Adjusted Cosine Similarity

Question

Hello there. Can you help me, please. I was confused to make PHP code about adjusted cosine similarity. I have build data like this : $data[UserID][ItemID] = Rating

data example :
$data[1][1] = 5;
$data[1][2] = 3;
$data[1][3] = 4;

$data[2][1] = 3;
$data[2][2] = 2;
$data[2][4] = 3;
$data[2][5] = 3;

$data[3][1] = 4;
$data[3][3] = 3;
$data[3][5] = 5;

$data[4][1] = 1;
$data[4][2] = 4;
$data[4][4] = 2;
$data[4][5] = 1;

$data[5][3] = 4;
$data[5][4] = 3;

If anyone can help me to build the function of this? The function to calculate the adjusted cosine of 2 items. like adjusted_cosine(itemID1,itemID2).

You're help is very helping me. Thanks before.

Answer 1

I think this ought to do it:

sim(i,j) {
    item1 = 0
    item2 = 0

    // calculate the sums for the ith and jth items
    // minus each users' avg rating.
    for (k = 0; k < length(data); k++) {
        item1 += (data[k][i] - avg(data[k]))
        item2 += (data[k][j] - avg(data[k]))
    }

    result (item1*item2)/(sqrt(item1*item1)*sqrt(item2*item2))
    return result
}

You'll still need to implement the average function but I suppose a simple mean will do for that.