Document (#34012)

Author

Egghe, L.

Title

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

Source

Information processing and management. 43(2007) no.1, S.265-272

Year

2007

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.

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5. Bollmann, P.; Cherniavsky, V.S.: Probleme der Bewertung von Information-Retrieval-Systemen (1980) 0.18

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