Requirements for query evaluation in weighted information retrieval

Abstract In this article, a general mathematical framework for information retrieval models is presented, giving more insight into the evaluation mechanisms that may be used in IR. In this framework a number of requirements for operators improving recall and precision are investigated. It is shown that these requirements can be satisfied by using descriptor weights and one combination operator only. Moreover, information items and queries—virtual items—can be treated in exactly the same way, reflecting the fact, that they both are descriptions of a number of concepts. Evaluation is performed by formulating similarity homomorphisms from query descriptions to retrieval status values that allow ranking items accordingly. For good comparisons, however, ranking must be done by the achieved proportion of perfect similarity rather than by similarity itself. In term independence models, this normalization process may satisfy the homomorphism requirement of algebra under certain conditions, but it contradicts the requirement in the term dependence case. Nevertheless, by demanding separability for the unnormalized part of the evaluation measure, it can be guaranteed that the query is evaluated to each item descriptor by descriptor, and the normalization value must be calculated only once for the whole query, using the query as a whole. Also, for each real item, the normalization value must have been calculated only once, using the item as a whole.