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From Lance Norskog <goks...@gmail.com>
Subject Re: Singular vectors of a recommendation Item-Item space
Date Thu, 11 Aug 2011 05:22:58 GMT
A picture that might help explain the problem:

http://www.flickr.com/photos/54866255@N00/6031564308/in/photostream


On 8/10/11, Lance Norskog <goksron@gmail.com> 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 <goksron@gmail.com> wrote:
>> SVDRecommender is intriguing, thanks for the pointer.
>>
>> On Sun, Jul 10, 2011 at 12:15 PM, Ted Dunning <ted.dunning@gmail.com>
>> 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 <srowen@gmail.com> 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" <goksron@gmail.com> wrote:
>>>>
>>>
>>
>>
>>
>> --
>> Lance Norskog
>> goksron@gmail.com
>>
>
>
>
> --
> Lance Norskog
> goksron@gmail.com
>


-- 
Lance Norskog
goksron@gmail.com

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