function Model = EM_init( m, x )
% EM_init
%      initialization the probabilistic model parameters
%      Model = EM_init( m, x )
%      input
%         m : mixture number
%         x : reference data
%      output
%         Model : model structure
%
% *** scalar variance version ***

[ d, T ] = size( x ); % d : data dimension, T : data length

range = max( max(x) - min(x));
sigma = range * sqrt( m ) * 0.1;
sigma = 0.1;

Model.T = T;

for k = 1:m
  p.mu = x( :, floor( rand(1)*T + 1 ) );
  p.sigma = sigma;
  p.nu    = 1/m;
  r.z    = 1/m;
  r.zx   = p.mu;
  r.zx2 = eye(2)*sigma^2 + p.mu*p.mu';
  Model.p(k) = p;
  Model.r(k) = r;
end