graphtools.data

[scottgigante]

graphtools should provide certain canonical manifold learning datasets.

MATLAB implementation courtesy of Nick Marshall

function [X,C,name] = benchmark(code,N,alpha)
% BENCHMARK   Generates manifold learning benchmark datasets.
%    [X,C,name] = benchmark(code,N,alpha) generates dataset X with color C and
%    description name. The inputs are the number of points N, and a parameter
%    ALPHA which will somehow deform the data set X. The code is an integer
%    1-10 which corresponds to one of the following:
%           1  'SwissRolll'
%           2  'SwissHole'
%           3  'CornerPlanes'
%           4  'PuncturedSphere'
%           5  'TwinPeaks'
%           6  'ToroidalHelix'
%           7  'GaussianExample'
%           8  'Uniform spaced ellipse'
%           9  'Uniform random ellipse'
%           10 'Barbell'

% Nicholas F Marshall - Dec 2015

    dataNames = {'swissroll','swisshole','cornerplanes',...
        'puncturedsphere','twinpeaks','toroidalhelix ',...
        'gaussianexample'};
    if isnumeric(code)
        exampleValue = code;
    else
        exampleValue = strmatch(lower(code),dataNames);
    end
    switch exampleValue
        case 1  % Swiss Roll
            tt = (3*pi/2)*(1+2*rand(1,N));  
            height = 21*rand(1,N);
            X = [tt.*cos(tt); height; alpha*tt.*sin(tt)]';
            C = tt';
            name = 'Swiss Rolll';
        case 2  % Swiss Hole
            % Swiss Roll w/ hole example taken from Donoho & Grimes
            tt = (3*pi/2)*(1+2*rand(1,2*N));  
            height = 21*rand(1,2*N);
            kl = zeros(1,2*N);
            for ii = 1:2*N
                if ( (tt(ii) > 9)&&(tt(ii) < 12))
                    if ((height(ii) > 9) && (height(ii) <14))
                        kl(ii) = 1;
                    end
                end
            end
            kkz = find(kl==0);
            tt = tt(kkz(1:N));
            height = height(kkz(1:N));
            X = [tt.*cos(tt); height; alpha*tt.*sin(tt)]';     
            C = tt';
            name = 'Swiss Hole';
        case 3  % Corner Planes
            k = 1;
            xMax = floor(sqrt(N))+1;
            yMax = floor(N/xMax);
            cornerPoint = floor(yMax/2);
            for x = 1:xMax
                for y = 1:yMax
                    if y <= cornerPoint
                        X(k,:) = [x,y,0];
                        C(k) = y;
                    else
                        X(k,:) = [x,...
                           cornerPoint+(y-cornerPoint)*cos(pi*alpha/180),...
                           (y-cornerPoint)*sin(pi*alpha/180)];
                        C(k) = y;
                    end
                    k = k+1;
                end
            end
            X = X;
            C = C';
            name = 'Corner Planes';
        case 4  % Punctured Sphere by Saul & Roweis
            inc = 9/sqrt(N);   %inc = 1/4;
            [xx,yy] = meshgrid(-5:inc:5);
            rr2 = xx(:).^2 + yy(:).^2;
            [tmp ii] = sort(rr2);
            Y = [xx(ii(1:N))'; yy(ii(1:N))'];
            a = 4./(4+sum(Y.^2));
            X = [a.*Y(1,:); a.*Y(2,:); alpha*2*(1-a)]';
            C = X(:,3);
            name = 'Punctured Sphere';
        case 5  % Twin Peaks by Saul & Roweis
            inc = 1.5 / sqrt(N);  % inc = 0.1;
            [xx2,yy2] = meshgrid(-1:inc:1);
            zz2 = sin(pi*xx2).*tanh(3*yy2);
            xy = 1-2*rand(2,N);
            X = [xy; sin(pi*xy(1,:)).*tanh(3*xy(2,:))]';
            X(:,3) = alpha * X(:,3);
            C = X(:,3);
            name = 'Twin Peaks';
        case 6  % Toroidal Helix by Coifman & Lafon
            noiseSigma=0.05;   %noise parameter
            t = (1:N)'/N;
            t = t.^(alpha)*2*pi;
            X = [(2+cos(8*t)).*cos(t) (2+cos(8*t)).*sin(t) sin(8*t)]+...
               noiseSigma*randn(N,3);
            C = t;
            name = 'Toroidal Helix ';
        case 7  % Gaussian randomly sampled
            X = alpha * randn(N,3);
            X(:,3) = 1 / (alpha^2 * 2 * pi) *...
                exp ( (-X(:,1).^2 - X(:,2).^2) / (2*alpha^2) );
            C = X(:,3);
            name = 'Gaussian example';
        case 8  % Uniform spaced ellipse
           theta =( (0:1/N:1-1/N)*2*pi)';
           X = [cos(theta) sin(theta)];
           C = theta;
           name = 'Uniformed spaced ellipse';
        case 9 % Uniform random ellipse
           theta =2*pi*rand(N,1);
           X = [cos(theta) sin(theta)];
           C =theta;
           name = 'Uniform random ellipse';
        case 10 % Barbell
           k = 1;
           while k<=N
               x = (2+alpha/2)*rand;
               y = (2+alpha/2)*rand;
               if (x-.5)^2+(y-.5)^2<=.25
                  X(k,:) = [x,y];
                  C(k,1) = 0;
                  k = k+1;
               elseif abs(x-1-alpha/4)<alpha/4 && abs(y-.5)<.125
                  X(k,:) = [x,y];
                  C(k,1) = 1;
                  k = k+1;
               elseif (x-1.5-alpha/2)^2+(y-.5)^2<=.25
                  X(k,:) = [x,y];
                  C(k,1) = 2;
                  k = k+1;
               end
           end 
           name = 'Barbell';
    end