Let be a vector space retrieval model embedded in
. The set
specifies the
dimensions of the vector space V such that
, and each object in
is a
vector in V. Formally, if
, then
<
>. The
function
can be tfidf or one of its derivatives or a measure based on the
distribution of tokens in the retrievable objects. The function
can be equal to either the
dot product measure or the cosine measure. Given an object
, the function
ranks an object
on the basis of the similarity between
<
> and
computed by
.