%
% Plot the documents and terms on the same set of 2D axes after
% using a rank-2 approximation of the term-document matrix, to
% see where "clusters" might happen.

A = [...
0   1   0   1   1   0   1
0   1   1   0   0   0   0
0   0   0   0   0   1   1
0   0   0   1   0   0   0
0   1   1   0   0   0   0
1   0   0   1   0   0   0
0   0   0   0   1   1   0
0   0   1   1   0   0   0
1   0   0   1   0   0   0 ];

[m,n] = size(A);

for k = 1:n
	A(:,k) = A(:,k)/norm(A(:,k));
end

% -------------------------
% Compute the full SVD of A
% -------------------------

[U,S,V] = svd(A);

% -------------------------------------------
% Get the rank-2 approximation to A with SVD:
% -------------------------------------------
A2 = U(:,1:2)*S(1:2,1:2)*[V(:,1:2)]' ;

% -----------------------------------------------------------
% See what the terms and documents look like in reduced space
% -----------------------------------------------------------

docs = -U(:,1:2)'*A;
terms = -A*V(:,1:2);

plot(docs(1,:),   docs(2,:), 'b+', ...
     terms(:,1), terms(:,2), 'g*')
terms = terms';

% -------------------------------------
% Fudge factor to slightly shift points
% -------------------------------------
e = 0.05;
text(terms(1,1), terms(2,1), 'baby')
text(terms(1,2), terms(2,2)+e, 'child')
text(terms(1,3), terms(2,3), 'guide')
text(terms(1,4), terms(2,4), 'health')
text(terms(1,5), terms(2,5), 'home')
text(terms(1,6), terms(2,6), 'infant')
text(terms(1,7), terms(2,7)+e, 'proofing')
text(terms(1,8), terms(2,8), 'safety')
text(terms(1,9)-e, terms(2,9)+e, 'toddler')

text(docs(1,1), docs(2,1), 'D1')
text(docs(1,2), docs(2,2), 'D2')
text(docs(1,3), docs(2,3), 'D3')
text(docs(1,4), docs(2,4), 'D4')
text(docs(1,5), docs(2,5), 'D5')
text(docs(1,6), docs(2,6), 'D6')
text(docs(1,7), docs(2,7), 'D7')