generate_data.m

function [X, labels, t] = generate_data(dataname, n, noise)
%GENERATE_DATA Generates an artificial dataset (manifold)
%
%	[X, labels, t] = generate_data(dataname, n, noise)
%
% Generates an artificial dataset. Possible datasets are: 'swiss' for the Swiss roll
% dataset, 'helix' for the helix dataset, 'twinpeaks' for the twinpeaks dataset,
% '3d_clusters' for the 3D clusters dataset, and 'intersect' for the intersecting
% dataset. The variable n indicates the number of datapoints to generate 
% (default = 1000). The variable noise indicates the amount of noise that
% is added to the data (default = 0.05). The function returns the
% high-dimensional dataset in X, and corresponding labels in labels. In
% addition, the function returns the coordinates of the datapoints on the
% underlying manifold in t.
%
%

% This file is part of the Matlab Toolbox for Dimensionality Reduction.
% The toolbox can be obtained from http://homepage.tudelft.nl/19j49
% You are free to use, change, or redistribute this code in any way you
% want for non-commercial purposes. However, it is appreciated if you 
% maintain the name of the original author.
%
% (C) Laurens van der Maaten, Delft University of Technology


    welcome;
    
	if ~exist('n', 'var')
		n = 1000;
    end
    if ~exist('noise', 'var')
        noise = 0.05;
    end

	switch dataname
        case 'swiss'
            t = (3 * pi / 2) * (1 + 2 * rand(n, 1));  
            height = 30 * rand(n, 1);
            X = [t .* cos(t) height t .* sin(t)] + noise * randn(n, 3);
            %labels = uint8(t);
            labels = rem(sum([round(t / 2) round(height / 12)], 2), 2);
            t = [t height];
            
        case 'brokenswiss'
            t = [(3 * pi / 2) * (1 + 2 * rand(ceil(n / 2), 1) * .4); (3 * pi / 2) * (1 + 2 * (rand(floor(n / 2), 1) * .4 + .6))];  
            height = 30 * rand(n, 1);
            X = [t .* cos(t) height t .* sin(t)] + noise * randn(n, 3);
            labels = uint8(t);
            %labels = rem(sum([round(t / 2) round(height / 12)], 2), 2);
            t = [t height];
            
        case 'changing_swiss'
            r = zeros(1, n);
            for i=1:n
                pass = 0;
                while ~pass
                    rr = rand(1);
                    if rand(1) > rr
                        r(i) = rr;
                        pass = 1;
                    end
                end
            end
            t = (3 * pi / 2) * (1 + 2 * r);  
            height = 21 * rand(1, n);
            X = [t .* cos(t); height; t .* sin(t)]' + noise * randn(n, 3);
            %labels = uint8(t)';
            labels = rem(sum([round(t / 2); round(height / 10)], 1), 2)';
            
        case 'helix'
        	t = [1:n]' / n;
        	t = t .^ (1.0) * 2 * pi;
			X = [(2 + cos(8 * t)) .* cos(t) (2 + cos(8 * t)) .* sin(t) sin(8 * t)] + noise * randn(n, 3);
        	%labels = uint8(t);
            labels = rem(round(t * 1.5), 2);
            
        case 'twinpeaks'
            inc = 1.5 / sqrt(n);
            [xx2, yy2] = meshgrid(-1:inc:1);
            xy = 1 - 2 * rand(2, n);
            X = [xy; sin(pi * xy(1,:)) .* tanh(3 * xy(2,:))]' + noise * randn(n, 3);
            X(:,3) = X(:,3) * 10;
            t = xy';
            %labels = uint8(X(:,3));
            labels = rem(sum(round((X + repmat(min(X, [], 1), [size(X, 1) 1])) ./ 10), 2), 2);
            
        case '3d_clusters'
            numClusters = 5;
            centers = 10 * rand(numClusters, 3);
            D = L2_distance(centers', centers');
            minDistance = min(D(D > 0));
            k = 1;
            n2 = n - (numClusters - 1) * 9;
            X = repmat(0, [n 3]);
            labels = repmat(0, [n 1]);
            for i=1:numClusters
                for j=1:ceil(n2 / numClusters)
                   X(k, 1:3) = centers(i, 1:3) + (rand(1, 3) - 0.5) * minDistance / sqrt(12);
                   labels(k) = i;
                   k = k + 1;
                end
            end
            X = X + noise * randn(size(X, 1), 3);
            t = [];
            
        case 'intersect'
            t = [1:n]' ./ n .* (2 * pi);
            x = cos(t);
            y = sin(t);
            height = rand(length(x), 1) * 5;
            X = [x x .* y height] + noise * randn(n, 3);
            %labels = uint8(5 * t);
            labels = rem(sum([round(t / 2) round(height / 2)], 2), 2);
            
        case 'difficult'            
            % Generate underlying manifold
            no_dims = 5;
            no_points_per_dim = round(n ^ (1 / no_dims));
            l = linspace(0, 1, no_points_per_dim);
            t = combn(l, no_dims);
            
            % Generate high-dimensional dataset
            X = [cos(t(:,1)) tanh(3 * t(:,2)) t(:,1) + t(:,3) t(:,4) .* sin(t(:,2)) sin(t(:,1) + t(:,5)) t(:,5) .* cos(t(:,2)) t(:,5) + t(:,4) t(:,2) t(:,3) .* t(:,4) t(:,1)];
            X = X + noise * randn(size(X));
            
            % Generate labels for dataset (2x2x2x2x2 checkerboard pattern)
            tt = 1 + round(t);
            labels = rem(sum(tt, 2), 2);
            
		otherwise
			error('Unknown dataset name.');
	end