Harman [Har92c] suggests two possible methods for implementing RF on Boolean systems. The first is 

to present the user with a list of possible new query terms. These can be chosen, for example, by the 

term distribution in the relevant documents. This means selecting those terms that appear more often in 

the relevant than non relevant documents and which would be useful to include in a new query. The 

second approach is for the system to automatically modify Boolean queries. An example of the latter 

type of query modification can be found in the system proposed by Khoo and Poo, [KP94], which is 

intended to automatically modify both the terms and the Boolean connectives of queries based on the 

documents marked relevant by a user. 

An alternative to exact match systems, such as the Boolean model, are best match systems. These 

systems use term weights, such as tf and idf, to rank documents in decreasing order of matching score 

or estimation of relevance. The two most common best match models are the vector space model, 

which orders documents in decreasing similarity of query and document, [Sal71], and the probabilistic 

model, [RSJ76], which orders documents based on an estimate of the probability of relevance of a 

document to a query. In section 2.2.2 we discuss the vector space model, in section 2.2.3 we discuss the 

probabilistic model. 

2.2.2 Vector space model 

In the vector space model, a document is represented by a vector of n weights, where n is the number of 

unique terms in the document collection. Figure 4 shows an example vector where xi is the weight

3

 of 

the ith term in document x if x contains the term, and 0 if the term is not present in x. 

x = (x , x ,..., x )

1

2

n

Figure 4: Document vector 

Queries are also represented as a vector of length n, and the similarity of the document vectors to a 

query vector gives a retrieval score to each document, allowing comparison and ranking of documents. 

A range of similarity measures exists to calculate this similarity, e.g. DICE, inner product, cosine 

correlation, [VR79, Chap 3]. Equation 3 shows the cosine correlation, one of the more common vector 

space matching functions. 

n

(term

ik

  qterm

jk

)

k =1

cos(doc

i

, query

j

) =

n

n

(term

ik

)

2

(qterm

k=1

jk

)

2

k=1

Equation 3: Cosine correlation between document doci and queryj 

Unlike the Boolean model, which retrieves documents according to the query terms and query 

connectives, in the best match models all documents that contain at least one query term will receive a 

non zero score; the highest score going to documents that contain all the query terms. Documents that 

contain only some of the query terms will be ranked according to the sum of the weights of the query 

terms they contain. The documents that contain more query terms or contain query terms with a higher 

discriminatory power (term weight) will be retrieved above those that contain fewer query terms or 

query terms with lower weights. Similarity is then a function of term overlap between query and 

document, and the weights assigned to the terms. 

Rocchio [Roc71] is generally credited with the first formalisation of a RF technique, developed on the 

vector space model. In [Roc71] he defines the problem of retrieval as that of defining an optimal query; 

one that maximises the difference between the average vector of the relevant documents and the 

average vector of the non relevant documents. As discussed in section 1, it may not always be possible 

for a user to submit such an optimal query, so RF is required to bring the query vector closer to the 

mean of the relevant documents, and further from the mean of the non relevant documents. This is 

3

Some implementations of the vector space model use 1 if a term occurs in a document, 0 if it does not occur. 

Most implementations will use some form of tf*idf weighting and some form of length normalisation will usually 

be performed to avoid retrieval bias towards long documents. 

 6