The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation

Table 5 Bioinformatics scenario: binary classification of colon tissue gene expression

Rank	Method	MCC	BA	BM	MK	TPR	TNR	PPV	NPV
	MCC ranking:
1	Decision Tree	0.447	0.715	0.429	0.477	0.728	0.701	0.774	0.702
2	Radial SVM	0.423	0.695	0.390	0.517	0.891	0.498	0.754	0.726
3	k-Nearest Neighbors	0.418	0.706	0.412	0.443	0.887	0.525	0.826	0.617
4	Naïve Bayes	0.408	0.722	0.444	0.375	0.778	0.667	0.875	0.500
	BA ranking:
1	Naïve Bayes	0.408	0.722	0.444	0.375	0.778	0.667	0.875	0.500
2	Decision Tree	0.447	0.715	0.429	0.477	0.728	0.701	0.774	0.702
3	k-Nearest Neighbors	0.418	0.706	0.412	0.443	0.887	0.525	0.826	0.617
4	Radial SVM	0.423	0.695	0.390	0.517	0.891	0.498	0.754	0.726
	BM ranking:
1	Naïve Bayes	0.408	0.722	0.444	0.375	0.778	0.667	0.875	0.500
2	Decision Tree	0.447	0.715	0.429	0.477	0.728	0.701	0.774	0.702
3	k-Nearest Neighbors	0.418	0.706	0.412	0.443	0.887	0.525	0.826	0.617
4	Radial SVM	0.423	0.695	0.390	0.517	0.891	0.498	0.754	0.726
	MK ranking:
1	Radial SVM	0.423	0.695	0.390	0.517	0.891	0.498	0.754	0.726
2	Decision Tree	0.447	0.715	0.429	0.477	0.728	0.701	0.774	0.702
3	k-Nearest Neighbors	0.418	0.706	0.412	0.443	0.887	0.525	0.826	0.617
4	Naïve Bayes	0.408	0.722	0.444	0.375	0.778	0.667	0.875	0.500

Radial SVM: Support Vector Machine with radial Gaussian kernel. Positives: patients diagnosed with colon cancer. Negatives: healthy controls. MCC: Matthews correlation coefficient(Eq. 5). BA: balanced accuracy (Eq. 6). BM: bookmaker informedness (Eq. 7). MK: markedness (Eq. 8). TPR: true positive rate. TNR: true negative rate. PPV: positive predictive value. NPV: negative predictive value. MCC, BM, MK value interval: [−1,+1]. BA, TPR, TNR, PPV, NPV value interval: [0,1].
Bold values represent the corresponding ranking for each metric

ISSN: 1756-0381