Generalized vector space model

Wong et al. presented an analysis of the problems that the pairwise orthogonality assumption of the Vector space model(VSM) creates. From here they extended the VSM to the generalized vector space model (GVSM).

Definitions

GVSM introduces term to term correlations, which deprecate the pairwise orthogonality assumption. More specifically, they considered a new space, where each term vector t_i was expressed as a linear combination of 2ⁿ vectors m_r where r = 1...2ⁿ.

For a document d_k and a query q the similarity function now becomes:

$sim(d_{k},q)={\frac {\sum _{j=1}^{n}\sum _{i=1}^{n}w_{i,k}*w_{i,q}*t_{i}\cdot t_{j}}{{\sqrt {\sum _{i=1}^{n}w_{i,k}^{2}}}*{\sqrt {\sum _{i=1}^{n}w_{i,q}^{2}}}}}$

where t_i and t_j are now vectors of a 2ⁿ dimensional space.

Term correlation $t_{i}\cdot t_{j}$ can be implemented in several ways. As an example Wong et al. use as input to their algorithm the term occurrence frequency matrix obtained from automatic indexing and the output is term correlation between any pair of index terms.

Semantic information on GVSM

There are at least two basic directions for embedding term to term relatedness, other than exact keyword matching, into a retrieval model:

1. compute semantic correlations between terms
2. compute frequency co-occurrence statistics from large corpora

Recently Tsatsaronis focused on the first approach.

They measure semantic relatedness (SR) using a thesaurus (O) like WordNet. It considers the path length, captured by compactness (SCM), and the path depth, captured by semantic path elaboration (SPE). They estimate the $t_{i}\cdot t_{j}$ inner product by:

$t_{i}\cdot t_{j}=SR((t_{i},t_{j}),(s_{i},s_{j}),O)$

where s_i and s_j are senses of terms t_i and t_j respectively, maximizing $SCM\cdot SPE$.