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Abstract

The paper shows that the present evaluation methods in information retrieval (basically recall R and precision P and in some cases fallout F ) lack universal comparability in the sense that their values depend on the generality of the IR problem. A solution is given by using all "parts" of the database, including the non-relevant documents and also the not-retrieved documents. It turns out that the solution is given by introducing the measure M being the fraction of the not-retrieved documents that are relevant (hence the "miss" measure). We prove that - independent of the IR problem or of the IR action - the quadruple (P,R,F,M) belongs to a universal IR surface, being the same for all IR-activities. This universality is then exploited by defining a new measure for evaluation in IR allowing for unbiased comparisons of all IR results. We also show that only using one, two or even three measures from the set {P,R,F,M} necessary leads to evaluation measures that are non-universal and hence not capable of comparing different IR situations.

Date

14. 8.2004 19:17:22

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Abstract

It is shown that vector information retrieval (IR) and general fuzzy IR uses two types of fuzzy set operations: the original "Zadeh min-max operations" and the so-called "probabilistic sum and algebraic product operations". The universal IR surface, valid for classical 0-1 IR (i.e. where ordinary sets are used) and used in IR evaluation, is extended to and reproved for vector IR, using the probabilistic sum and algebraic product model. We also show (by counterexample) that, using the "Zadeh min-max" fuzzy model, yields a breakdown of this IR surface.

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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.

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Date

14. 2.2012 12:53:22

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Source

Journal of information science. 22(1996) no.3, S.165-170