Cosine similarity is a measure of similarity between two vectors of an inner product space that measures the cosine of the angle between them. It is a popular similarity measure between two vectors because it is calculated as a normalized dot product between the two vectors, which can be calculated with simple mathematical operations.
From Wikipedia:
Cosine similarity is a measure of similarity between two vectors of an inner product space that measures the cosine of the angle between them. The cosine of 0 degrees is 1, and it is less than 1 for any other angle. It is thus a judgement of orientation and not magnitude: two vectors with the same orientation have a cosine similarity of 1, two vectors at 90 degrees have a similarity of 0, and two vectors diametrically opposed have a similarity of -1, independent of their magnitude.
Cosine similarity is a popular similarity measure between two vectors a and b because it can be computed efficiently dividing the dot product of the two vectors by the Euclidean norm of each (the square root of the sum of the squared terms). For instance, vectors (0, 3, 4) and (-3, 4, 0) have dot product 12 and each have norm 5, so their dot product similarity is 12/5/5 = 0.48.
