alt Hacker NewsThe Pearson correlation coefficient is covariance normalised to the range [-1, 1] by dividing with the standard deviations (https://en.wikipedia.org/wiki/Pearson_correlation_coefficien...). So not quite same as the normalised scalar product, even though the formulas look related.
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mkehrt • last Friday at 7:07 PM
That 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.
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Pearson 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.