Table 2.

Performance measures for multi-class classifiers. t p _i, t n _i, f p _i and f n _i are, in turn, tp, tn, fp and fn for class i [59]. The multi-class MCC is calculated taking into account all the entries of the confusion matrix C _K×K involving all K classes [60]. The ij-th entry (c _ij) is the number of examples of the true class i that have been assigned to the class j by the classifier

Measure	Formula
Accuracy	$\frac{\sum _{i=1}^K\frac{t{p}_i+t{n}_i}{t{p}_i+f{n}_i+f{p}_i+t{n}_i}}{K}$
MCC	$\frac{\sum _{k,l,m=1}^K{C}_{\mathit{\text{kk}}}{C}_{\mathit{\text{ml}}}-C_{\mathit{\text{lk}}}{C}_{\mathit{\text{km}}}}{\sqrt{\sum _{k=1}^K\left[\left(\sum _{l=1}^K{C}_{\mathit{\text{lk}}}\right)\left(\sum _{f,g=1f\ne k}^K{C}_{\mathit{\text{gf}}}\right)\right]}\sqrt{\sum _{k=1}^K\left[\left(\sum _{l=1}^K{C}_{\mathit{\text{kl}}}\right)\left(\sum _{f,g=1f\ne k}^K{C}_{\mathit{\text{fg}}}\right)\right]}}$