Progress in Artificial Intelligence

, Volume 8, Issue 2, pp 215–228 | Cite as

Instance selection improves geometric mean accuracy: a study on imbalanced data classification

  • Ludmila I. Kuncheva
  • Álvar Arnaiz-González
  • José-Francisco Díez-PastorEmail author
  • Iain A. D. Gunn
Regular Paper


A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the geometric mean (GM) of the true positive and true negative rates. Here we prove that GM can be improved upon by instance selection, and give the theoretical conditions for such an improvement. We demonstrate that GM is non-monotonic with respect to the number of retained instances, which discourages systematic instance selection. We also show that balancing the distribution frequencies is inferior to a direct maximisation of GM. To verify our theoretical findings, we carried out an experimental study of 12 instance selection methods for imbalanced data, using 66 standard benchmark data sets. The results reveal possible room for new instance selection methods for imbalanced data.


Imbalanced data Geometric mean (GM) Instance/prototype selection Nearest neighbour Ensemble methods Theoretical perspective 



This work was done under project RPG-2015-188 funded by the Leverhulme Trust, UK; the project TIN2015-67534-P funded by the Ministerio de Economía y Competitividad of the Spanish Government; and the BU085P17 funded by the Junta de Castilla y León. The authors gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer ScienceBangor UniversityBangorUK
  2. 2.Escuela Politécnica SuperiorUniversidad de BurgosBurgosSpain
  3. 3.Department of Computer ScienceMiddlesex UniversityLondonUK

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