### 3.4.1.1:
Vector Space Model of IR:

Let *D={d*_{1},...,d_{m}} be a set of documents and
*A={A*_{1},...,A_{n}} be a set of attributes. A
*
document vector*
*w*_{i}=(w_{i,1},...,w_{i,n})R^{n} for a document
*d*_{i}D is defined by a set of
*
weights* *{w*_{i,k}R, k=1,...,n} . In the same way a
*
query
vector* *q=(q*_{1},...,q_{n})R^{n} is defined for a query.

If further a similarity measure *s:R*^{n}×R^{n}->R is given that assigns a real value to every pair of
vectors, the whole system is called a
*
vector space
model of IR*.

In text retrieval
the attributes
are in general defined by the occurrence of
terms in the text. In this case
the weight *w*_{i,k}R describes the importance of
term *t*_{k}T for the document
*d*_{i}D . In the same way the
weight *q*_{k}R describes the importance of
term *t*_{k}T for the query.

© 1998 / HTML-Version 17. 11. 1998: R. Ferber