Vector space model

[1] In this section we consider a particular vector space model based on the bag-of-words representation.

If a term occurs in the document, its value in the vector is non-zero.

Several different ways of computing these values, also known as (term) weights, have been developed.

Typically terms are single words, keywords, or longer phrases.

Vector operations can be used to compare documents with queries.

[2] Candidate documents from the corpus can be retrieved and ranked using a variety of methods.

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 a vector with same dimension as the vectors that represent the other documents.

The norm of a vector is calculated as such: Using the cosine the similarity between document dj and query q can be calculated as: As all vectors under consideration by this model are element-wise 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).

[2] In the classic vector space model proposed by Salton, Wong and Yang [3] the term-specific weights in the document vectors are products of local and global parameters.

, where and The vector space model has the following advantages over the Standard Boolean model: Most of these advantages are a consequence of the difference in the density of the document collection representation between Boolean and term frequency-inverse document frequency approaches.

When using Boolean weights, any document lies in a vertex in a n-dimensional hypercube.

This behavior models the original motivation of Salton and his colleagues that a document collection represented in a low density region could yield better retrieval results.

The vector space model has the following limitations: Many of these difficulties can, however, be overcome by the integration of various tools, including mathematical techniques such as singular value decomposition and lexical databases such as WordNet.