# Cosine Similarity Intuition

I understand what cosine similarity is and how to calculate it, specifically in the context of text mining (i.e. comparing tf-idf document vectors to find similar documents). What I'm looking for is some better intuition for interpreting the results/similarity scores I come up with.

My question: If I have a cosine similarity of less than 0.707 (i.e. an angle greater than 45 degrees), is is fair to say that those respective documents/vectors are more "different" (less "similar") since the angle between them is more orthogonal? My initial thought was 'yes,' but in practice for me so far it doesn't seem like that's the right way to read into the numbers.

• Cosine similarity is like Pearson correlation, only done on not centered data. For binary data, it is known also as Ochiai coefficient. Yes, cosine similarity bw two vectors is, like r, is the cosine of the angle between them. – ttnphns Jan 17 '17 at 20:59
• You are asking specifically about using it in text mining. I'm not text analyst, I just suppose the compared documents are formed as binary data, yes? Then probably the meaning is the meaning of Ochiai? (see its formula). – ttnphns Jan 17 '17 at 21:04

I believe another difference between cosine similarity and TF-IDF is that cosine similarity is done in an embedding space, such as one created by doc2vec.
1. An embedding like doc2vec encodes information in direction and distance. Look at the examples of king - man + woman yielding queen. I'd guess that direction dominates this comparison.