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A Comparison of MCC and CEN Error Measures in Multi-Class Prediction
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We show that the Confusion Entropy, a measure of performance in multiclass problems has a strong (monotone) relation with the multiclass generalization of a classical metric, the Matthews Correlation Coefficient. Analytical results are provided for the limit cases of general no-information (n-face dice rolling) of the binary classification. Computational evidence supports the claim in the general case.
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“MCC is the only binary classification rate that generates a high score only if the binary predictor was able to correctly predict the majority of positive data instances and the majority of negative data instances [80, 97].”
From The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation (2020) · cites this paper as [80]
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“This latter function was introduced in (Matthews, 1975) and it is also known as the φ -coe ffi cient, corresponding for a 2 × 2 contingency table to the square root of the average χ 2 statistic χ 2 / n . p MCC has recently attracted the attention of the machine learning community (Baldi et al., 2000)…”
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Research works printed but not linked: 2
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Metadata
- Authors
- Jurman, G., Riccadonna, S., & Furlanello, C.
- Affiliations
- Fondazione Bruno Kessler (IT)
- Corresponding author
- Jurman, Giuseppe
- Venue
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2012-08-08
- Volume
- 7
- Issue
- 8
- Pages
- e41882
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC3414515
- OpenAlex
- W1988301066
- Cited by
- 406
- References
- 43
- Citations by year
- 2026: 17 · 2025: 29 · 2024: 38 · 2023: 54 · 2022: 47 · 2021: 54 · 2020: 32 · 2019: 36 · 2018: 25 · 2017: 23 · 2016: 15 · 2015: 12 · 2014: 14 · 2013: 10
- FWCI
- 11.34
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS ONE (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- European Commission
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Physical Sciences › Computer Science › Information Systems › Data Mining and Machine Learning Applications
- Keywords
- Matthews correlation coefficient, multi-class classification, generalization, binary classification, monotonicity
- MeSH terms
- Algorithms, Artificial Intelligence, Computers, Genotype, Probability, ROC Curve, Software, Statistics as Topic, Reproducibility of Results, Models, Statistical, Entropy, Computational Biology, Area Under Curve, Oligonucleotide Array Sequence Analysis
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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