2.2 Generalized Vector Space ModelW

2.2 Generalized Vector Space Model
Wong et al. (1987) presented an analysis of the
problems that the pairwise orthogonality assumption
of the VSM creates. They were the first to
address these problems by expanding the VSM.
They introduced term to term correlations, which
deprecated the pairwise orthogonality assumption,
but they kept the assumption that the term vectors
are linearly independent1, creating the first GVSM
model. More specifically, they considered a new
space, where each term vector ~ti was expressed as
a linear combination of 2n vectors m~r, r = 1..2n.
The similarity measure between a document and a
query then became as shown in equation 2, where
~ti and ~tj are now term vectors in a 2n dimensional
vector space, ~ dk, ~q are the document and the query vectors, respectively, as before, a´ki, q´j are the new
weights, and ´n the new space dimensions