Consider now a retrieval strategy that has been implemented by means of a matching function M. Furthermore, let us suppose that both the query Q and document representatives D are t-dimensional vectors with real components where t is the number of index terms. Because it is my purpose to explain feedback I will consider its applications to a serial search only.

It is the aim of every retrieval strategy to retrieve the relevant documents A and withhold the non-relevant documents `A. Unfortunately relevance is defined with respect to the user's semantic interpretation of his query. From the point of view of the retrieval system his formulation of it may not be ideal. An ideal formulation would be one which retrieved only the relevant documents. In the case of a serial search the system will retrieve all D for which M(Q,D) > T and not retrieve any D for which M(Q,D) <= T, where T is a specified threshold. It so happens that in the case where M is the cosine correlation function, i.e.

the decision procedure

M(Q,D) - T > 0

corresponds to a linear discriminant function used to linearly separate two sets A and `A in R[t]. Nilsson[14] has discussed in great detail how functions such as this may be 'trained' by modifying the weights qi to discriminate correctly between two categories. Let us suppose for the moment that A and `A are known in advance, then the correct query formulation Q0 would be one for which

M(Q0,D) > T whenever D [[propersubset]] A

and

M(Q0,D) <= T whenever D [[propersubset]] `[[Alpha]]

The interesting thing is that starting with any Q we can adjust it iteratively using feedback information so that it will converge to Q0. There is a theorem (Nilsson[14], page 81) whichstates that providing Q0