Database Reference
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regularization with a resulting increase of quality by removing noise from the data.
It is also possible to develop incremental factorization models such as the Brand's
incremental SVD.
At the same time, the difficulties related to factorization for recommendation
engines have clearly emerged. First, it has unequivocally turned out that the
SVD-based factorization of the matrix of transition probabilities is effective with
respect to neither of data compression nor increase of prediction rates. The only
advantage consists in the opportunity of generating new recommendations by virtue
of the low-rank approximation. A factorization of transactions over the sessions has
turned out to be sensible, especially with regard to an increase of the prediction rate,
but the yield was rather poor and, moreover, required longer sessions, which rarely
occur in practice.
Modified formulations did not seem to help very much. Especially the nonneg-
ative matrix factorization and the one based on Lanczos vectors did (in line with
theory) lead to even worse prediction results than the SVD. Whereas the Lanczos
vector calculation is at least cheaper than the SVD, for the NMF no comparable
standard algorithms exist. In practice, here the ALS turns out to be most powerful.
We also studied and validated the matrix completion approach, which considers all
non-observed transitions to be unknown instead of zero. However, practical results
turned out to be even worse.
All in all, we must conclude that the direct matrix factorization barely gives rise
to a significant improvement of the prediction rate of the recommendation models -
a circumstance which (as applied to prediction methods in general) has already
Of course, this does not imply that devising better factorization models with
regard to prediction rate is impossible in principle. One way is to incorporate
additional RE-related assumptions into the factorization model. Another way is to
include further dimensions into the factorization. This will be studied in the next
chapter.
