Validation Metrics for Landslide Susceptibility Models

In this study, Sensitivity (SST), Specificity (SPF) and Accuracy (ACC) are popular statistical indexes used for validation of model performance. Out of these, the SST and SPF are the proportion of the landslide and non-landslide instances which are correctly predicted as landslide and non-landslide, respectively [37 (link),63 (link)]. Values of these indexes are calculated using the values extracted from confusion matrix as below: $\mathrm{SST}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$
$\mathrm{SPF}=\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}}$
$\mathrm{ACC}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{NT}+\mathrm{FP}+\mathrm{FN}}$
$\mathrm{Kappa}\mathrm{index}(\mathrm{K})=\frac{{\mathrm{P}}_{\mathrm{C}}-{\mathrm{P}}_{\exp }}{1-{\mathrm{P}}_{\exp }}$
${\mathrm{P}}_{\mathrm{C}}=(\mathrm{TP}+\mathrm{TN})/(\mathrm{TP}+\mathrm{TN}+\mathrm{FN}+\mathrm{FP})$
$\mathrm{Pexp}=\left(\left(\mathrm{TP}+\mathrm{FN}\right)\left(\mathrm{TP}+\mathrm{FP}\right)+\left(\mathrm{FP}+\mathrm{TN}\right)\left(\mathrm{FN}+\mathrm{TN}\right)/\sqrt{(\mathrm{TP}+\mathrm{TN}+\mathrm{FN}+\mathrm{FP})}\right)$
$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{n}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{X}}_{\mathrm{pred}.}}-{\mathrm{X}}_{\mathrm{act}.}{)}^2$
where TP (true positive) and TN (true negative) are the number of instances predicted correctly, whereas FP (false positive) and FN (false negative) refer the numbers of instances predicted erroneously. P_c is the proportion of number of pixels that have been classified correctly as landslide or non-landslide pixels. P_exp means the expected agreements. ${\mathrm{X}}_{\mathrm{pred}.}$ is the predicted values in the training dataset or the validation dataset. ${\mathrm{X}}_{\mathrm{act}.}$ is the actual (output) values from the landslide susceptibility models [20 (link)].