cosine similarity

is a measure of closeness of two vectors.
a common use case is lifting a collection of real life datum objects into a dense vector space and being able to comment on their semantic closeness/farness using the notions of vector similarity.

(defun dot-product (vec-a vec-b)
  (assert (= (len vec-a) (len vec-b)))
  (reduce #'+
          (mapcar #'* vec-a vec-b)
          0))

(defun l2-norm (vec)
  (sqrt (reduce #'+ (mapcar #'square vec) 0)))

(defun cosine-similarity (vec-a vec-b)
  (/ (dot-product vec-a vec-b)
     (* (l2-norm vec-a)
        (l2-norm vec-b))))