% [ K, D2, NN, [D2full] ] = graphDistKernel( X, D2, NN, idxSet, param, [D2full] )% computes a kernel matrix 'K' based on graph distances.%% INPUT / OUTPUT:%   X       double[d*m]  'm' data points in Euclidean 'd'-space%   D2     double[nn*m]  distances of 'm' data points to 'nn' respective nearest neighbors%   NN      int32[nn*m]  indices of 'nn' nearest neighbors for each of 'm' data points%   idxSet  double[1*l]  indices of subset for which kernel matrix rows will be computed%   D2full  double[m*m]  full matrix of pairwise distances%   K       double[m*l]  resulting kernel matrix%   param        struct of parameters%     .pathNorm  norm used for path distance computation%                NOTE: distances will be normalized before%     .nofNn     number of nearest neighbors; 0 for full graph%     .annEps    allowed approximation error for approx. nearest neighbor;%                if <0 then the full distance matrix will be sorted%     .rbf       name of rbf: 'gauss', 'laplace'%     .sigma     kernel width; +inf for matrix of squared path distances%                NOTE: taken relative to "default" sigma% % USAGE:%   graphDistKernel( X,  D2, NN, idxSet, param )%   graphDistKernel( [], D2, NN, idxSet, param )%     'NN' and 'D2' will be used as given.%   graphDistKernel( X, [], [], idxSet, param )%     'NN' and 'D2' will be computed from 'X'.%   graphDistKernel( [], [], [], idxSet, param, D2full )%     'NN' and 'D2' will be computed from 'D2full', if 'param.annEps' < 0.% % (C) A. Zien and O. Chapelle, MPI for biol. Cybernetics, Germanyfunction [ K, D2, NN, D2full ] = graphDistKernelC( X, D2, NN, idxSet, param, D2full );% ==== check inputassert( 5 <= nargin & nargin <= 6 );assert( 0 <= param.pathNorm );assert( 0 <= param.nofNn );assert( 0 < param.sigma && param.sigma <= +inf );if( ~ exist( 'D2full', 'var' ) )  D2full = [];end;% --- check NN and D2, if suppliedif( length(D2) ~= 0 )  if( param.nofNn == 0 )    [ m, m_ ] = size( D2 );    assert( m == m_ );    assert( length(NN) == 0 );  else    [ nofNn, m ] = size( D2 );    assert( nofNn == param.nofNn );    assert( size(NN,1) == nofNn );    assert( size(NN,2) == m );  end;  if( length(X) ~= 0 )    assert( size(X,2) == m );  end;end;% === compute nearest neighbors (NN) and squared distances (D2)if( length(D2) == 0 )  assert( length(NN) == 0 );  [ NN, D2 ] = calcNnDists( X, D2full, param.nofNn, param.annEps );end;% === compute matrix of squared path distances (E2)meanD2 = mean( sqrt( D2(:) ) ) ^ 2;if( param.pathNorm == 0 & param.nofNn == 0 & 0 )  % - for pathNorm==0, the direct connection is always shortest  E2 = D2( :, idxSet ) / meanD2;else  E2 = rhoPathDists2( D2/meanD2, NN, idxSet, param.pathNorm );end;% --- return path distance matrix?if( param.sigma == +inf )  K = E2;  %%% % --- symmetrize distances  %%% if( param.nofNn ~= 0 )  %%%   %K(idxSet,:) = min( K(idxSet,:), K(idxSet,:)' );  %%%   K(idxSet,:) = ( K(idxSet,:) + K(idxSet,:)' ) ./ 2;  %%% end;  return;end;% === choose default kernel width (sigma)k = length( param.ks );sigma = param.sigma * calcDefaultSigma( E2(:), k );% === compute kernel matrix (K)mustSymmetrize = param.nofNn ~= 0;K = calcRbfKernel( E2, param.rbf, sigma, mustSymmetrize );