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On measuring the performance of binary classifiers


If one is given two binary classifiers and a set of test data, it should be straightforward to determine which of the two classifiers is the superior. Recent work, however, has called into question many of the methods heretofore accepted as standard for this task. In this paper, we analyze seven ways of determining whether one classifier is better than another, given the same test data. Five of these are long established, and two are relative newcomers. We review and extend work showing that one of these methods is clearly inappropriate and then conduct an empirical analysis with a large number of datasets to evaluate the real-world implications of our theoretical analysis. Both our empirical and theoretical results converge strongly toward one of the newer methods.

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  1. Note that this F1 is not directly related the cumulative distribution function of the negative class \(F_1(s)\). In order to remain consistent with [28] and avoid too much ambiguity, we use the non-traditional notation \(M_{F1}(t)\) to refer to the F1-Measure at a given threshold \(t\).

  2. For these measures, where the upper bound is unity and larger values mean better classifiers, the implied loss would be \(1 - m(t)\), where \(m\) is the measure.






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Parker, C. On measuring the performance of binary classifiers. Knowl Inf Syst 35, 131–152 (2013).

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  • Performance measures
  • Binary classification
  • Supervised learning
  • Evaluation