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Weighted Cosine Similarity

Consider the code chunk below. In theory, a weighted cosine similarity formula would include the weight in the numerator to reduce the scalar product. I can't find any documentation to explain the current formula that incorporates weights. The current output of 'wtVCosSimilarity' does not match.

Please provide clarification or explicitly list the weighted formula.

x = c(1,2,3)
y = c(1,5,12)
w = c(0.5,1,1)

# Function result = 0.9720782
wtVCosSimilarity(x,y,w)

# Weighting the scalar product in the numerator
# Result = 0.9531571
sum(x*y*w)/(sqrt(sum(x^2))*sqrt(sum(y^2)))

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