# Quantifying Aggregate Vector Strength/Vector Arithmatic

Say I have 5 vectors and I measure the similarity of each one to a fixed reference vector using cosine similarity. But now what I want to do is understand the aggregate or collective strength of these 5 vectors as it relates to how similar they are collectively to the reference vector. Is this simply an average of the 5 cossim values I calculate; or do I add up each scalar position of the 5 vectors together and then do a cossim; or do I average the scalar positions of the 5 vectors and then do a cossim. Or is there a better way to measure the collective similarity (or strength) of the 5 vectors to the reference vector? Thanks for any insight that you may have !

Additional Context So lets say that each of the 5 vectors represent 5 sentences in a document that are considered the most salient bits of information in the document on a topic like say Pneumonia. The question I am asking of the 5 vectors (sentences) is how likely or strong do these 5 sentences represent a positive Pneumonia case? I don't want to consider all sentences in the document because typically these documents are super noisy. What I want is a relative strength or conviction of the 5 vectors (sentences) to represent a Pneumonia case. But how do I determine their aggregate strength? I can measure each vector (sentence) relative to a reference vector for Pneumonia but how do I aggregate the separate results?

Or maybe can I somehow quantify the cluster density around the reference vector?

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