wolffd@0: function rmlr_demo()
wolffd@0: 
wolffd@0:     display('Loading Wine data');
wolffd@0:     load Wine;
wolffd@0: 
wolffd@0:     noisedim = 96;
wolffd@0:     [d,n] = size(X); 
wolffd@0:     d = d + noisedim;
wolffd@0: 
wolffd@0:     %create covariance matrix
wolffd@0:     var = randn(noisedim); var = var'*var;
wolffd@0:     noise = sqrtm(var)* randn(noisedim, n);
wolffd@0:     X = [X; noise];
wolffd@0:     
wolffd@0:     % z-score the input dimensions
wolffd@0:     display('z-scoring features');
wolffd@0:     X = zscore(X')';
wolffd@0: 
wolffd@0:     display('Generating a 80/20 training/test split');
wolffd@0:     P       = randperm(n);
wolffd@0:     Xtrain  = X(:,P(1:floor(0.8 * n)));
wolffd@0:     Ytrain  = Y(P(1:floor(0.8*n)));
wolffd@0:     Xtest   = X(:,P((1+floor(0.8*n)):end));
wolffd@0:     Ytest   = Y(P((1+floor(0.8*n)):end));
wolffd@0:     
wolffd@0:     C = 1e2;
wolffd@0:     lam = 0.5;
wolffd@0:    
wolffd@0:     display(sprintf('Training with C=%.2e, Delta=MAP', C));
wolffd@0:     %learn metric with R-MLR
wolffd@0:     [W_rmlr, Xi, Diagnostics_rmlr] = rmlr_train(Xtrain, Ytrain, C, 'map',3,1,0,0,lam);
wolffd@0:     
wolffd@0:     %learn metric with MLR
wolffd@0:     [W_mlr, Xi, Diagnostics_mlr] = mlr_train(Xtrain, Ytrain, C, 'map');
wolffd@0:     
wolffd@0:     display('Test performance in the native (normalized) metric');
wolffd@0:     mlr_test(eye(d), 3, Xtrain, Ytrain, Xtest, Ytest)
wolffd@0: 
wolffd@0:     display('Test performance with R-MLR metric');
wolffd@0:     mlr_test(W_rmlr, 3, Xtrain, Ytrain, Xtest, Ytest)
wolffd@0: 
wolffd@0:     display('Test performance with MLR metric');
wolffd@0:     mlr_test(W_mlr, 3, Xtrain, Ytrain, Xtest, Ytest)
wolffd@0: 
wolffd@0:     % Scatter-plot
wolffd@0:     figure;
wolffd@0:     subplot(1,3,1), drawData(eye(d), Xtrain, Ytrain, Xtest, Ytest), title('Native metric (z-scored)');
wolffd@0:     subplot(1,3,2), drawData(W_mlr, Xtrain, Ytrain, Xtest, Ytest), title('Learned metric (MLR)');
wolffd@0:     subplot(1,3,3), drawData(W_rmlr, Xtrain, Ytrain, Xtest, Ytest), title('Learned metric (RMLR)');
wolffd@0: 
wolffd@0:     figure;
wolffd@0:     subplot(121), imagesc(W_mlr), title('W: MLR');
wolffd@0:     subplot(122), imagesc(W_rmlr), title('W: RMLR');
wolffd@0:     Diagnostics_rmlr
wolffd@0:     Diagnostics_mlr
wolffd@0: 
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: function drawData(W, Xtrain, Ytrain, Xtest, Ytest);
wolffd@0: 
wolffd@0:     n = length(Ytrain);
wolffd@0:     m = length(Ytest);
wolffd@0: 
wolffd@0:     if size(W,2) == 1
wolffd@0:         W = diag(W);
wolffd@0:     end
wolffd@0:     % PCA the learned metric
wolffd@0:     Z = [Xtrain Xtest];
wolffd@0:     A = Z' * W * Z;
wolffd@0:     [v,d] = eig(A);
wolffd@0: 
wolffd@0:     L = (d.^0.5) * v';
wolffd@0:     L = L(1:2,:);
wolffd@0: 
wolffd@0:     % Draw training points
wolffd@0:     hold on;
wolffd@0:     trmarkers = {'b+', 'r+', 'g+'};
wolffd@0:     tsmarkers = {'bo', 'ro', 'go'};
wolffd@0:     for i = min(Ytrain):max(Ytrain)
wolffd@0:         points = find(Ytrain == i);
wolffd@0:         scatter(L(1,points), L(2,points), trmarkers{i});
wolffd@0:         points = n + find(Ytest == i);
wolffd@0:         scatter(L(1,points), L(2,points), tsmarkers{i});
wolffd@0:     end
wolffd@0:     legend({'Training', 'Test'});
wolffd@0: end