Daniel@0: % Compare my code with
Daniel@0: % http://www.media.mit.edu/physics/publications/books/nmm/files/index.html
Daniel@0: %
Daniel@0: % cwm.m
Daniel@0: % (c) Neil Gershenfeld  9/1/97
Daniel@0: % 1D Cluster-Weighted Modeling example
Daniel@0: %
Daniel@0: clear all
Daniel@0: figure;
Daniel@0: seed = 0;
Daniel@0: rand('state', seed);
Daniel@0: randn('state', seed);
Daniel@0: x = (-10:10)';
Daniel@0: y = (x > 0);
Daniel@0: npts = length(x);
Daniel@0: plot(x,y,'+')
Daniel@0: xlabel('x')
Daniel@0: ylabel('y')
Daniel@0: nclusters = 4;
Daniel@0: nplot = 100;
Daniel@0: xplot = 24*(1:nplot)'/nplot - 12;
Daniel@0: 
Daniel@0: mux = 20*rand(1,nclusters) - 10;
Daniel@0: muy = zeros(1,nclusters);
Daniel@0: varx = ones(1,nclusters);
Daniel@0: vary = ones(1,nclusters);
Daniel@0: pc = 1/nclusters * ones(1,nclusters);
Daniel@0: niterations = 5;
Daniel@0: eps = 0.01;
Daniel@0:   
Daniel@0: 
Daniel@0: I = repmat(eye(1,1), [1 1 nclusters]);
Daniel@0: O = repmat(zeros(1,1), [1 1 nclusters]);
Daniel@0: X = x(:)';
Daniel@0: Y = y(:)';
Daniel@0: 
Daniel@0: cwr = cwr_em(X, Y, nclusters, 'muX', mux, 'muY', muy,  'SigmaX', I, ...
Daniel@0: 	     'cov_typeX', 'spherical', 'SigmaY', I, 'cov_typeY', 'spherical', ...
Daniel@0: 	     'priorC', pc, 'weightsY', O,  'create_init_params', 0, ...
Daniel@0: 	     'clamp_weights', 1, 'max_iter', niterations, ...
Daniel@0: 	     'cov_priorX', eps*ones(1,1,nclusters), ...
Daniel@0: 	     'cov_priorY', eps*ones(1,1,nclusters));
Daniel@0: 
Daniel@0: 
Daniel@0: % Gershenfeld's EM code
Daniel@0: for step = 1:niterations
Daniel@0:     pplot = exp(-(kron(xplot,ones(1,nclusters)) ...
Daniel@0: 		  - kron(ones(nplot,1),mux)).^2 ...
Daniel@0: 		./ (2*kron(ones(nplot,1),varx))) ...
Daniel@0: 	    ./ sqrt(2*pi*kron(ones(nplot,1),varx)) ...
Daniel@0: 	    .* kron(ones(nplot,1),pc);
Daniel@0:     plot(xplot,pplot,'k');
Daniel@0:     pause(0);
Daniel@0:     px = exp(-(kron(x,ones(1,nclusters)) ...
Daniel@0: 	       - kron(ones(npts,1),mux)).^2 ...
Daniel@0: 	     ./ (2*kron(ones(npts,1),varx))) ...
Daniel@0: 	 ./ sqrt(2*pi*kron(ones(npts,1),varx));
Daniel@0:     py = exp(-(kron(y,ones(1,nclusters)) ...
Daniel@0: 	       - kron(ones(npts,1),muy)).^2 ...
Daniel@0: 	     ./ (2*kron(ones(npts,1),vary))) ...
Daniel@0: 	 ./ sqrt(2*pi*kron(ones(npts,1),vary));
Daniel@0:     p = px .* py .* kron(ones(npts,1),pc);
Daniel@0:     pp = p ./ kron(sum(p,2),ones(1,nclusters));
Daniel@0:     pc = sum(pp)/npts;
Daniel@0:     yfit = sum(kron(ones(npts,1),muy) .* p,2) ...
Daniel@0: 	   ./ sum(p,2);
Daniel@0:     mux = sum(kron(x,ones(1,nclusters)) .* pp) ...
Daniel@0: 	  ./ (npts*pc);
Daniel@0:     varx = eps + sum((kron(x,ones(1,nclusters)) ...
Daniel@0: 		      - kron(ones(npts,1),mux)).^2 .* pp) ...
Daniel@0: 	   ./ (npts*pc);
Daniel@0:     muy = sum(kron(y,ones(1,nclusters)) .* pp) ...
Daniel@0: 	  ./ (npts*pc);
Daniel@0:     vary = eps + sum((kron(y,ones(1,nclusters)) ...
Daniel@0: 		      - kron(ones(npts,1),muy)).^2 .* pp) ...
Daniel@0: 	   ./ (npts*pc);
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: % Check equal
Daniel@0: cwr_pc = cwr.priorC';
Daniel@0: assert(approxeq(cwr_pc, pc))
Daniel@0: cwr_mux = cwr.muX;
Daniel@0: assert(approxeq(mux, cwr_mux))
Daniel@0: cwr_SigmaX = squeeze(cwr.SigmaX)';
Daniel@0: assert(approxeq(varx, cwr_SigmaX))
Daniel@0: cwr_muy = cwr.muY;
Daniel@0: assert(approxeq(muy, cwr_muy))
Daniel@0: cwr_SigmaY = squeeze(cwr.SigmaY)';
Daniel@0: assert(approxeq(vary, cwr_SigmaY))
Daniel@0: 
Daniel@0: 
Daniel@0: % Prediction
Daniel@0: 
Daniel@0: X = xplot(:)';
Daniel@0: [cwr_mu, Sigma, post] = cwr_predict(cwr, X);
Daniel@0: cwr_ystd = squeeze(Sigma)';
Daniel@0: 
Daniel@0: % pplot(t,c)
Daniel@0: pplot = exp(-(kron(xplot,ones(1,nclusters)) ...
Daniel@0:    - kron(ones(nplot,1),mux)).^2 ...
Daniel@0:    ./ (2*kron(ones(nplot,1),varx))) ...
Daniel@0:    ./ sqrt(2*pi*kron(ones(nplot,1),varx)) ...
Daniel@0:    .* kron(ones(nplot,1),pc);
Daniel@0: yplot = sum(kron(ones(nplot,1),muy) .* pplot,2) ...
Daniel@0:    ./ sum(pplot,2);
Daniel@0: ystdplot = sum(kron(ones(nplot,1),(muy.^2+vary)) .* pplot,2) ...
Daniel@0:    ./ sum(pplot,2) - yplot.^2;
Daniel@0: 
Daniel@0: 
Daniel@0: % Check equal
Daniel@0: assert(approxeq(yplot(:)', cwr_mu(:)'))
Daniel@0: assert(approxeq(ystdplot, cwr_ystd))
Daniel@0: assert(approxeq(pplot ./ repmat(sum(pplot,2), 1, nclusters),post') )
Daniel@0: 
Daniel@0: plot(xplot,yplot,'k');
Daniel@0: hold on
Daniel@0: plot(xplot,yplot+ystdplot,'k--');
Daniel@0: plot(xplot,yplot-ystdplot,'k--');
Daniel@0: plot(x,y,'k+');
Daniel@0: axis([-12 12 -1 1.1]);
Daniel@0: plot(xplot,.8*pplot/max(max(pplot))-1,'k')
Daniel@0: hold off
Daniel@0: