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I was learning derivatives. I understood the theoretical concept behind it. When I was searching for the real-life example in machine learning I came across one of the answers in this question How do we use derivatives in our daily lives.

Gist is : If netflix has to suggest a movie to a user, then it will check which of the movies he has liked and based on the ratings of those movies, the algorithm will try to find the movie closes to that range.

I have tried (my best) to understand this but failed to find out how exactly the math behind it would go.

So I want your help to solve this concrete example :

Suppose I have a user x and he has liked or upvoted movies with star rating 5,6,8,3 and has disliked movies with remaining values. (I am considering domain of stars is in the range 0-10).

Now how would I use derivatives to solve this problem ?

Thanks in advance :)

If its a very stupid question, atleast let me know why :)

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Akshay Deo
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  • Why do you think that derivatives are applicable to the particular problem of movie rating that you describe. Derivatives are useful, but they aren't a tool for every job. Some fairly complex computations and algorithms involve no derivatives at all. From what I see, you would actually not want to use derivatives in solving that problem. – Kuba hasn't forgotten Monica Aug 20 '14 at 21:44
  • http://math.stackexchange.com/questions/323342/how-do-we-use-derivatives-in-our-daily-lives. In one of its answered this example is given n I didn't understand how it would be done – Akshay Deo Aug 21 '14 at 03:34

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If a person $x$ likes a movie with a certain rating $y$, it doesn't imply he that likes all movies with rating $y$. The only use of the derivative would be to find how fast he is changing his taste from low rating movies to higher ones or vice versa at a certain moment, but the function wouldn't be continuous so you'd have to interpolate a polynomial and find its derivative instead. But it is completely useless.

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