update

DataGeneration/generateManifold.m

+function [X, labels, t] = generateManifold(dataname, n, noise)
+%GENERATE_DATA Generates an artificial dataset (manifold)
+%
+%	[X, labels, t] = generateManifold(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