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Fun fact: cosine similarity's first use in recommendation systems to recommend usenet groups. (https://dl.acm.org/doi/epdf/10.1145/192844.192905 https://dl.acm
by mkehrt 9mo ago
Fun fact: cosine similarity's first use in recommendation systems to recommend usenet groups.
(https://dl.acm.org/doi/epdf/10.1145/192844.192905 https://dl.acm.org/doi/epdf/10.1145/192844.192905 although they don't call it cosine similarity; they do compute a "correlation coefficient" between two people by adding together the products of scores each gave to a post)
- zahlman 9mo ago> they do compute a "correlation coefficient" between two people by adding together the products of scores each gave to a post I've heard the term "cosine similarity" before but not really looked into it. What does this computation have to do with trigonometry?
- Edwinr95 9mo agoThe dot product is computed between two vectors. For these use cases that dot product is equal to the cosine of the angle between these angles. (Strictly speaking we have that the angle is actually defined in terms of the dot/inner product in more abstract spaces like function spaces or L^p/l^p)
- armcat 9mo agoIt's grounded in basic trigonometry, i.e. it calculates the angle `theta` between two entities/vectors, `a` and `b`. If `theta` is close to 180 degrees, cos(theta) is -1, and cosine similarity dictates these are opposite concepts, i.e. unrelated.
- jmalicki 9mo agoUnrelated would be a cosine of 0. Being opposites is a very strong relation.
- yobbo 9mo agoThe Pearson correlation coefficient is covariance normalised to the range [-1, 1] by dividing with the standard deviations (https://en.wikipedia.org/wiki/Pearson_correlation_coefficient https://en.wikipedia.org/wiki/Pearson_correlation_coefficien...). So not quite same as the normalised scalar product, even though the formulas look related.
- mkehrt 9mo agoThat makes sense; I don't actually know much about this. That being said, weirdly, the normalization by standard deviation happens outside the call to `cov` in the paper (page 181, column 1, equations (unnumbered) 1 and 2). And in equation 2 they've expanded `cov` to be the sum of pointwise multiplication of the (scores - average score) people have given to posts. Again, not my area of expertise, just looking at the math here.
- yobbo 9mo agoYes, they are basically the same thing, but for correlation the values are first zero-centred.
- LudwigNagasena 9mo agoPearson correlation = cosine of the angle between centered random variables. Finite-variance centered random variables form a Hilbert space so it’s not a coincedence. Standard deviation is the length of the random variable as a vector in that space.