function mappedX = isomap(X, no_dims, k); %ISOMAP Runs the Isomap algorithm%%   mappedX = isomap(X, no_dims, k); %% The functions runs the Isomap algorithm on dataset X to reduce the% dimensionality of the dataset to no_dims. The number of neighbors used in% the compuations is set by k (default = 12). This implementation does not% use the Landmark-Isomap algorithm.%% If the neighborhood graph that is constructed is not completely% connected, only the largest connected component is embedded.%%% This file is part of the Matlab Toolbox for Dimensionality Reduction v0.1b.% The toolbox can be obtained from http://www.cs.unimaas.nl/l.vandermaaten% You are free to use, change, or redistribute this code in any way you% want. However, it is appreciated if you maintain the name of the original% author.%% (C) Laurens van der Maaten% Maastricht University, 2007    if ~exist('no_dims')        no_dims = 2;    end    if ~exist('k')        k = 12;    end    % Construct neighborhood graph    disp('Constructing neighborhood graph...');     D = find_nn(X, k);    % Select largest connected component    blocks = components(D)';    count = zeros(1, max(blocks));    for i=1:max(blocks)        count(i) = length(find(blocks == i));    end    [count, block_no] = max(count);    conn_comp = find(blocks == block_no);    D = D(conn_comp,:);    D = D(:,conn_comp);    n = size(D, 1);    % Compute shortest paths    disp('Computing shortest paths...');    D = dijkstra(D, [1:n]);        % Performing MDS using eigenvector implementation    disp('Constructing low-dimensional embedding...');    M = -.5 * (D .^ 2 - sum(D .^ 2)' * ones(1, n) / n - ones(n, 1) * sum(D .^ 2) / n + sum(sum(D .^ 2)) / (n ^ 2));	M(isnan(M)) = 0;	M(isinf(M)) = 0;    [vec, val] = eig(M);	if size(vec, 2) < no_dims		no_dims = size(vec, 2);		warning(['Target dimensionality reduced to ' num2str(no_dims) '...']);	end	    % Computing final embedding    h = real(diag(val));     [foo, sorth] = sort(h, 'descend');      val = real(diag(val(sorth, sorth)));     vec = vec(:,sorth);    mappedX = real(vec(:,1:no_dims) .* (ones(n, 1) * sqrt(val(1:no_dims))'));