Instance Selection Improves Geometric Mean Accuracy: A Study on Imbalanced Data Classification

TL;DR

This paper proves that instance selection can enhance the geometric mean accuracy in imbalanced data classification, challenging traditional balancing methods and providing theoretical and experimental insights.

Contribution

It offers a theoretical analysis showing GM improvement via instance selection and compares it with balancing strategies, supported by extensive experiments.

Findings

GM can be improved through instance selection

Balancing class frequencies is less effective than direct GM maximization

Experimental results suggest potential for new instance selection methods

Abstract

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.