#1




movie ratings
What is the intuition behind the form of the hypothesis function for movie ratings?
I'm trying to understand why it makes sense to multiply user factor by movie factor, to get that factor's contribution to the rating. E.g. if user doesn't like horror movies and the movie has a low "horror movie" rating, multiplying these together gives a low number. Shouldn't the rating be based on the distance/difference between a user's value for a factor and a movie's value for that factor? I understand that in a learning situation the factors do not have specific interpretations  there is just a list of factors. Still, the motivation was clearly that there are factors (horrorness, comedyness etc). So what is the motivation behind taking the product of factors instead of some form of their difference? 
#2




Re: movie ratings
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#3




Re: movie ratings
Ah, if each vector is normalized to unit length then this makes sense. But, there is no way to constrain the vector component values during gradient descent so that the vectors stay at unit length. Or is it that each vector is normalized every time we compute the dot product? I understand wanting the vectors to point in the same direction, but the vector magnitude seems like a distraction.
I know that model parameters needn't have a humanunderstandable interpretation (cf. hidden layers of neural networks), but if they do, it helps to see that the intuition makes sense 
#4




Re: movie ratings
Quote:
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#5




Re: movie ratings
Got it. I guess the learning algorithm cares most about the number of parameters, and forcing normalization would only reduce that by two.
Point of learning is to not have to guess the target function or even its form, but it's hard to resist micromanaging the process Thanks! 
#6




Re: movie ratings
Nicely put. Sometimes there is a compelling reason to introduce a particular functional form or constraint, but this is the exception not the rule.
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