def regularized_correlation(size, dot_product, rating_sum, \
rating2sum, rating_norm_squared, rating2_norm_squared,
virtual_cont, prior_correlation):
'''
The Regularized Correlation between two vectors A, B
RegularizedCorrelation = w * ActualCorrelation + (1 - w) * PriorCorrelation
where w = # actualPairs / (# actualPairs + # virtualPairs).
'''
unregularizedCorrelation = correlation(size, dot_product, rating_sum, \
rating2sum, rating_norm_squared, rating2_norm_squared)
w = size / float(size + virtual_cont)
return w * unregularizedCorrelation + (1.0 - w)
def calculate_similarity(self, pair_key, lines):
'''
Sum components of each corating pair across all users who rated both
item x and item y, then calculate pairwise pearson similarity and
corating counts. The similarities are normalized to the [0,1] scale
because we do a numerical sort.
19,21 0.4,2
21,19 0.4,2
19,70 0.6,1
70,19 0.6,1
21,70 0.1,1
70,21 0.1,1
'''
sum_xx, sum_xy, sum_yy, sum_x, sum_y, n = (0.0, 0.0, 0.0, 0.0, 0.0, 0)
item_pair, co_ratings = pair_key, lines
item_xname, item_yname = item_pair
items_x = []
items_y = []
for item_x, item_y in lines:
sum_xx += item_x * item_x
sum_yy += item_y * item_y
sum_xy += item_x * item_y
sum_y += item_y
sum_x += item_x
n += 1
# items_x.append(item_x)
# items_y.append(item_y)
corr_sim = correlation(n, sum_xy, sum_x, \
sum_y, sum_xx, sum_yy)
#corr_sim = correlation(items_x, items_y)
reg_corr_sim = regularized_correlation(n, sum_xy, sum_x, \
sum_y, sum_xx, sum_yy, PRIOR_COUNT, PRIOR_CORRELATION)
cos_sim = cosine(sum_xy, sqrt(sum_xx), sqrt(sum_yy))
jaccard_sim = 0.0
yield (item_xname, item_yname), (corr_sim, \
cos_sim, reg_corr_sim, jaccard_sim, n)