fs1.m

wekaUT是 university texas austin 开发的基于weka的半指导学习(semi supervised learning)的分类器

function fs_1st_d = fS1(X, S, A, N, d)

% the gradient of the similarity constraint function w.r.t. A
% f = \sum_{ij}(x_i-x_j)A(x_i-x_j)' = \sum_{ij}d_ij*A*d_ij'
% df/dA = d(d_ij*A*d_ij')/dA
%
% note that d_ij*A*d_ij' = tr(d_ij*A*d_ij') = tr(d_ij'*d_ij*A)
% so, d(d_ij*A*d_ij')/dA = d_ij'*d_ij

%[N d] = size(X);
fs_1st_d = zeros(d,d); 

fudge = 0.000001;  % regularizes derivates a little if necessary

for i = 1:N
  for j= i+1:N
    if S(i,j) == 1
      d_ij = X(i,:) - X(j,:);
      % distij = d_ij * A * d_ij';         % distance between 'i' and 'j'    
      % full first derivative of the distance constraints
      fs_1st_d = fs_1st_d + d_ij'*d_ij;
    end  
  end
end