How can we calculate adjusted cosine similarity for two items represented by their ratings?

Question

I want to compute adjusted cosine similarity value for two items represented by a and b respectively. We take two vectors a={2,3,1,0} and b={1,0,4,2}. I know how cosine similarity work but I am stuck with adjusted cosine similarity approach.

Answer 1

This may work for you:

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

    for (k = 0; k < length(data); k++) {
        item1 += (data[k][i] - avg(data[k]))
        item2 += (data[k][j] - avg(data[k]))
    }

    var numerator = item1*item2
    var denominator =(sqrt(item1*item1)*sqrt(item2*item2)
    var result = (numerator /denominator )
    return result
}