This paper doesn't address how to compute the SVD. There are two approaches implemented with SVDRecommender. One computes a SVD, one doesn't :) Really it ought to be called something like MatrixFactorizationRecommender. The SVD factorizer uses a fairly simple expectation maximization approach. I don't know how well this scales. The other factorizer uses alternating-least-squares.
What you come out with are not 3 matrices, from an SVD, but 2. The "S" matrix in the SVD of singular values is mashed into the left/right singular vectors. So to answer your question now, the prediction expression is essentially the same, with two caveats: 1. It shows it as the product of U, sqrt(S), sqrt(S), and V. What you get out of the factorizer are really more like the "U" and "V" with the two sqrt(S) bits already multiplied in. The product comes out the same, there is a conceptual difference I suppose but not a practical one. In both cases you're really just multiplying the matrix factors all back together to make the predictions. 2. This model subtracts the customer average rating in the beginning, and adds it back at the end here. The SVDRecommender doesn't do that, because, quite crucially, it turns sparse data into dense data (all the zeroes become non-zero) and this crushes scalability. The answer is "mostly the same thing" yes. In fact this is broadly how all matrix factorization approaches work. On Wed, Apr 18, 2012 at 2:49 PM, Daniel Quach <[email protected]> wrote: > I am basing my knowledge off this paper: > http://www.grouplens.org/papers/pdf/webKDD00.pdf > > Your book provided algorithms for the user-based, item-based, and slope one > recommendation, but none for the SVDRecommender (I'm guessing because it was > experimental) > > Does the SVDRecommender just compute the resultant matrices and follow a > formula similar to the one at the top of page 5 in the linked paper? I think > I understand the process of SVD but I'm just wondering how it's exactly > applied to obtain recommendations in mahout's case. > > > On Apr 18, 2012, at 12:13 PM, Sean Owen wrote: > >> Yes you could call it a model-based approach. I suppose I was thinking >> more of Bayesian implementations when I wrote that sentence. >> >> SVD is the Singular Value Decomposition -- are you asking what the SVD >> is, or what matrix factorization is, or something about specific code >> here? You can look up the SVD online. >> >> On Wed, Apr 18, 2012 at 12:49 PM, Daniel Quach <[email protected]> wrote: >>> I had originally thought the experimental SVDrecommender in mahout was a >>> model-based collaborative filtering technique. Looking at the book "Mahout >>> in Action", it mentions that model-based recommenders are a future goal for >>> mahout, which implies to me that the SVDRecommender is not considered >>> model-based. >>> >>> How exactly does the SVDRecommender work in mahout? I can't seem to find >>> any description of the algorithm underneath it >
