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Why Cohen’s Kappa should be avoided as performance measure in classification
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We show that Cohen's Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behaviour, i.e. a worse classifier gets higher Kappa score, differing qualitatively from that of MCC. The debate about the incoherence in the behaviour of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies an scenario in which the contradictory behaviour among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rise, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.
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“Cohen’s Kappa is an useful metric for imbalanced datasets; however, the interpretation of its value is problematic [84].”
From A Survey of Underwater Acoustic Data Classification Methods Using Deep Learning for Shoreline Surveillance (2022) · cites this paper as [84]
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Metadata
- Authors
- Delgado, R., & Tibau, X.-A.
- Affiliations
- Universitat Autònoma de Barcelona (ES)
- Corresponding author
- Delgado, Rosario
- Venue
- PLOS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2019-09-26
- Volume
- 14
- Issue
- 9
- Pages
- e0222916
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC6762152
- OpenAlex
- W2975256032
- Cited by
- 324
- References
- 53
- Citations by year
- 2026: 22 · 2025: 47 · 2024: 53 · 2023: 60 · 2022: 69 · 2021: 50 · 2020: 22 · 2019: 1
- FWCI
- 16.20
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS ONE (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Dipòsit Digital de Documents de la UAB (Universitat Autònoma de Barcelona) (submittedVersion, cc-by)
- RePEc: Research Papers in Economics (submittedVersion)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
- Keywords
- Cohen's kappa, Matthews correlation coefficient, multi-class classification, class imbalance, confusion matrix, entropy (information theory), classifier comparison
- MeSH terms
- Supervised Machine Learning, Data Analysis, Classification, Models, Theoretical, Reproducibility of Results, Datasets as Topic
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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