The 200x10 matrix is indeed a matrix of 10 singular vectors, which are eigenvectors of AA'. It's the columns, not rows, that are eigenvectors.
The rows do mean something. I think it's fair to interpret the 10 singular values / vectors as corresponding to some underlying features of tastes. The rows say how much each user expresses those 10 tastes. The matrix of right singular vectors on the other side tells you the same thing about items. The diagonal matrix of singular values in the middle also comes into play -- it's like a set of multipliers that say how important each feature is. (This is why we cut out the singular vectors / values that have the smallest singular values; it's like removing the least-important features.) So really you'd have to stick those values somewhere; Ted says it's conventional to put "half" of each (their square roots) with each side if anything. I don't have as good a grasp on an intuition for the columns as eigenvectors. They're also a set of basis vectors, and I had understood them as like the "real" bases of the reduced feature space expressed in user-item space. But I'd have to go back and think that intuition through again since I can't really justify it from scratch again in my head just now. On Thu, Aug 25, 2011 at 10:21 PM, Jeff Hansen <[email protected]> wrote: > Well, I think my problem may have had more to do with what I was calling the > eigenvector... I was referring to the rows rather than the columns of U and > V. While the columns may be characteristic of the overall matrix, the rows > are characteristic of the user or item (in that they are a rank reduced > representation of that person or thing). I guess you could say I just had to > tilt my head to the side and change my perspective 90 degrees =) >
