% data characteristics
dim = 2;		% dimension of the inputs
N   = 10000;		% number of samples

x   = randn(N,dim);	% generate data
A   = [1 .1; 5 -.1];	% transformation matrix
vN  = 0.08;		% variance of added noise

nn= randn(N,dim);	% noise

% generating the outputs
z = (A * x')' + sqrt(vN)*nn;

% task:
% 1. Generate a THREE dimensional gaussian distribution which contains TWO
%    relevant directions.
%    You may choose 
%       the transformation matrix A and
%       the additive noise variance
% 2. Display the cloud of sampled points and ensure that MOST of the data
%    is in a lower-dimensional subspace.
% 3. Find the relevant directions.
