wolffd@0: % Verify that my code gives the same results as the 1D example at
wolffd@0: % http://www.media.mit.edu/physics/publications/books/nmm/files/cwm.m
wolffd@0: 
wolffd@0: seed = 0;
wolffd@0: rand('state', seed);
wolffd@0: randn('state', seed);
wolffd@0: x = (-10:10)';
wolffd@0: y = double(x > 0);
wolffd@0: npts = length(x);
wolffd@0: plot(x,y,'+')
wolffd@0: 
wolffd@0: nclusters = 4;
wolffd@0: nplot = 100;
wolffd@0: xplot = 24*(1:nplot)'/nplot - 12;
wolffd@0: 
wolffd@0: mux = 20*rand(1,nclusters) - 10;
wolffd@0: muy = zeros(1,nclusters);
wolffd@0: varx = ones(1,nclusters);
wolffd@0: vary = ones(1,nclusters);
wolffd@0: pc = 1/nclusters * ones(1,nclusters);
wolffd@0: 
wolffd@0: 
wolffd@0: I = repmat(eye(1,1), [1 1 nclusters]);
wolffd@0: O = repmat(zeros(1,1), [1 1 nclusters]);
wolffd@0: X = x(:)';
wolffd@0: Y = y(:)';
wolffd@0: 
wolffd@0: % Do 1 iteration of EM
wolffd@0: 
wolffd@0: %cwr = cwr_em(X, Y, nclusters, 'muX', mux, 'muY', muy,  'SigmaX', I, 'cov_typeX', 'spherical', 'SigmaY', I, 'cov_typeY', 'spherical', 'priorC', pc, 'weightsY', O,  'init_params', 0, 'clamp_weights', 1, 'max_iter', 1, 'cov_priorX', zeros(1,1,nclusters), 'cov_priorY', zeros(1,1,nclusters));
wolffd@0: 
wolffd@0: cwr = cwr_em(X, Y, nclusters, 'muX', mux, 'muY', muy,  'SigmaX', I, 'cov_typeX', 'spherical', 'SigmaY', I, 'cov_typeY', 'spherical', 'priorC', pc, 'weightsY', O,  'create_init_params', 0, 'clamp_weights', 1, 'max_iter', 1);
wolffd@0: 
wolffd@0: 
wolffd@0: % Check this matches Gershenfeld's code
wolffd@0: 
wolffd@0: % E step
wolffd@0: % px(t,c) = prob(x(t) | c)
wolffd@0: px = exp(-(kron(x,ones(1,nclusters)) ...
wolffd@0: 	   - kron(ones(npts,1),mux)).^2 ...
wolffd@0: 	 ./ (2*kron(ones(npts,1),varx))) ...
wolffd@0:      ./ sqrt(2*pi*kron(ones(npts,1),varx));
wolffd@0: py = exp(-(kron(y,ones(1,nclusters)) ...
wolffd@0: 	   - kron(ones(npts,1),muy)).^2 ...
wolffd@0: 	 ./ (2*kron(ones(npts,1),vary))) ...
wolffd@0:      ./ sqrt(2*pi*kron(ones(npts,1),vary));
wolffd@0: p = px .* py .* kron(ones(npts,1),pc);
wolffd@0: pp = p ./ kron(sum(p,2),ones(1,nclusters));
wolffd@0: 
wolffd@0: % M step
wolffd@0: eps = 0.01;
wolffd@0: pc2 = sum(pp)/npts;
wolffd@0: 
wolffd@0: mux2 = sum(kron(x,ones(1,nclusters)) .* pp) ...
wolffd@0:       ./ (npts*pc2);
wolffd@0: varx2 = eps + sum((kron(x,ones(1,nclusters)) ...
wolffd@0: 		  - kron(ones(npts,1),mux2)).^2 .* pp) ...
wolffd@0:        ./ (npts*pc2);
wolffd@0: muy2 = sum(kron(y,ones(1,nclusters)) .* pp) ...
wolffd@0:       ./ (npts*pc2);
wolffd@0: vary2 = eps + sum((kron(y,ones(1,nclusters)) ...
wolffd@0: 		  - kron(ones(npts,1),muy2)).^2 .* pp) ...
wolffd@0:        ./ (npts*pc2);
wolffd@0: 
wolffd@0: 
wolffd@0: denom = (npts*pc2);
wolffd@0: % denom(c) = N*pc(c) = w(c) = sum_t pp(c,t)
wolffd@0: % since pc(c) = sum_t pp(c,t) / N
wolffd@0: 
wolffd@0: cwr_mux = cwr.muX;
wolffd@0: assert(approxeq(mux2, cwr_mux))
wolffd@0: cwr_SigmaX = squeeze(cwr.SigmaX)';
wolffd@0: assert(approxeq(varx2, cwr_SigmaX))
wolffd@0: 
wolffd@0: cwr_muy = cwr.muY;
wolffd@0: assert(approxeq(muy2, cwr_muy))
wolffd@0: cwr_SigmaY = squeeze(cwr.SigmaY)';
wolffd@0: assert(approxeq(vary2, cwr_SigmaY))
wolffd@0: 
wolffd@0: