# Document (#5516)

Author
Heine, M.H.
Title
Distance between sets as an objective measure of retrieval effectiveness
Source
Information storage and retrieval. 9(1973), S.181-198
Year
1973
Abstract
A general measure of retrieval effectiveness having full metric properties and treating the 'retrieval system - arbiter of relevance' situation symmetrically, is the Marczewski-Steinhaus metric, D, measuring the distance between the set of relevant documents, A, and set of retrieved documents, B, according to D=1-(n(A´B)/n(AvB)). D can be expressed as a function of precision and recall, or of generality, fallout and recall, and of other sets of traditional measures. Acceptance of the measure allows criteria for retrieval optimality and degeneracy to be stated, defined by minimum and constant values of D respectively. Precision-recall degeneracy curves for D are given and compared with those for another general measure: the probability that a document will be correctly identfied by a retrieval system. Statistical extensions of D are examined, and these and other properties of the metric are illustrated with seven examples

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