There is no inherent mathematical difference, but there may be some pretty significant practical differences.
Using the three matrix form (X = USV') puts the normalization constants into a place where you can control them a bit easier. This can be useful if you want *both* user and item vectors that are normalized. If you only want item vectors, then it really doesn't matter since you can incorporate as much of S as you like into the item vectors as you like and the rest winds up in the factor that you aren't looking at anyway. On Thu, Nov 20, 2014 at 1:34 AM, Parimi Rohit <rohit.par...@gmail.com> wrote: > Hi All, > > Are there any (dis)advantages of using tri-factorization (||X - USV'||) as > opposed to bi-factorization ((||X - UV'||)) for recommender systems? I have > been reading a lot about tri-factorization and how they can be seen as > co-clustering of rows and columns and was wondering if such as technique is > implemented in Mahout? > > Also, I am particularly interested in implicit-feedback datasets and the > only MF approach I am aware of is the ALS-WR for implicit feedback data > implemented in mahout. Are there any other MF techniques? If not, is it > possible (and useful) to extend some tri-factorization to handle > implicit-feedback along the lines of "Collaborative Filtering for Implicit > Feedback Datasets" (the approach implemented in Mahout). > > I apologize for any inconvenience as this question is very general and > might not be relevant to Mahout and I would really appreciate any > thoughts/feedback. > > Thanks, > Rohit >
