If you take the item vector an existing user, multiply that by the
lefthand SVD matrix, and multthe resulting vector[i] *
1/singularvalues[i], you should get the item's row in the lefthand
column. So, the lefthand column times 1/singular values gives you the
projection for a new user's item vector >into this space of users<.
Which gives you a useruser recommender for new users.
On Thu, Aug 25, 2011 at 2:50 PM, Sean Owen <srowen@gmail.com> wrote:
> 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 leastimportant 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 useritem 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 <dscheffy@gmail.com> 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 =)
>>
>

Lance Norskog
goksron@gmail.com
