visualize.m

% Visualization of Gaussian embeddings
% Requires LSSVMlab already imported: http://www.esat.kuleuven.be/sista/lssvmlab/
%
% The three files generated by the binary2text tool are needed:
% Means of the distributions: embeddings.bin_mu.txt
% Covariance matrices: embeddings.bin_sigma.txt
% Vocabulary: embeddings.bin_words.txt

MU = import_vectors('embeddings.bin_mu.txt', 1);
SIGMA = import_vectors('embeddings.bin_sigma.txt', 1);
vocab = import_words('embeddings.bin_words.txt',1);

%Example to show "Madrid"-"Spain"+"France" ~ "Paris"
words = {'madrid' 'paris' 'spain' 'france'};
colors={'r' 'g' 'b' 'c' 'm' 'y' 'k'};
vectors = [];
variances = [];
for w = words
    i = find(strcmp(vocab,w));
    vectors = [vectors ; MU(i,:)];
    variances = [variances ; SIGMA(i,:)];
end


% calculate the eigenvectors in the feature space (principal components)
sig2 = 50;
[U,V] = kpca(vectors','RBF_kernel',sig2,[],'eigs', 2,'o');
%[U,V] = kpca(vectors','lin_kernel',[],[],'eigs', 2);


% calculate the projections on the principal components
 Xax = -3:.1:3; Yax = -3.2:.1:3.2;
 [A,B] = meshgrid(Xax,Yax);
 grid = [reshape(A,prod(size(A)),1) reshape(B,1,prod(size(B)))'];
 mu_projections = vectors*V;
 
 figure;
 x = -5:.1:5; %// x axis
y = -4:.1:4; %// y axis
[X Y] = meshgrid(x,y); %// all combinations of x, y
 sigma_projections = [];
 color_i = 1;
 for i=1:length(words)
    sigma_projections = V'*diag(variances(i,:))*V; 
    Z = mvnpdf([X(:) Y(:)],mu_projections(i,:),sigma_projections); %// compute Gaussian pdf
    Z = reshape(Z,size(X)); %// put into same size as X, Y
    
    contour(X,Y,Z, [0.05 0.05],  colors{color_i}), axis equal  %// contour plot; set same scale for x and y...        
    text(mu_projections(i,1),mu_projections(i,2), words(i), 'color', colors{color_i} );
    color_i =  mod(color_i, length(colors)) +1;    
    disp(words(i));
    disp(prod(sigma_projections(:)));
    hold on
end
hold off