A picture that might help explain the problem: http://www.flickr.com/photos/54866255@N00/6031564308/in/photostream
On 8/10/11, Lance Norskog <[email protected]> wrote: > Zeroing in on the topic: > > I have: > 1) a set of raw input vectors of a given length, one for each item. > Each value in the vectors are geometric, not bag-of-words or other. > The matrix is [# items , # dimensions]. > 2) An SVD of same: > left matrix of [ # items, #d features per item] * singular > vector[# features] * right matrix of [#dimensions features per > dimension, #dimensions]. > 3) The first few columns of the left matrix are interesting singular > eigenvectors. > > I would like to: > 1) relate the singular vectors to the item vectors, such that they > create points in the "hot spots" of the item vectors. > 2) find the inverses: a singular vector has two endpoints, and both > represent "hot spots" in the item space. > > Given the first 3 singular vectors, there are 6 "hot spots" in the > item vectors, one for each end of the vector. What transforms are > needed to get the item vectors and the singular vector endpoints in > the same space? I'm not finding the exact sequence. > > A use case for this is a new user. It gives a quick assessment by > asking where the user is on the few common axes of items: > "Transformers 3: The Stupiding" v.s. "Crazy Bride Wedding Love > Planner"? > > On Mon, Jul 11, 2011 at 8:56 PM, Lance Norskog <[email protected]> wrote: >> SVDRecommender is intriguing, thanks for the pointer. >> >> On Sun, Jul 10, 2011 at 12:15 PM, Ted Dunning <[email protected]> >> wrote: >>> Also, item-item similarity is often (nearly) the result of a matrix >>> product. >>> If yours is, then you can decompose the user x item matrix and the >>> desired >>> eigenvalues are the singular values squared and the eigen vectors are >>> the >>> right singular vectors for the decomposition. >>> >>> On Sun, Jul 10, 2011 at 2:51 AM, Sean Owen <[email protected]> wrote: >>> >>>> So it sounds like you want the SVD of the item-item similarity matrix? >>>> Sure, >>>> you can use Mahout for that. If you are not in Hadoop land then look at >>>> SVDRecomnender to crib some related code. It is decomposing the user >>>> item >>>> matrix though. >>>> >>>> But for this special case of a symmetric matrix your singular vectors >>>> are >>>> the eigenvectors which you may find much easier to compute. >>>> >>>> I might restate the interpretation. >>>> The 'size' of these vectors is not what matters to your question. It is >>>> which elements (items) have the smallest vs largest values . >>>> On Jul 10, 2011 3:08 AM, "Lance Norskog" <[email protected]> wrote: >>>> >>> >> >> >> >> -- >> Lance Norskog >> [email protected] >> > > > > -- > Lance Norskog > [email protected] > -- Lance Norskog [email protected]
