협업 필터링(Collaborative Filtering) 예제

% Collaborative Filtering
% 2014. 8. 29
% refopen.blogspot.com

A = [9 2 1 8;
    8 5 6 10;
    7 9 8 9;
    2 3 4 8;
    5 9 5 7];

rank = 2;

m = mean(A, 2);
s = std(A, 1, 2);
matm = repmat(m, 1, 4);
mats = repmat(s, 1, 4);

% normalization
normA = (A - matm) ./ mats;

[u d v] = svd(normA)

vt = v';
temp = u(:, 1:rank)*d(1:rank, 1:rank)*vt(1:rank, :)

% denormalization
Ahat = matm + (temp .* mats)

u =

   -0.5699   -0.1579   -0.5892   -0.5351   -0.1297
   -0.5471   -0.3829   -0.0037    0.7322   -0.1339
    0.3887   -0.5537    0.0504   -0.1310   -0.7230
   -0.1319   -0.6232    0.4847   -0.3305    0.5001
    0.4554   -0.3654   -0.6445    0.2261    0.4388


d =

    3.0336         0         0         0
         0    2.9144         0         0
         0         0    1.5179         0
         0         0         0    0.0000
         0         0         0         0


v =

   -0.5690    0.4985   -0.4216    0.5000
    0.7368   -0.0436   -0.4530    0.5000
    0.1603    0.3410    0.7798    0.5000
   -0.3281   -0.7958    0.0948    0.5000


temp =

    0.7543   -1.2537   -0.4339    0.9334
    0.3882   -1.1743   -0.6465    1.4326
   -1.4753    0.9392   -0.3612    0.8973
   -0.6777   -0.2156   -0.6834    1.5767
   -1.3170    1.0644   -0.1417    0.3943


Ahat =

    7.6667    0.5676    3.4658    8.2999
    7.9954    4.9950    6.0085   10.0010
    7.0268    9.0288    7.9505    8.9940
    2.7065    3.7590    2.6934    7.8411
    4.3160    8.2652    6.2650    7.1538

Published with MATLAB® R2013b