Angular Separation and Chord Distance: fix cosine similarity calculation#142
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Fixes evllabs#140. Both functions had the wrong denominator for cosine similarity. They were accumulating the sum of raw frequencies instead of the sum of squared frequencies. For a normalized histogram sum(xi) = 1, so the denominator collapsed to 1 * 1 = 1 and both functions were effectively returning the dot product with no normalization. Fixed by accumulating sum(xi^2) and sum(yi^2) in the loop and using sqrt(sumXX * sumYY) as the denominator, which is the standard L2 norm. Angular Separation now returns arccos(cosine) / pi instead of 1 - cosine. The old formula is a cosine distance approximation, not an actual angular measure. The arccos version gives a properly normalized angle in [0, 1]. Chord Distance's sqrt(2 - 2 * cosine) formula was already mathematically correct and just needed an accurate cosine value to work properly. Test expected values updated: identical vectors now correctly return 0.0 for both functions instead of 0.9 and sqrt(1.8). Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Fixes #140
Both functions had the wrong denominator for cosine similarity. They were summing raw frequencies instead of squared frequencies, which for a normalized histogram means the denominator collapses to sum(xi) * sum(yi) = 1 * 1 = 1. Effectively both were computing the dot product with no normalization at all.
Fixed by accumulating sum(xi^2) and sum(yi^2) in the loop and using sqrt(sumXX * sumYY) as the denominator, which is the standard L2 norm approach.
Angular Separation also now returns arccos(cosine) / pi instead of 1 - cosine. The old formula is a cosine distance approximation, not an actual angular measure. The arccos version gives a properly normalized angle in the range [0, 1].
Chord Distance's sqrt(2 - 2 * cosine) formula was already mathematically correct and just needed an accurate cosine value to work. Test expected values updated to match corrected output — identical vectors now return 0.0 for both functions instead of 0.9 and sqrt(1.8).