Existence theorem of the quadruple (P, R, F, M): precision, recall, fallout and miss

Authors:
L. Egghe
Affiliations:
Universiteit Hasselt (UHasselt), Campus Diepenbeek, Agoralaan, Diepenbeek, Belgium and Universiteit Antwerpen (UA), Campus Drie Eiken, Wilrijk, Belgium
Venue:
Information Processing and Management: an International Journal
Year:
2007

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Abstract

In an earlier paper [Egghe, L. (2004). A universal method of information retrieval evaluation: the "missing" link M and the universal IR surface. Information Processing and Management, 40, 21-30] we showed that, given an IR system, and if P denotes precision, R recall, F fallout and M miss (re-introduced in the paper mentioned above), we have the following relationship between P, R, F and M P/1-P 1-R/R F/1-F 1-M/M=1 In this paper we prove the (more difficult) converse: given any four rational numbers in the interval ]0,1[satisfying the above equation, then there exists an IR system such that these four numbers (in any order) are the precision, recall, fallout and miss of this IR system. As a consequence we show that any three rational numbers in ]0, 1 [ represent any three measures taken from precision, recall, fallout and miss of a certain IR system. We also show that this result is also true for two numbers instead of three.