On Sat, Mar 11, 2017 at 02:31:04AM +0530, Lakshya Agrawal wrote:
> Hello everyone,
> I was going through the research paper "
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.129.4662&rep=rep1&type=pdf";
> (Alternatives to neighborhood based collaborative filtering) .I have
> understood the paper but was not able to comprehend "Normalizing by
> removing global effects(Methods)" properly.
>
> I have understood that we estimate one "effect" at a time,in sequence . Is
> it that initially the values "X(ui)" are all set to one for all "i" ? Also
> what about "Theta(u)" for the first effect is it that initially
> "n"(number of movies rated my user) random values are assigned to it from a
> Normal Distribution and on later stages it is calculated by using
> "Thetacap(u)"?Also does for
> "X(ui)" depend upon the effect ?
>
> It would be of great help if I could be provided more information/paper
> relating to this.
Hi Lakshya,
x_ui corresponds to the user rating for user u and item i (the
"explanatory variable"), so that is what your data is. But the authors
appear to abuse notation a little, and use different x_ui for different
global effects. So x_ui does not _depend_ on the global or user effects
but different x_ui may be used depending on the type of effect being
modeled. I hope that makes sense; personally I think the paper could
have been written better to be more clear about this. But maybe there
were space limits they had to conform to?
So anyway I think, your total model in the end is
r_ui = \theta_u1 x_ui1 + \theta_u2 x_ui2 + ... + error
where \theta_u1 and x_ui1 correspond to the 'user main effects' (where
x_ui1 = 1 for all u, i) and \theta_u2 and x_ui2 correspond to other
global effects, and so forth.
\theta_u can be estimated by using the estimator they give at the end of
section 3.1. You can calculate \hat{\theta}_u easily with the last
equation on page 9, and then you can "shrink" this with the last
equation of Section 3.1 to obtain a good estimator for \theta_u.
I hope this clarifies things. You might also consider looking around to
see if any follow-up work that cites this paper has a better or more
usable perspective.
Thanks,
Ryan
--
Ryan Curtin | "Indeed!"
[email protected] | - David Lo Pan
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