## 4 Results
### Frequency Ratio and Classification Systems Comparative  
Table 10 shows the values obtained for the indices as a mean for the three provinces. The row and column means are also included for comparisons between the FR and classification methods. In this table, the value of Sen for all cases of the ELSUS classification is 75. This is due to the very definition of its classification, which determines this value for the lower limit of the 'high' class (Table 2).  
Figure 6: Surface percentage for high susceptibility classes (very high and high) in Valencia Region.  
After applying the ELSUS classification system, no major differences are observed among FR methods, and none stands out from the others (except GFR). In the case of the GY classification, an improved overall performance is observed. In particular, the better performance of Rind seems to be due to the two lower levels that are better resolved in GY.  
In terms of classification, NBreaks shows the lowest sensitivity, indicating that its hit ratio (TP) is low in high classes (H and VH). However, its failure ratio (TN) is very high. Therefore, as Figure 6 reveals, this is an excessively optimistic classification. In contrast, the quantiles classification has a high sensitivity and a very low specificity, resulting in an excessively pessimistic classification. This is the result of defining large surface areas for high susceptibilities (VH and H) with excessive false positives.  
In general, GFR shows worse values than EFR, CFR, and RFR (except for the NBreaks classification). The GFR classification is very discriminating of high values, as the GFR sections are defined every 10\({}^{\circ}\), which is beneficial and offers higher sensitivity than the rest. This is consistent with its higher percentage of pixels in high classes (H and VH) as shown in Figure 6. In contrast, the other FR methods have wider intervals in the high sections and show a worse fit due to their poor definition. This situation is reversed for all other and much less optimistic classifications.  
LSMs based on cluster FR and regression (CFR and RFR) have better defined high LSI (landslide susceptibility index) values and show higher specificity. The ELSUS classification, based on sensitivity alone, does not satisfactorily define the best specificity results. In contrast, the GY classification improves on these results and does take specificity into account.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & & & \multicolumn{3}{c}{**Classification Systems**} \\ \cline{5-8}  & & **GY** & **ELSUS** & **NBreaks** & **Quantiil** & **G.Mean** \\ \hline \multirow{8}{*}{GFR} & \multirow{2}{*}{FR} & Rind & 0.771 & 0.717 & 0.789 & 0.761 & 0.759 \\ \cline{3-8}  & & pAUC & 0.745 & 0.711 & 0.674 & 0.794 & 0.731 \\ \cline{3-8}  & & Sen & 75 & 75 & 56 & 86 & 73 \\ \cline{3-8}  & & Spe & 80 & 79 & 91 & 64 & 79 \\ \cline{3-8}  & & Rind & 0.782 & 0.765 & 0.758 & 0.812 & 0.779 \\ \cline{3-8}  & & pAUC & 0.747 & 0.742 & 0.615 & 0.809 & 0.728 \\ \cline{3-8}  & & Sen & 77 & 75 & 40 & 89 & 70 \\ \cline{3-8}  & & Spe & 81 & 81 & 96 & 63 & 80 \\ \cline{3-8}  & & Rind & 0.789 & 0.764 & 0.769 & 0.794 & 0.779 \\ \cline{3-8}  & & pAUC & 0.761 & 0.755 & 0.597 & 0.823 & 0.734 \\ \cline{3-8}  & & Sen & 77 & 75 & 44 & 89 & 71 \\ \cline{3-8}  & & Spe & 80 & 82 & 98 & 62 & 80 \\ \cline{3-8}  & & Rind & 0.802 & 0.762 & 0.768 & 0.820 & 0.788 \\ \cline{3-8}  & & pAUC & 0.758 & 0.758 & 0.684 & 0.818 & 0.755 \\ \cline{3-8}  & & Sen & 80 & 75 & 56 & 90 & 75 \\ \cline{3-8}  & & Spe & 79 & 83 & 93 & 62 & 79 \\ \hline \multirow{3}{*}{Global mean} & Rind & 0.786 & 0.752 & 0.768 & 0.797 & 0.776 \\ \cline{3-8}  & & pAUC & 0.753 & 0.742 & 0.643 & 0.811 & 0.737 \\ \cline{3-8}  & & Sen & 77 & 75 & 49 & 89 & 72 \\ \cline{3-8}  & & Spe & 80 & 81 & 94 & 63 & 80 \\ \hline \end{tabular}
\end{table}
Table 10: Mean values of indicators for the three provinces.