I'm working on a project in which I want to estimate biases from a large corpus of newspaper articles using word2vec. Following this and this paper, biases are calculated as follows. First, a dimension x is constructed as a normalized vector derived from the embeddings of antonym word pairs (say, rich - poor). Next, I project the normalized embeddings for different groups (say, different professions) on that axis by matrix multuplication. So what I end up with are cosine similarity scores ranging from -1 to 1 (also see this answer).
Now my idea was to plot the various groups in a 3d space with dimensions x, y, z. Can I just plot the cosine similarities as coordinates in a geometrical space? Or am I then violating some mathematical principle?
So far I've run some tests and the output seem valid from a qualitative perspective (as in: it confirms my own biases).
