[tavilach]

Let's say we have a correlation matrix for the ratings of different songs.

Now, let's say that one of the songs, song 2, is rated with a rating (between -5 and 5) of 2.5. Another one, song 3, is rated with a rating of -1.0. Using the correlation matrix, I also determine that the correlation between song 2 and song 7 is 0.2, and the correlation between song 3 and song 7 is -0.8.

I want to update the expected value of the rating of song 7, based on the fact that song 2's rating is a 2.5 and the correlation of song 2 and song 7 is 0.2, and on the fact that song 3's rating is a -1.1 and the correlation of song 3 and song 7 is -0.8.

I could multiply the correlations by the ratings, taking the average of 0.2 * 2.5 and -0.8 * -1.1, but is this the correct way to update the expected value? As I rate more songs, the averaged value would constantly be decreasing (because abs(correlation) <= 1).

Is there a proper way to do this?

Thanks .

[rehoot]

You can't calculate a correlation between two numbers--a correlation is between two sets of numbers that have been paired in some way. For songs, correlations don't make much sense because there isn't much logical basis for putting them in matched sets.

You could find the MEAN ratings of songs in each genre or by each artist and makes some predictions using that, but there is so much variation between songs that it probably won't be a good predictor. For me, any album by one band might have a few great songs, a few average songs, and a few crappy songs. If you find a band that makes albums full of great songs, then maybe you could predict that you will like the next album by that band, and you don't need a computer to tell you that.

[tavilach]

Forget the fact that this is songs. That's just an example. Let's call them pickles.

Each song is a random variable that holds a rating. It does make sense to have a correlation between two random variables: