Average in Adjusted cosine Similarity

what is the denominator in average rating of a user in Adjusted cosine similarity? (Item Based Collaborative Filtering)

Is it number all Items in system?? Or Just number of rated items by user??

and

is there a function in MatLab for Adjusted Cosine?

thanks

Solution

Question 1: Is it number all Items in system?? Or Just number of rated items by user??

Answer 1: Neither

If you see this formula:

$sim(i,j) = \frac{ \sum\limits_{u\in U}(R_{u,i}-\bar{R}_{u})(R_{u,j}- \bar{R}_{u})}{\sqrt{\sum\limits_{u\in U}(R_{u,i}-\bar{R}_{u})^2}\sqrt{\sum\limits_{u\in U}(R_{u,j}-\bar{R}_{u})^2}}$

in the denominator you need to calculate the rooted sum for each Rating of user u for item i minus the average rating of this User (mean rating) and this subtraction is squared then it is the same thing for item j which you have to multiply together.

Question 2: is there a function in MatLab for Adjusted Cosine?

Answer 2: By default no. But it should be relatively easy to write it your self given that you have the formula.