In the context of the rating prediction problem, the answer is no, because the items rated by AB, BC, and AC could be different.

A Question regarding Predicted Rating/ Pearson Correlation Coefficient:

In the video lecture, the example for calculating r average of Meg to be (2+4)/2 , and not (2+4+3)/3. My question is, for r average of Ken, in order to calculate the Similarity (W) of ken and meg, do we do (1+5)/2 = 3 or (1+5+2+4)/4 = 3.

2nd question regarding the Predicting the rating of item i by user x:

In order to calculate the predicted rating for user x on item i, we need to add the average of the user x, so for that average, do we take the average of all of the items that user x has rated, even the ones that other users have not rated? Or else user x might have a different average against each users, and the formula might be different.

Thanks

-Phanit

alomo wrote:

At first I was having same kind of doubts on that formula. However, the Pearson correlation coefficients are the similarity weights between the active user and other users sharing the rating history. For each pair of users we calculate coefficient W based on specific (different) set of items that they both rated. So the formula is correct.

yes, so my first question was: In the video lecture, the example for calculating r average of Meg to be (2+4)/2 , and not (2+4+3)/3. My question is, for r average of Ken, in order to calculate the Similarity (W) of ken and meg, do we do r average of ken = (1+5)/2 = 3 since meg only had the first 2 items rated, or r average of ken = (1+5+2+4)/4 = 3?

2nd question regarding the Predicting the rating of item i by user x:

In order to calculate the predicted rating for user x on item i, we need to add the average of the user x, so for that average, do we take the average of all of the items that user x has rated, even the ones that other users have not rated? example could be Ken rates 3rd item although Lee and Meg did not rate it. Or else user x might have a different average against each users, and the formula might be different. For example, if ken had a different average rating such that (2+5)/2 = 3.5 is the r average of ken with respect to meg, but his average rating could be (2+5+1+4) = 3 with respect to Lee, since Lee rated 4 items similar. Sorry if the question is confusing.

-Phanit

 

Thanks.