Matrix Factorization in recommendation system

0

Hi, I am trying to learn latent models in recommendation systems which is nothing but factorization of a user-item matrix. I was going thru this slides http://www.hpi.uni-potsdam.de/fileadmin/hpi/FG_Naumann/lehre/SS2011/Collaborative_Filtering/pres1-matrixfactorization.pdf

In slide 6: They decomposed a matrix M (user-item matrix) into = user feature matrix *movie feature matrix

And they say they did SVD but isnt SVD suppose to give three matrices U,S,V? If I plug the values in octave, I get this as SVD decomposition of that matrix:

u =

-0.825066 -0.047735 -0.563016
-0.443084 -0.563669 0.697104
-0.350631 0.824620 0.443914

s =

Diagonal Matrix

9.2654 0 0

    0   3.2340        0

    0        0   1.3016

v =

-0.636527 -0.770982 -0.020485
-0.476317 0.372083 0.796666
-0.606593 0.516857 -0.604073

How did the author got those values? :( Please suggest Thanks

asked Jan 01 '13 at 03:57

Jamal's gravatar image

Jamal
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edited Jan 01 '13 at 04:10

One Answer:
oldest newest most voted
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The middle matrix of an SVD is diagonal and only serves to allow the features in other 2 matrices to be scaled to have unit variance. It does not really carry any information about the users or items. So they may just multiply one of the other 2 by it.

answered Jan 01 '13 at 15:08

Daniel%20Mahler's gravatar image

Daniel Mahler
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