metrics

metrics.py

from math import sqrt


def correlation(size, dot_product, rating_sum, \
            rating2sum, rating_norm_squared, rating2_norm_squared):
    '''
      The correlation between two vectors A, B is
      cov(A, B) / (stdDev(A) * stdDev(B))

    '''
    numerator = size * dot_product - rating_sum * rating2sum
    denominator = sqrt(size * rating_norm_squared - rating_sum * rating_sum) * \
                    sqrt(size * rating2_norm_squared - rating2sum * rating2sum)

    return (numerator / (float(denominator))) if denominator else 0.0


def normalized_correlation(size, dot_product, rating_sum, \
            rating2sum, rating_norm_squared, rating2_norm_squared):
    '''
      The correlation between two vectors A, B is
      cov(A, B) / (stdDev(A) * stdDev(B))
      The normalization is to give the scale between [0,1].

    '''
    similarity = correlation(size, dot_product, rating_sum, \
            rating2sum, rating_norm_squared, rating2_norm_squared)

    return (similarity + 1.0) / 2.0