Applications
Relevance rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as the same kind of vector as the documents.
In practice, it is easier to calculate the cosine of the angle between the vectors, instead of the angle itself:
Where is the intersection (i.e. the dot product) of the document (d2 in the figure to the right) and the query (q in the figure) vectors, is the norm of vector d2, and is the norm of vector q. The norm of a vector is calculated as such:
As all vectors under consideration by this model are elementwise nonnegative, a cosine value of zero means that the query and document vector are orthogonal and have no match (i.e. the query term does not exist in the document being considered). See cosine similarity for further information.
Read more about this topic: Vector Space Model