' * supp_vect) + coefficient) .^ degree;

% Calculate the first term in the sum (fixed term)
DJ_1 = 0.5 * alpha_Y  * H * alpha_Y';

% Calculate the second term in the sum (the term varies according to the eliminated feature)
DJ_2 = ones(1,N_feat);
K = ones(N_sv, N_sv);
for i = 1:N_feat
    K = H - supp_vect(i,:)' * supp_vect(i,:);
    DJ_2(i) = 0.5 * alpha_Y  * K * alpha_Y';
end

% Calculate the weight of each feature
DJ = DJ_1 + DJ_2;

% Ranking considering the weight of each feature
[rank_feat, ind_feat] = sort(DJ);

% % Weights' plot
% t = 1:N_feat;
% plot(t,rank_feat);