Cosine similarity: Top pca component vs she-he

[santoshbs]

Hello Debiaswe Research Team, Thank you for making the code related to your paper available. This is very helpful! I am writing to seek clarification on analyzing gender bias in word vectors associated with professions.

In your paper, you suggest using cosine similarity between a given profession vector and the top PCA component. I am trying to replicate the same in the wiki context. Unfortunately, I am getting results opposite to expected.

For example, when I compute the cosine similarity between the waitress vector (or nurse vector) and the top gender principal component, I get a -ve score. However, when I compute the cosine similarity between the same profession vector and she - he vector (as you show in the example here), I get a +ve score.

I am confused about why the sign flips when using PCA and straightforward gender vector. I request your help.

Thank you!
sbs