%GAUSS Generation of a multivariate Gaussian dataset
%
% A = GAUSS(N,U,G,LABTYPE)
%
% INPUT (in case of generation a 1-class dataset in K dimensions)
% N Number of objects to be generated (default 50).
% U Desired mean (vector of length K).
% G K x K covariance matrix. Default eye(K).
% LABTYPE Label type (default 'crisp')
%
% INPUT (in case of generation a C-class dataset in K dimensions)
% N Vector of length C with numbers of objects per class.
% U C x K matrix with class means, or
% Dataset with means, labels and priors of classes
% (default: zeros(C,K))
% G K x K x C covariance matrix of right size.
% Default eye(K);
% LABTYPE Label type (default 'crisp')
%
% OUTPUT
% A Dataset containing multivariate Gaussian data
%
% DESCRIPTION
% Generation of N K-dimensional Gaussian distributed samples for C classes.
% The covariance matrices should be specified in G (size K*K*C) and the
% means, labels and prior probabilities can be defined by the dataset U with
% size (C*K). If U is not a dataset, it should be a C*K matrix and A will
% be a dataset with C classes.
%
% If N is a vector, exactly N(I) objects are generated for class I, I = 1..C.
%
% EXAMPLES
% 1. Generation of 100 points in 2D with mean [1 1] and default covariance
% matrix:
%
% GAUSS(100,[1 1])
%
% 2. Generation of 50 points for each of two 1-dimensional distributions with
% mean -1 and 1 and with variances 1 and 2:
%
% GAUSS([50 50],[-1;1],CAT(3,1,2))
%
% Note that the two 1-dimensional class means should be given as a column
% vector [1;-1], as [1 -1] defines a single 2-dimensional mean. Note that
% the 1-dimensional covariance matrices degenerate to scalar variances,
% but have still to be combined into a collection of square matrices using
% the CAT(3,....) function.
%
% 3. Generation of 300 points for 3 classes with means [0 0], [0 1] and
% [1 1] and covariance matrices [2 1; 1 4], EYE(2) and EYE(2):
%
% GAUSS(300,[0 0; 0 1; 1 1]*3,CAT(3,[2 1; 1 4],EYE(2),EYE(2)))
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, PRDATASETS
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
function a = gauss(n,u,g,labtype)
if (nargin < 1)
prwarning (2,'number of samples not specified, assuming N = 50');
n = 50;
end
cn = length(n);
if (nargin < 2)
prwarning (2,'means not specified; assuming one dimension, mean zero');
u = zeros(cn,1);
end;
if (nargin < 3)
prwarning (2,'covariances not specified, assuming unity');
g = eye(size(u,2));
end
if (nargin < 4)
prwarning (3,'label type not specified, assuming crisp');
labtype = 'crisp';
end
% Return an empty dataset if the number of samples requested is 0.
if (length(n) == 1) & (n == 0)
a = prdataset([]);
return
end
% Find C, desired number of classes based on U and K, the number of
% dimensions. Make sure U is a dataset containing the means.
if (isa(u,'prdataset'))
[m,k,c] = getsize(u);
lablist = getlablist(u);
p = getprior(u);
if c == 0
u = double(u);
end
end
if isa(u,'double')
[m,k] = size(u);
c = m;
lablist = genlab(ones(c,1));
u = prdataset(u,lablist);
p = ones(1,c)/c;
end
if (cn ~= c) & (cn ~= 1)
error('The number of classes specified by N and U does not match');
end
% Generate a class frequency distribution according to the desired priors.
n = genclass(n,p);
% Find CG, the number of classes according to G.
% Make sure G is not a dataset.
if (isempty(g))
g = eye(k);
cg = 1;
else
g = real(+g); [k1,k2,cg] = size(g);
if (k1 ~= k) | (k2 ~= k)
error('The number of dimensions of the means U and covariance matrices G do not match');
end
if (cg ~= m & cg ~= 1)
error('The number of classes specified by the means U and covariance matrices G do not match');
end
end
% Create the data A by rotating and scaling standard normal distributions
% using the eigenvectors of the specified covariance matrices, and adding
% the means.
%a = [];
a = zeros(sum(n),k);
nn = 0;
for i = 1:m
j = min(i,cg); % Just in case CG = 1 (if G was not specified).
% Sanity check: user can pass non-positive definite G.
[V,D] = preig(g(:,:,j)); V = real(V); D = real(D); D = max(D,0);
a(nn+1:nn+n(i),:) = randn(n(i),k)*sqrt(D)*V' + repmat(+u(i,:),n(i),1);
%a = [a; randn(n(i),k)*sqrt(D)*V' + repmat(+u(i,:),n(i),1)];
nn = nn+n(i);
end
% Convert A to dataset by adding labels and priors.
labels = genlab(n,lablist);
a = prdataset(a,labels,'lablist',lablist,'prior',p);
% If non-crisp labels are requested, use output of Bayes classifier.
switch (labtype)
case 'crisp'
;
case 'soft'
w = nbayesc(u,g);
targets = a*w*classc;
a = setlabtype(a,'soft',targets);
otherwise
error(['Label type ' labtype ' not supported'])
end
a = setname(a,'Gaussian Data');
return