Weighted Cosine Similarity about rportfoliosimilarity

[vh-d]

this link may help

[dalekube]

After testing a couple alternatives, I figured out that the weighted cosine similarity function is using the following formula (matching this example):

sum(x*y*w)/(sqrt(sum(x^2*w))*sqrt(sum(y^2*w)))

This includes the weights in the denominator, multiplying each vector value, raised to the second power, by the corresponding weight.

[dalekube]

It would be great if the formulas are explicitly listed in the docs!

[vh-d]

After testing a couple alternatives, I figured out that the weighted cosine similarity function is using the following formula (matching this example):

sum(x*y*w)/(sqrt(sum(x^2*w))*sqrt(sum(y^2*w)))

This includes the weights in the denominator, multiplying each vector value, raised to the second power, by the corresponding weight.

Yep, thanks, a look in the source code confirms that:

double wtVCosSimilarity(NumericVector a, NumericVector b, NumericVector w) {
  double sA, sB, sI;

  sA = sum(w*a*a);
  sB = sum(w*b*b);
  sI = sum(w*a*b);
  return (sI/sqrt(sA * sB));
}

I will put in the docs.

[dalekube]

Great, thanks for confirming the formula. Do you have a link to an external source that helps to confirm this formula? It makes sense as I experiment with it, but a general online search does not return any robust use cases or studies that help with validation.

[vh-d]

Closed in 8a4094d

[vh-d]

I am not aware of any solid reference right now. It has been some time since I wrote this part of my dissertation. But I think this was the only formula that behaved well (a.k.a. met some basic requirements on edge cases, equal weights etc...).