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The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation
Open accessAbstract
Background: To evaluate binary classifications and their confusion matrices, scientific researchers can employ several statistical rates, accordingly to the goal of the experiment they are investigating. Despite being a crucial issue in machine learning, no widespread consensus has been reached on a unified elective chosen measure yet. Accuracy and F 1 score computed on confusion matrices have been (and still are) among the most popular adopted metrics in binary classification tasks. However, these statistical measures can dangerously show overoptimistic inflated results, especially on imbalanced datasets. Results: The Matthews correlation coefficient (MCC), instead, is a more reliable statistical rate which produces a high score only if the prediction obtained good results in all of the four confusion matrix categories (true positives, false negatives, true negatives, and false positives), proportionally both to the size of positive elements and the size of negative elements in the dataset. Conclusions: In this article, we show how MCC produces a more informative and truthful score in evaluating binary classifications than accuracy and F 1 score, by first explaining the mathematical properties, and then the asset of MCC in six synthetic use cases and in a real genomics scenario. We believe that the Matthews correlation coefficient should be preferred to accuracy and F 1 score in evaluating binary classification tasks by all scientific communities.
Overview
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TL;DR
The paper argues that the Matthews correlation coefficient (MCC) is a more reliable metric than accuracy and F1 score for evaluating binary classifications, especially on imbalanced datasets, because MCC requires good performance on both positive and negative classes. It supports this through mathematical analysis, six synthetic use cases, and a real colon cancer gene expression experiment.
Key findings
- In six synthetic use cases, MCC was the only metric that correctly indicated the prediction problem in all six. For Use case A1 (91 positives, 9 negatives; TP=90, FN=1, TN=0, FP=9), accuracy=0.90 and F1=0.95, but MCC=−0.03. For Use case C2 (11 positives, 89 negatives; TP=2, FN=9, TN=88, FP=1), accuracy=0.90, F1=0.29, and MCC=+0.31.
- Correlation analysis over all possible confusion matrices showed MCC and accuracy were strongly correlated, while F1 correlated less than 0.8 with the other two measures. For N=1000, PCC(MCC,F1)=0.775982, PCC(MCC,accuracy)=0.921030, and PCC(accuracy,F1)=0.778652.
- In the colon cancer gene expression dataset (2,000 gene probesets, 62 patients: 22 healthy controls and 40 colon cancer; 35.48% negatives, 64.52% positives), rankings differed by metric. MCC ranked gradient boosting top (MCC=+0.55, TP rate=0.85, TN rate=0.69), while F1 and accuracy ranked k-NN top (F1=0.87, accuracy=0.80, TP rate=0.92, TN rate=0.52). Radial SVM had F1=0.75 and accuracy=0.67 but TN rate=0.40 and MCC=+0.29.
- MCC produces a high score only if the classifier correctly predicts the majority of positive and negative instances; F1 is independent of true negatives and is not symmetric for class swapping, while accuracy can be overoptimistic on imbalanced datasets.
Methods
- The paper defines accuracy, MCC, and F1 score mathematically, explores their relationships using Pearson correlation coefficient over all possible confusion matrices for N≥10 up to 1000, and plots all 21,084,251 possible confusion matrices for a 500-sample dataset on the MCC/F1 plane.
- Six synthetic use cases vary class balance and imbalance with specified confusion matrices to compare metric behavior.
- The real genomics experiment uses colon cancer gene expression data from Alon et al. via the plsgenomics R package, applying gradient boosting, decision tree, k-nearest neighbors, linear SVM, and radial SVM. Training/test splits were 80/20 or 60/20/20 with validation for hyperparameter grid search; experiments were repeated ten times and averaged for MCC, F1, accuracy, TP rate, and TN rate.
Limitations
- The paper states that additional comparisons with other rates such as Cohen’s Kappa, Cramér’s V, and K measure would have provided further information, but the authors focused on accuracy and F1 because they are more commonly used in biomedical machine learning studies.
- The paper notes that MCC can be undefined when a whole row or column of the confusion matrix is zero, and handles these cases via an approximation using an arbitrarily small value ε; it also cites situations where MCC can display large fluctuations due to imbalanced outcomes.
- Evident from the text: the real-world validation uses a single colon cancer gene expression dataset, the six use cases are synthetic, and Table 5 excludes standard deviations to keep the table simple.
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![Fig. 2 Use case A1 — Positively imbalanced dataset. a Barplot representing accuracy, F1, and normalized Matthews correlation coefficient (normMCC = (MCC + 1) / 2), all in the [0, 1] interval, where 0 is the worst possible score and 1 is the best possible score, applied to the Use case A1 positively imbalanced dataset. b Pie chart representing the amounts of true positives (TP), false negatives (FN), true negatives (TN), and false positives (FP). c Pie chart representing the dataset balance, as the amounts of positive data instances and negative data instances](/paper-figures/988371a13eb649a5bff767f781052a4f/the-advantages-of-the-matthews-correlation-coefficient-mcc-over-f1-score-and-figure-2.jpg)
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29 Own interpretation · 28 Own result · 15 Not checked yet · 13 No basis given
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In the paper
“A potential problem with MCC lies in the fact that MCC is undefined when a whole row or column of M is zero, as it happens in the previously cited case of the trivial majority classifier.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
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“Second, F1 score is independent from the number of samples correctly classified as negative.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
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“she/he would notice good results (F1 score = 0.75 and accuracy = 0.67)”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
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“For the Use case A1 (negatively imbalanced dataset), the machine learning classifier was unable to correctly predict negative data instances, and it therefore produced confusion matrices featuring few true negatives (TN).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“First, the top classifier changes when we consider the ranking based on MCC, F1 score, or accuracy.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
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“MCC = +0.31 in the [–1, +1] interval”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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In the paper
“In the Use case B1 (balanced dataset), the machine learning method was unable to correctly predict negative data instances, and therefore produced a confusion matrix featuring few true negatives (TN).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“Finally, in the last Use case C2 (positively imbalanced dataset), the prediction technique failed in predicting negative elements, and therefore its confusion matrix showed a low percentage of true negatives.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“F1 score = 0.29 in the [0, 1] interval”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“the radial SVM has performed poorly on the true negatives (TN rate = 0.40), by correctly predicting less than half patients.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
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“Here, accuracy showed a high value: 0.90 in the [0, 1] interval.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“In this case, all three statistical rates showed a low score which emphasized the deficiency in the prediction process (accuracy = 0.24, F1 score = 0.12, and MCC = −0.24).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“It ranges in the interval [−1,+1], with extreme values –1 and +1 reached in case of perfect misclassification and perfect classification, respectively, while MCC=0 is the expected value for the coin tossing classifier.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
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“F1 ranges in [0,1], where the minimum is reached for TP=0, that is, when all the positive samples are misclassified, and the maximum for FN=FP=0, that is for perfect classification.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
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“Like for the Use case A2, accuracy, F1 and MCC show average or low result scores (accuracy = 0.56, F1 score = 0.31, and MCC = +0.17), correctly informing you about the non-optimal performance of the prediction method (Additional file 3a).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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“If M has only one non-zero entry, this means that all samples in the dataset belong to one class, and they are either all correctly (for TP≠0 or TN≠0) or incorrectly (for FP≠0 or FN≠0) classified. In this situations, MCC=1 for the former case and MCC=−1 for the latter case.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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“If the dataset is highly unbalanced, ni≈1, and thus the accuracy measure gives an unreliable estimation of the goodness of the classifier.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
plaindirect- Asserted: passes — The authors put it forward as true.
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“Checking only F1, one would read a good value (0.66 in the [0, 1] interval), and would be overall satisfied about the prediction (Additional file 2a).”
- Also stated in: § Use cases · hedged
“The Matthews correlation coefficient, instead, by showing a score close to random guessing (+0.07 in the [–1, +1] interval) would be able to inform that the machine learning method has been on the wrong track. Also, it is worth noticing that accuracy would provide with an informative result in this case (0.52 in the [0, 1] interval).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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- Also stated in: § Use cases · hedged
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“However, accuracy and of F1 showed high values in this case: accuracy = 0.90 and F1 score = 0.95, both close to the best possible value 1.00 in the [0, 1] interval (Fig. 2a).”
- Also stated in: § Use cases · hedged
“Instead, if one decided to take advantage of the Matthews correlation coefficient in the Use case A1, he/she would notice the resulting MCC = –0.03 (Fig. 2a).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
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- Also stated in: § Use cases · hedged
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“Similar to the Use case A2 and B2, all three statistical scores generated low results that reflect the mediocre quality of the prediction: F1 score = 0.17 and accuracy = 0.10 in the [0, 1] interval, and MCC = −0.19 in the [–1, +1] interval (Additional file 4a).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plainSingle case- Asserted: passes — The authors put it forward as true.
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“On the other hand, for a given value MCC=μ, the F1 score can range in [0,μ+1] if μ≤0 and in [μ,1] if μ>0, so that the width of the range is 1−|μ|, that is, it depends on the MCC value μ.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The two measures are reasonably concordant, but the scatterplot cloud is wide, implying that for each value of F1 score there is a corresponding range of values of MCC and vice versa, although with different width.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Overall, accuracy, F1, and MCC show reliable concordant scores for predictions that correctly classify both positives and negatives (having therefore many TP and TN), and for predictions that incorrectly classify both positives and negatives (having therefore few TP and TN); however, these measures show discordant behaviors when the prediction performs well just with one of the two binary classes.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
plaincorrelational- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“First, F1 varies for class swapping, while MCC is invariant if the positive class is renamed negative and vice versa.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Interestingly, the correlation grows with N, but the increments are limited.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“With these positions MCC is now defined for all confusion matrices M. As a consequences, MCC=0 for the trivial majority classifier, and 0 is also the expected value for the coin tossing classifier.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Notation and mathematical foundations
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In the paper
“MCC and accuracy resulted strongly correlated, while the Pearson coefficient is less than 0.8 for the correlation of F1 with the other two measures (Table 3).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In fact, for any value F1=ϕ, the MCC varies approximately between [ϕ−1,ϕ], so that the width of the variability range is 1, independent from the value of ϕ.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The micro/macro averaged F1 is invariant for class swapping and its behaviour is more similar to MCC.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
plaincorrelational- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
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In the paper
“Here, accuracy showed a high value: 0.90 in the [0, 1] interval.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“linear SVM is ranked forth in the MCC ranking and in the accuracy ranking, but ranked second in the F1 score ranking.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
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In the paper
“k-NN, that is the top performing method both in the F1 score ranking and in the accuracy ranking, instead, obtained an excellent score for recall (TP rate = 0.92) but just sufficient on the specificity (TN rate = 0.52).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“However, ROC AUC presents several flaws [92], and it is sensitive to class imbalance [93].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [92] Lobo JM, Jiménez-Valverde A, Real R. AUC: a misleading measure of the performance of predictive distribution models. Glob Ecol Biogeogr. 2008; 17(2):145–51. source
- Not checked yetcites [93] Hanczar B, Hua J, Sima C, Weinstein J, Bittner M, Dougherty ER. Small-sample precision of ROC-related estimates. Bioinformatics. 2010; 26(6):822–30. source
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In the paper
“Once again, this score would hide the truth: the classification algorithm has performed poorly on the negative subset.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one. The quote only partly states this claim.
None of the sources cited for this claim have been checked yet.
In the paper
“The effectiveness of MCC has been shown in other scientific fields as well [43, 44].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [43] Liu Y, Cheng J, Yan C, Wu X, Chen F. Research on the Matthews correlation coefficients metrics of personalized recommendation algorithm evaluation. Int J Hybrid Informa Technol. 2015; 8(1):163–72. source
- Not checked yetcites [44] Naulaerts S, Dang CC, Ballester PJ. Precision and recall oncology: combining multiple gene mutations for improved identification of drug-sensitive tumours. Oncotarget. 2017; 8(57):97025. source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Even if less common than the ROC curve, several scientists consider the PR curve more informative than the ROC curve, especially on imbalanced biological and medical datasets [48, 97, 98].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [48] Saito T, Rehmsmeier M. The precision-recall plot is more informative than the ROC plot when evaluating binary classifiers on imbalanced datasets. PLoS ONE. 2015; 10(3):0118432. source
- Not checked yetcites [97] Chicco D. Ten quick tips for machine learning in computational biology. BioData Min. 2017; 10(35):1–17.
- Not checked yetcites [98] Ozenne B, Subtil F, Maucort-Boulch D. The precision–recall curve overcame the optimism of the receiver operating characteristic curve in rare diseases. J Clin Epidemiol. 2015; 68(8):855–9. source
plain- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“MCC was re-proposed by Baldi and colleagues [39] in 2000 as a standard performance metric for machine learning with a natural extension to the multiclass case [40].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [39] Baldi P, Brunak S, Chauvin Y, Andersen CA, Nielsen H. Assessing the accuracy of prediction algorithms for classification: an overview. Bioinformatics. 2000; 16(5):412–24. source
- Not checked yetcites [40] Gorodkin J. Comparing two K-category assignments by a K-category correlation coefficient. Comput Biol Chem. 2004; 28(5–6):367–74. source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“For example, when Whalen and colleagues released TargetFinder, a tool to predict enhancer-promoters interactions in genomics, they showed its results measured only by F1 score [13], making it impossible to detect the actual true positive rate and true negative rate of their tests [69].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [13] Whalen S, Truty RM, Pollard KS. Enhancer–promoter interactions are encoded by complex genomic signatures on looping chromatin. Nat Genet. 2016; 48(5):488. source
- Not checked yetcites [69] Xi W, Beer MA. Local epigenomic state cannot discriminate interacting and non-interacting enhancer–promoter pairs with high accuracy. PLoS Comput Biol. 2018; 14(12):1006625. source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Although being widely acknowledged as a reliable metric, there are situations - albeit extreme - where either MCC cannot be defined or it displays large fluctuations [45], due to imbalanced outcomes in the classification.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [45] Brown JB. Classifiers and their metrics quantified. Mol Inform. 2018; 37:1700127. source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“An effective solution overcoming the class imbalance issue comes from the Matthews correlation coefficient (MCC), a special case of the ϕ phi coefficient [36].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [36] Guilford JP. Psychometric Methods. New York City: McGraw-Hill; 1954.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“for instance, the Food and Drug Administration (FDA) agency of the USA employed the MCC as the main evaluation measure in the MicroArray II / Sequencing Quality Control (MAQC/SEQC) projects [41, 42].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [41] The MicroArray Quality Control (MAQC) Consortium. The MAQC-II Project: a comprehensive study of common practices for the development and validation of microarray-based predictive models. Nat Biotechnol. 2010; 28(8):827–38. source
- Not checked yetcites [42] The SEQC/MAQC-III Consortium. A comprehensive assessment of RNA-seq accuracy, reproducibility and information content by the Sequence Quality Control consortium. Nat Biotechnol. 2014; 32:903–14. source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“However, this procedure is biased [65], and it is still far from being accepted as a standard practice by the community.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [65] Van Asch V. Macro-and micro-averaged evaluation measures. Technical report. 2013:1–27.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this case, the algorithm showed its ability to predict the positive data instances (90 sick patients out of 91 were correctly predicted), but it also displayed its lack of talent in identifying healthy controls (only 1 healthy individual out of 9 was correctly recognized) (Fig. 2b). Therefore, the overall performance should be judged poor.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similar to the Use case A1 and B1, the method was able to correctly identify multiple negative data instances (88 healthy patients out of 89), but unable to correctly predict most of sick patients (only 2 true positives out of 11 possible elements).”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plainn = 88- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Originally developed by Matthews in 1975 for comparison of chemical structures [38]”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [38] Matthews BW. Comparison of the predicted and observed secondary structure of T4 phage lysozyme. Biochim Biophys Acta (BBA) Protein Struct. 1975; 405(2):442–51. source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Despite its popularity, in the learning context there are a number of issues causing the kappa measure to produce unreliable results (for instance, its high sensitivity to the distribution of the marginal totals [73–75])”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Background
What the sources say
- Not checked yetcites [73] Flight L, Julious SA. The disagreeable behaviour of the kappa statistic. Pharm Stat. 2015; 14:74–8. source
- Not checked yetcites [74] Powers DMW. The problem with Kappa. In: Proceedings of EACL 2012 – the 13th Conference of the European Chapter of the Association for Computational Linguistics. Avignon: ACL: 2012. p. 345–55.
- Not checked yetcites [75] Delgado R, Tibau X-A. Why Cohen’s Kappa should be avoided as performance measure in classification. PloS ONE. 2019; 14(9):0222916.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In fact, when a prediction displays many true positives but few true negatives (or many true negatives but few true positives) we will show that F1 and accuracy can provide misleading information, while MCC always generates results that reflect the overall prediction issues.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These results show that, while accuracy and F1 score often generate high scores that do not inform the user about ongoing prediction issues, the MCC is a robust, useful, reliable, truthful statistical measure able to correctly reflect the deficiency of any prediction in any dataset.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
boosteddirectn = 6- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Here accuracy again generated overoptimistic, misleading, and inflated high results”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The F1 score ranking and the accuracy ranking, in conclusion, are hiding this important flaw of the top classifier: k-NN was unable top correctly predict a high percentage of patients.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“There, accuracy and F1 generated overoptimistic and inflated results”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Accuracy and F1 score, although popular, can generate misleading results on imbalanced datasets, because they fail to consider the ratio between positive and negative elements.”
- Also stated in: § Conclusions · plain
“F1 and accuracy, instead, generate reliable results only when applied to balanced datasets, and produce misleading results when applied to imbalanced cases.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Conclusions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Also stated in: § Conclusions · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“With its low value (MCC = +0.29), the MCC informs the readers about the poor general outcome of the radial SVM, while the accuracy and F1 score show misleading values.”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“The dataset contains 2,000 gene probsets for 62 patients, of which 22 are healthy controls and 40 have colon cancer (35.48% negatives and 64.52% positives) [106].”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
What the sources say
- Not checked yetcites [106] Alon U, Barkai N, Notterman DA, Gish K, Ybarra S, Mack D, Levine AJ. Data pertaining to the article ‘Broad patterns of gene expression revealed by clustering of tumor and normal colon tissues probed by oligonucleotide arrays’. 2000. http://genomics-pubs.princeton.edu/oncology/affydata/index.html. Accessed 10 Dec 2019.
plainn = 62- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
Accuracy and F1 score are the most common metrics used for binary classification in machine learning.
“We decided to focus on accuracy and F1 score because they are the most common metrics used for binary classification in machine learning.”
The paper relies on this without support.
The synthetic use cases are realistic representations of binary classification scenarios.
“here we describe some synthetic, realistic scenarios where MCC results are more informative and truthful than the other two measures analyzed.”
The paper relies on this without support.
Accuracy and F1 score are more commonly used in machine learning studies related to biomedical applications than other rates.
“because accuracy and F1 score are more commonly used in machine learning studies related to biomedical applications.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“MCC is a more reliable metric, whereby a high score is assigned only if the prediction was correct for the four base categories (TP, FP, TN and FP), taking into account the size of P and N [85].”
From A Survey of Underwater Acoustic Data Classification Methods Using Deep Learning for Shoreline Surveillance (2022) · cites this paper as [85]
In the citing paper
“since it has been shown to present a balanced score when dealing with imbalanced data [11, 6] as is our case with fewer manipulated images.”
From BioFors: A Large Biomedical Image Forensics Dataset (2021) · cites this paper as [11]
In the citing paper
“(3) the absolute value of F1 changes by simply switching the outcome labels (ie, when 1 becomes 0 and 0 becomes 1).”
From Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance (2025) · cites this paper as [77]
In the citing paper
“(2) F1 has no intuitive interpretation”
From Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance (2025) · cites this paper as [77]
In the citing paper
“(1) F1 ignores true negatives”
From Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance (2025) · cites this paper as [77]
In the citing paper
“F1 and MCC were introduced to address the challenges caused by class imbalance, where classification accuracy can be inflated by classifying all patients as low risk when the event is rare.”
From Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance (2025) · cites this paper as [77]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated major: it would touch a result — a value a result rests on, reported and recomputed p-values on opposite sides of the significance level, two passages that conflict with no sign which is right, or a cited work retracted before this paper was published.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“Here, accuracy again generated an overoptimistic inflated score”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“all three statistical scores generated low results that reflect the mediocre quality of the prediction: F1 score = 0.17 and accuracy = 0.10 in the [0, 1] interval”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“the prediction technique failed in predicting negative elements, and therefore its confusion matrix showed a low percentage of true negatives”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“the method was able to correctly identify multiple negative data instances (88 healthy patients out of 89), but unable to correctly predict most of sick patients (only 2 true positives out of 11 possible elements)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“Even if accuracy showed an excessively high result score”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“all three statistical rates showed a low score which emphasized the deficiency in the prediction process (accuracy = 0.24, F1 score = 0.12, and MCC = −0.24)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
“the best classifier resulted being k-NN (F1 score = 0.87 and accuracy = 0.81)”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Genomics scenario: colon cancer gene expression
“k-nearest neighbors | +0.48 | 0.87 | 0.80 | 0.92 | 0.52”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“only 1 healthy individual out of 9 was correctly recognized”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“TP=90, FN=1, TN=0, FP=9”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“Finally, in the last Use case C2 (positively imbalanced dataset)”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“Use case C2 Negatively imbalanced dataset | 11 | 89 | 2 | 9 | 88 | 1”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“For the Use case A1 (negatively imbalanced dataset)”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“made of 9 healthy individuals (negatives =9%) and 91 sick patients (positives =91%)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“Also in the Use case C1 (positively imbalanced dataset)”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“90 healthy controls (negatives =90%) and 10 sick patients (positives =10%)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“only 5 sick patients out of 70”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“TP = 5, FN = 70, TN = 19, FP = 6”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Results and discussion > Use cases
“the resulting MCC = –0.03”
§ The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation > Methods > Relationship between measures
“In red, the (−0.04, 0.95) point corresponding to use case A1”
Citations
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- Akosa JS. Predictive accuracy: a misleading performance measure for highly imbalanced data. In: Proceedings of the SAS Global Forum 2017 Conference. Cary, North Carolina: SAS Institute Inc.: 2017. p. 942–2017.
- Guilford JP. Psychometric Methods. New York City: McGraw-Hill; 1954.
- van Rijsbergen CJ, Joost C. Information Retrieval. New York City: Butterworths; 1979.
- Sasaki Y. The truth of the F-measure. Teach Tutor Mater. 2007; 1(5):1–5.
- Dubey A, Tarar S. Evaluation of approximate rank-order clustering using Matthews correlation coefficient. Int J Eng Adv Technol. 2018; 8(2):106–13.
- Suresh Babu N. Various performance measures in binary classification – An overview of ROC study. Int J Innov Sci Eng Technol. 2015; 2(9):596–605.
- Ferri C, Hernández-Orallo J, Flach PA. A coherent interpretation of AUC as a measure of aggregated classification performance. In: Proceedings of ICML 2011 – the 28th International Conference on Machine Learning. Norristown: Omnipress: 2011. p. 657–64.
Cited by
Sorted by citations
Items 401–500 of 1,016
Zukaib, U., Cui, X., Zheng, C., Dong, L., & Din, S. U. (2024) · Journal of Parallel and Distributed Computing · doi:10.1016/j.jpdc.2024.104934 · Cited by 48
Ochoa, S., & Milam, V. T. (2025) · ACS Synthetic Biology · doi:10.1021/acssynbio.5c00196 · Cited by 50
LSCIDMR: Large-Scale Satellite Cloud Image Database for Meteorological Research
Bai, C., Zhang, M., Zhang, J., Zheng, J., & Chen, S. (2021) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2021.3080121 · Cited by 46
“The activation function in the added fully connected layer of the last layer of these four networks was set as Sigmoid [68], and the loss function is changed to binary cross entropy [69], [70].”
MethodBiologically relevant transfer learning improves transcription factor binding prediction
Novakovsky, G., Saraswat, M., Fornés, O., Mostafavi, S., & Wasserman, W. W. (2021) · Genome biology · doi:10.1186/s13059-021-02499-5 · Cited by 44
“Given the advantages of the Matthews correlation coefficient (MCC) over other more popular metrics for evaluating binary classification tasks [43], we chose MCC as our performance metric.”
MethodSelection of the Right Undergraduate Major by Students Using Supervised Learning Techniques
Alsayed, A. O., Rahim, M. S. M., Albidewi, I., et al. (2021) · Applied Sciences · doi:10.3390/app112210639 · Cited by 44
Jackson‐Blake, L., Clayer, F., Haande, S., Sample, J. E., & Moe, S. J. (2022) · Hydrology and earth system sciences · doi:10.5194/hess-26-3103-2022 · Cited by 44
Thakur, M., Dhanalakshmi, S., Kuresan, H., et al. (2022) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-022-04361-3 · Cited by 44
“This is specifically suited for binary classification problems (Chicco 2020).”
BackgroundPerforma Klasifikasi K-NN dan Cross Validation Pada Data Pasien Pengidap Penyakit Jantung
Azis, H., Purnawansyah, P., Fattah, F., & Putri, I. P. (2020) · ILKOM Jurnal Ilmiah · doi:10.33096/ilkom.v12i2.507.81-86 · Cited by 42
“…+ 𝐹𝑁 𝑇𝑁 + 𝐹𝑃 Proses klasifikasi multiclass , perhitungan performa presisi, recall , dan f-measure dapat diterapkan pada setiap label secara independen [19], [20]. presisi menggunakan persamaan 3, persamaan 4 menunjukan perhitungan performa recall dan persamaan 5 untuk f-measure [21], [22].”
BackgroundOgunleye, A. Z., Piyawajanusorn, C., Gonçalvès, A., Ghislat, G., & Ballester, P. J. (2022) · Advanced Science · doi:10.1002/advs.202201501 · Cited by 43
Review and assessment of Boolean approaches for inference of gene regulatory networks
Pušnik, Ž., Mraz, M., Zimic, N., & Moškon, M. (2022) · Heliyon · doi:10.1016/j.heliyon.2022.e10222 · Cited by 47
“It yields a high score only if the predictor correctly predicts the majority of positive as well as the majority of negative cases [64].”
BackgroundJiang, T., Zhou, L., Hu, X., Zeng, L.-Z., Ma, X., Huang, J.-B., Cui, J. W., Tu, L., Zhou, C., Yao, X., et al. (2022) · Evidence-based Complementary and Alternative Medicine · doi:10.1155/2022/3384209 · Cited by 52
Allesøe, R. L., Thompson, W. K., Bybjerg‐Grauholm, J., HOUGAARD, D. M., Nordentoft, M., Werge, T. M., Rasmussen, S., & Benros, M. E. (2022) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2022.4076 · Cited by 47
MacNell, N., Feinstein, L., Wilkerson, J., Salo, P. M., Molsberry, S. A., Fessler, M. B., Thorne, P. S., Motsinger‐Reif, A. A., & Zeldin, D. C. (2023) · PLoS ONE · doi:10.1371/journal.pone.0280387 · Cited by 44
“We selected the F1 score because it and the related precision-recall plot have been shown to have advantages compared to the area under the curve (AUC) in the presence of class imbalance [25,26] although the Mathews correlation coefficient may offer additional advantages [27].”
MethodTeimouri, H., Medvedeva, A., & Kolomeisky, A. B. (2023) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c01551 · Cited by 46
Pearson–Matthews correlation coefficients for binary and multinary classification
Stoica, P., & Babu, P. (2024) · Signal Processing · doi:10.1016/j.sigpro.2024.109511 · Cited by 43
Antonijević, M., Zivkovic, M. Z., Djuric-Jovicic, M. D., Nikolić, B., Perišić, J., Milovanović, M., Jovanović, L., Abdel-Salam, M., & Bačanin, N. (2025) · Scientific Reports · doi:10.1038/s41598-025-88135-9 · Cited by 49
Detection of Online Fake News Using Blending Ensemble Learning
Hansrajh, A., Adeliyi, T. T., & Wing, J. (2021) · Scientific Programming · doi:10.1155/2021/3434458 · Cited by 46
“It reflects the data in connection with the true positives, false negatives, false positives, and true negatives [42].”
BackgroundEmenecker, R. J., Griffith, D., & Holehouse, A. S. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.06.06.494887 · Cited by 42
Zhao, X., Sui, Y., Ruan, X., Wang, X., He, K., Dong, W., Qu, H., & Fang, X. (2022) · Clinical Epigenetics · doi:10.1186/s13148-022-01232-8 · Cited by 41
“Here, AUC and Matthews correlation coefficient (MCC) were used to measure the results [32].”
MethodBraun, M., & Kellner, L. (2022) · Fatigue & Fracture of Engineering Materials & Structures · doi:10.1111/ffe.13800 · Cited by 42
Gharakhanlou, N. M., & Pérez, L. (2022) · Entropy · doi:10.3390/e24111630 · Cited by 42
“F1 score is calculated according to Equation (17) and auxiliary Equations (18) and (19) [93].”
MethodOmran, T., Sharef, B. T., Groşan, C., & Li, Y. (2022) · Data & Knowledge Engineering · doi:10.1016/j.datak.2022.102106 · Cited by 53
Hindi fake news detection using transformer ensembles
Praseed, A., Rodrigues, J., & Thilagam, P. S. (2022) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2022.105731 · Cited by 46
PASSerRank: Prediction of allosteric sites with learning to rank
Tian, H., Xiao, S., Jiang, X., & Tao, P. (2023) · Journal of Computational Chemistry · doi:10.1002/jcc.27193 · Cited by 38
Multi‐Hour‐Ahead Dst Index Prediction Using Multi‐Fidelity Boosted Neural Networks
Hu, A., Camporeale, E., & Swiger, B. M. (2023) · Space Weather · doi:10.1029/2022sw003286 · Cited by 42
“Those metrics have shown some advantages over the F1 score and accuracy in binary classification evaluation (Chicco & Jurman, 2020).”
Lee, H., Moon, S. J., Kim, S. W., Min, J. W., Park, H. S., Yoon, H. E., Kim, Y. S., Kim, H. W., Yang, C. W., Chung, S., et al. (2023) · Nephrology Dialysis Transplantation · doi:10.1093/ndt/gfad064 · Cited by 43
Control, coordination, and adaptation functions in construction contracts: A machine-coding model
Fu, Y., Xu, C., Zhang, L., & Chen, Y. (2023) · Automation in Construction · doi:10.1016/j.autcon.2023.104890 · Cited by 46
An intrusion detection system based on stacked ensemble learning for IoT network
Cao, Y., Wang, Z., Ding, H., et al. (2023) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2023.108836 · Cited by 42
Wang, J., Horlacher, M., Cheng, L., & Winther, O. (2023) · Briefings in Bioinformatics · doi:10.1093/bib/bbad249 · Cited by 42
“Additional metrics such as accuracy (ACC), F1 score and the more reliable Matthew’s correlation coefficient [131] can also be utilized.”
MethodRani, A., Gupta, S. K., Singh, S. K., et al. (2023) · Earth · doi:10.3390/earth4030039 · Cited by 42
Hong, H. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.121678 · Cited by 42
Automatic structuring of radiology reports with on-premise open-source large language models
Woźnicki, P., Laqua, C., Fiku, I., Hekalo, A., Truhn, D., Engelhardt, S., Kather, J. N., Foersch, S., D’Antonoli, T. A., dos Santos, D. P., et al. (2024) · European Radiology · doi:10.1007/s00330-024-11074-y · Cited by 58
A New Approach for Detecting Sleep Apnea Using a Contactless Bed Sensor: Comparison Study
Sadek, I., Heng, T. T. S., Seet, E. C. P., et al. (2020) · Journal of Medical Internet Research · doi:10.2196/18297 · Cited by 41
Deep learning improves identification of Radio Frequency Interference
Sadr, A. V., Bassett, B. A., Oozeer, N., et al. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa2724 · Cited by 42
Emotion Analysis in Human–Robot Interaction
Szabóová, M., Sarnovský, M., Krešňáková, V., & Machová, K. (2020) · Electronics · doi:10.3390/electronics9111761 · Cited by 43
Yik, B. J., Dood, A. J., de Arellano, D. C., Fields, K. B., & Raker, J. R. (2021) · Chemistry Education Research and Practice · doi:10.1039/d1rp00111f · Cited by 51
Agnostic CH-DT Technique for SCADA Network High-Dimensional Data-Aware Intrusion Detection System
Ahakonye, L. A. C., Nwakanma, C. I., Lee, J., & Kim, D. (2023) · IEEE Internet of Things Journal · doi:10.1109/jiot.2023.3237797 · Cited by 43
“Chicco and Jurman [43] completed extensive research and presented MCC as a viable approach.”
BackgroundA Comparative Analysis of Deep Learning Approaches for Predicting Breast Cancer Survivability
Gupta, S., & Gupta, M. K. (2021) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-021-09679-3 · Cited by 44
Grønning, A. G. B., Kacprowski, T., & Scheele, C. C. (2021) · Biology Methods and Protocols · doi:10.1093/biomethods/bpab021 · Cited by 41
“It has been suggested that the MCC function is a good performance metric for imbalanced data sets [42].”
BackgroundA Hybrid Deep Learning Approach for Intrusion Detection in IoT Networks
Emeç, M., & Özcanhan, M. H. (2022) · Advances in Electrical and Computer Engineering · doi:10.4316/aece.2022.01001 · Cited by 46
Liu, J.-C., Wei, J., Heidari, A. A., Kuang, F., Zhang, S., Gui, W., Chen, H., & Pan, Z. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.105356 · Cited by 41
Yoon, S., & Lee, W. (2022) · Ecological Indicators · doi:10.1016/j.ecolind.2022.109830 · Cited by 41
de Silva, K., & Kunz, H. (2023) · Intelligence-Based Medicine · doi:10.1016/j.ibmed.2023.100091 · Cited by 42
“This study used as an additional metric Matthew ’ s Correlation Coefficient (MCC) [40].”
Quantifying chatbots’ ability to learn business processes
Kecht, C., Egger, A., Kratsch, W., & Röglinger, M. (2023) · Information Systems · doi:10.1016/j.is.2023.102176 · Cited by 48
Mamo, D. N., Yilma, T. M., Tewelgne, M. F., Sebastian, Y., Demass, T. B., Melaku, M. S., & Walle, A. D. (2023) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-023-02167-7 · Cited by 44
“The matrix is made up of predictions that have been summarized into a total number of correct and incorrect predictions [70, 71] (Table 1).”
Detection of Cotton Verticillium Wilt Disease Severity Based on Hyperspectrum and GWO-SVM
Zhang, N., Zhang, X., Shang, P., et al. (2023) · Remote Sensing · doi:10.3390/rs15133373 · Cited by 41
“The commonly used evaluation parameters for multi-classification problems [59] include Accuracy, Recall, Precision, and F1-score.”
MethodRaiaan, M. A. K., Fahad, N. M., Mukta, M. S. H., et al. (2024) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2024.106279 · Cited by 41
Malavi, D., Raes, K., & Haute, S. V. (2024) · Current Research in Food Science · doi:10.1016/j.crfs.2024.100913 · Cited by 41
Yin, Z., Zhang, M., Liu, R., & Cai, Y. (2025) · Water Research · doi:10.1016/j.watres.2025.123500 · Cited by 44
Objective Evaluation Metrics for Automatic Classification of EEG Events
Shah, V., Golmohammadi, M., Obeid, I., & Picone, J. (2021) · Springer eBooks · doi:10.1007/978-3-030-67494-6_8 · Cited by 44
Naeem, S. M., Mabrouk, M. S., Marzouk, S. Y., & Eldosoky, M. A. A. (2020) · Briefings in Bioinformatics · doi:10.1093/bib/bbaa170 · Cited by 41
“They are accuracy (ACC), error rate, Matthews correlation coefficient (MCC) [53] and F1 score (the coordinated mean of precision and sensitivity) [54, 55] as follows:”
BackgroundSeo, S., Kim, Y., Han, H., Son, W., Hong, Z.-Y., Sohn, I., Shim, J., & Hwang, C. (2021) · Frontiers in Pharmacology · doi:10.3389/fphar.2021.670670 · Cited by 48
“Accuracy and F1-score have been among the most quintessential metrics for binary classi fi cation problems.”
BackgroundInfluentialA Novel Deep Learning Approach for Anomaly Detection of Time Series Data
Ji, Z., Gong, J., & Feng, J. (2021) · Scientific Programming · doi:10.1155/2021/6636270 · Cited by 44
“As reported in previous studies, MCC produces a more informative and truthful score in evaluating binary classifications, particularly for the imbalanced data [60, 61].”
ResultEnsemble Model of the Financial Distress Prediction in Visegrad Group Countries
Pavličko, M., Ďurica, M., & Mazanec, J. (2021) · Mathematics · doi:10.3390/math9161886 · Cited by 43
“F1 Score = 2 · TP 2 · TP + FN + FP. (1) As Chicco and Jurman [73] state, the accuracy, AUC, and F1 Score are biased by highly imbalanced class distribution while the Matthews correlation coefficient (MCC) is not.”
BackgroundIntroducing Image Classification Efficacies
Shao, G., Tang, L., & Zhang, H. (2021) · IEEE Access · doi:10.1109/access.2021.3116526 · Cited by 41
“but is still affected by class imbalance [17].”
BackgroundRehman, M. U., Tayara, H., & Chong, K. T. (2021) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2021.10.034 · Cited by 41
“As suggested in literature the binary classification evaluation is better carried out by MCC rather than other [38,39].”
BackgroundAn effectiveness analysis of transfer learning for the concept drift problem in malware detection
García, D. E., DeCastro‐García, N., & Castañeda, Á. L. M. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.118724 · Cited by 41
Jiang, T., Liu, S., Cao, S., Liu, Y., Cui, Z., Wang, Y., & Guo, H. (2021) · BMC Bioinformatics · doi:10.1186/s12859-021-04422-y · Cited by 39
“The benchmark results show that the overall F1 score and Matthews correlation coefficient (MCC) [25] rate increase along with the coverage, read length, and accuracy rate.”
BackgroundKubinski, R., Djamen-Kepaou, J.-Y., Zhanabaev, T., Hernández-García, Á., Bauer, S., Hildebrand, F., Korcsmáros, T., Karam, S., Jantchou, P., Kafi, K., et al. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.784397 · Cited by 40
Satellite flood detection integrating hydrogeomorphic and spectral indices
Samela, C., Coluzzi, R., Imbrenda, V., et al. (2022) · GIScience & Remote Sensing · doi:10.1080/15481603.2022.2143670 · Cited by 40
Advanced Persistent Threat Identification with Boosting and Explainable AI
Hasan, M. M., Islam, M. U., & Uddin, J. (2023) · SN Computer Science · doi:10.1007/s42979-023-01744-x · Cited by 40
“…merges precision and recall in a more interpretable domain, a formidable reliable performance measure is the Matthews Correlation Coefficient (MCC) [29], which is preferred over F1 score because of its balanced assessment of classifiers irrespective of class positivity or negativity for that…”
BackgroundSchilcher, J., Nilsson, A., Andlid, O., & Eklund, A. (2024) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2023.107704 · Cited by 41
Caro, F. D., Collin, A. J., Giannuzzi, G. M., Pisani, C., & Vaccaro, A. (2023) · IEEE Access · doi:10.1109/access.2023.3334394 · Cited by 44
“Various metrics can be derived from the elements of the confusion matrix to assess the accuracy of the model as shown in [37].”
MethodPredicting the success of startups using a machine learning approach
Bidgoli, M. R., Vanani, I. R., & Goodarzi, M. S. (2024) · Journal of Innovation and Entrepreneurship · doi:10.1186/s13731-024-00436-x · Cited by 40
“Accuracy presents the percentage among the correctly predicted and all the cases in the dataset (Chicco & Jurman, 2020): The other metrics used to investigate the performance of classification algorithms are ROC and AUC.”
BackgroundPredicting employee attrition and explaining its determinants
Varkiani, S. M., Pattarin, F., Fabbri, T., & Fantoni, G. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.126575 · Cited by 40
Ullah, I., Youn, H. Y., & Han, Y. (2021) · Future Generation Computer Systems · doi:10.1016/j.future.2021.06.012 · Cited by 40
Hua, Y., Shi, Y., Cui, X., & Li, X. (2021) · Molecular Diversity · doi:10.1007/s11030-021-10255-x · Cited by 41
Hulme, A., Stanton, N. A., Walker, G. H., Waterson, P. E., & Salmon, P. M. (2021) · Safety Science · doi:10.1016/j.ssci.2021.105454 · Cited by 39
Sürücü, M., İşler, Y., Perc, M., & Kara, R. (2021) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0069272 · Cited by 42
Färber, M., & Ao, L. (2022) · Quantitative Science Studies · doi:10.1162/qss_a_00183 · Cited by 43
“The MCC only achieves high values if all four classes of the diffusion matrix are classified accurately, and is therefore preferred for evaluating unbalanced data sets (Chicco & Jurman, 2020).”
BackgroundHyproBert: A Fake News Detection Model Based on Deep Hypercontext
Nadeem, M. I., Mohsan, S. A. H., Ahmed, K., Li, D., Zheng, Z., Shafiq, M., Karim, F. K., & Mostafa, S. M. (2023) · Symmetry · doi:10.3390/sym15020296 · Cited by 40
Convolution neural network for effective burn region segmentation of color images
Chauhan, J., & Goyal, P. (2020) · Burns · doi:10.1016/j.burns.2020.08.016 · Cited by 41
AI Algorithm for Mode Classification of PCF-SPR Sensor Design
Goswami, M., Khare, P., & Shakya, S. (2023) · Plasmonics · doi:10.1007/s11468-023-01997-5 · Cited by 42
Bulavas, V., Marcinkevičius, V., & Rumiński, J. (2021) · Informatica · doi:10.15388/21-infor457 · Cited by 44
Machine Learning Approach towards LoRaWAN Indoor Localization
Perković, T., Rodić, L. D., Šabić, J., & Šolić, P. (2023) · Electronics · doi:10.3390/electronics12020457 · Cited by 42
Accurate, interpretable predictions of materials properties within transformer language models
Korolev, V., & Protsenko, P. V. (2023) · Patterns · doi:10.1016/j.patter.2023.100803 · Cited by 44
Altamimi, A., Alarfaj, A. A., Umer, M., Alabdulqader, E. A., Alsubai, S., Kim, T.-H., & Ashraf, I. (2024) · BMC Medical Research Methodology · doi:10.1186/s12874-024-02324-0 · Cited by 52
“The following are the evaluation parameters that are offered: The Matthews Correlation Coefficient (MCC) is a metric used to evaluate the performance of binary classification models [44].”
MethodDeep learning for hate speech detection: a comparative study
Malik, J. S., Qiao, H., Pang, G., & van den Hengel, A. (2024) · International Journal of Data Science and Analytics · doi:10.1007/s41060-024-00650-6 · Cited by 101
“As shown in Table 2, the Glove and TF-IDF models do not have consistently superior effectiveness over each other.”
BackgroundPeng, D., Desmet, W., & Gryllias, K. (2025) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2025.110995 · Cited by 49
Liang, Z., & Martell, M. A. C. (2021) · Frontiers in Digital Health · doi:10.3389/fdgth.2021.665946 · Cited by 40
“On the other hand, MMCC is widely accepted as a more appropriate performance measure for imbalanced multi-class classification as it considers the accuracy and error rates on all classes and involves all elements of a confusion matrix (42, 43).”
BackgroundRahman, M., Kang, M.-W., & Biswas, P. (2021) · Transportation Research Part C Emerging Technologies · doi:10.1016/j.trc.2021.103310 · Cited by 39
Machine Learning and Its Applications for Protozoal Pathogens and Protozoal Infectious Diseases
Hu, R.-S., Hesham, A. E., & Zou, Q. (2022) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2022.882995 · Cited by 45
“Instead, MCC [equation (6)] considers positive and negative elements ratio in some classi fi cation tasks, which confers tremendous advantage in evaluating unbalanced datasets than accuracy (Chicco and Jurman, 2020).”
BackgroundTransfer Learning with Convolutional Neural Networks for Rainfall Detection in Single Images
Notarangelo, N. M., Hirano, K., Albano, R., & Sole, A. (2021) · Water · doi:10.3390/w13050588 · Cited by 44
“To measure the rain detection performance, several metrics are used and compared to reference values [41,55,56], as reported in Table 4.”
BackgroundMethodOtović, E., Njirjak, M., Kalafatović, D., & Mauša, G. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c00526 · Cited by 37
Automated detection of heart valve disorders with time-frequency and deep features on PCG signals
Arslan, Ö. (2022) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2022.103929 · Cited by 42
Reddy, V., Nafees, A., & Raman, S. (2023) · Current Opinion in Supportive and Palliative Care · doi:10.1097/spc.0000000000000645 · Cited by 39
“The metric F1 score is used to measure the accuracy of classifying items, where a score of 1.0 reveals perfect classi fi cation [54].”
MethodInfluentialFatima, M., Khan, M. A., Shaheen, S., Almujally, N. A., & Wang, S. (2023) · CAAI Transactions on Intelligence Technology · doi:10.1049/cit2.12219 · Cited by 40
Deep learning-based classification of microalgae using light and scanning electron microscopy images
Sonmez, M. E., Altinsoy, B., Ozturk, B. Y., Gumus, N. E., & Eczacioglu, N. (2023) · Micron · doi:10.1016/j.micron.2023.103506 · Cited by 38
Dube, L., & Verster, T. (2023) · Data Science in Finance and Economics · doi:10.3934/dsfe.2023021 · Cited by 38
Summer heatwaves on the Baltic Sea seabed contribute to oxygen deficiency in shallow areas
Safonova, K., Meier, H. E. M., & Gröger, M. (2024) · Communications Earth & Environment · doi:10.1038/s43247-024-01268-z · Cited by 42
“MCC evaluates each category of theconfusionmatrix(truepositives, falsenegatives, truenegatives, andfalse positives) with respect to the other ones, proportionally both to the size of positive elements and the size of negative elements in the dataset 67,68 .”
Identifying small-molecules binding sites in RNA conformational ensembles with SHAMAN
Panei, F. P., Gkeka, P., & Bonomi, M. (2024) · Nature Communications · doi:10.1038/s41467-024-49638-7 · Cited by 40
Vasavi, S., Aswarth, K., Pavan, T. S. D., et al. (2021) · Materials Today Proceedings · doi:10.1016/j.matpr.2021.03.658 · Cited by 38
Predicting non-state terrorism worldwide
Python, A., Bender, A., Nandi, A., Hancock, P., Arambepola, R., Brandsch, J., & Lucas, T. (2021) · Science Advances · doi:10.1126/sciadv.abg4778 · Cited by 34
Convolutional Networks and Transformers for Mammography Classification: An Experimental Study
Cantone, M., Marrocco, C., Tortorella, F., & Bria, A. (2023) · Sensors · doi:10.3390/s23031229 · Cited by 46
“MCC [42] is a correlation coefficient between prediction and true label, it produces a more informative and truthful score in evaluating binary classifications than accuracy giving a more realistic interpretation of classifier performance especially in the case of unbalanced datasets.”
BackgroundA Survey on Artificial Intelligence-Based Acoustic Source Identification
Zaheer, R., Ahmad, I., Habibi, D., Islam, K. Y., & Phung, Q. V. (2023) · IEEE Access · doi:10.1109/access.2023.3283982 · Cited by 45
“MCC offers numerous advantages over the F1 score and accuracy in binary classification problems [150].”
BackgroundKarpiński, R., Krakowski, P., Jonak, J., et al. (2023) · Applied Computer Science · doi:10.35784/acs-2023-40 · Cited by 37
“In practice, as with the value of the area under the ROC curve, the higher the F1 score, the better the binary classifier performs (Chicco & Jurman, 2020; Luque et al., 2019).”
MethodZero-Trust Marine Cyberdefense for IoT-Based Communications: An Explainable Approach
Nkoro, E. C., Njoku, J. N., Nwakanma, C. I., Lee, J., & Kim, D. (2024) · Electronics · doi:10.3390/electronics13020276 · Cited by 50
“The evaluation metrics within the experiment include the Mathew correlation coefficient (MCC) score [49], a weighted F1-Score, accuracy, test-loss value, and training time (computational resource requirements).”
Firmansyah, H. R., Sarli, P. W., Twinanda, A. P., Santoso, D., & Imran, I. (2024) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2023.107824 · Cited by 36
Machrowska, A., Karpiński, R., Maciejewski, M., et al. (2024) · Applied Computer Science · doi:10.35784/acs-2024-18 · Cited by 37
“A confusion matrix, ROC curves and their key parameters were used to compare the results of the obtained classifiers, as well as measures resistant to group differentiation such as Matthews correlation coefficient and F1 Score (Chicco & Jurman, 2020).”
MethodMostafaei, S. H., Tanha, J., & Sharafkhaneh, A. (2024) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2024.104689 · Cited by 38
Metadata
- Authors
- Chicco, D., & Jurman, G.
- Affiliations
- Krembil Research Institute (CA)
- Fondazione Bruno Kessler (IT)
- Corresponding author
- Chicco, Davide
- Venue
- BMC Genomics
- Published
- 2020-01-02
- Volume
- 21
- Issue
- 1
- Pages
- 6-6
- ISSN
- 1471-2164 (ISSN-L)
- PMC
- PMC6941312
- OpenAlex
- W2999309192
- Semantic Scholar
- 44858b662822d291a5e1e9e3501ad19a9f1572c2
- Cited by
- 6,143
- References
- 104
- Citations by year
- 2026: 1118 · 2025: 1152 · 2024: 1060 · 2023: 1032 · 2022: 883 · 2021: 682 · 2020: 211
- FWCI
- 276.55
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- BMC Genomics (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- BOA (University of Milano-Bicocca) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Iris (University of Trento) (submittedVersion)
- Funders
- University of Toronto
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- Matthews correlation coefficient, F1 score, accuracy, confusion matrix, class imbalance, classification metrics
- MeSH terms
- Machine Learning, Correlation of Data, Algorithms, Data Interpretation, Statistical, Computational Biology
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.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
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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