A theoretical study of recall and precision using a topological approach to information retrieval

Abstract

Topologies for retrieval systems are generated by certain subsets, called retrievals. In this article we show how recall and precision can be expressed using only retrievals. Different types of retrieval systems are investigated: both threshold systems and "close match" systems, and both "optimal" and "non-optimal" retrieval. The relation with the hypergeometric and some "non-standard" distributions is highlighted.