# A Hierarchical Feature-Based Methodology to Perform Cervical Cancer Classification
## 3 Experiments and Results
### Statistical Analysis  
The statistical analysis aims to verify whether there is a statistically significant difference between the implemented algorithms' results.  
Initially, we used the Shapiro-Wilk test [67] with a significance level of 0.05 to verify whether the normal distribution can approximate the probability distribution of the classifiers' results. It was found that the results obtained in all metrics do not follow a normal distribution.  
For this reason, the Kruskal-Wallis non-parametric test [68] was chosen to determine whether the results obtained suggest that the samples are from different populations or are just random variations among random samples from the same population.  
Thus, the best classifier found in the experiments, the RF, was compared pair-wise with the other classifiers using the non-parametric Kruskal-Wallis test with a significance level of 0.05 to check if there was a statistical difference between RF and the other classifiers concerning all performance metrics.  
Table 7 shows the \(p\)-value results obtained in the Kruskal-Wallis test when comparing the RF results with those of k-NN, Ridge, and DT for 2-class, 3-class, and 7-class hierarchical classification, and 7-class classification without hierarchy using the Herlev database. The results highlighted in bold have the same distribution as the RF results (\(p\)-value > 0.05). Table 7 reveals that in 7-class hierarchical classification, the Ridge results of accuracy and specificity have the same distribution of the RF results.  
In turn, Table 8 presents the \(p\)-value results obtained in the Kruskal-Wallis test when comparing the RF results with those of k-NN, Ridge, and DT for 2-class, 3-class, and 6-class hierarchical classification and 6-class classification without hierarchy using the CRIC database. As no \(p\)-value was higher than 0.05, it can be concluded that the RF statistically outperformed all other classifiers that classified the data from the CRIC database, considering all metrics.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & **Prec.** & **Rec.** & **F1** & **Acc.** & **Spec.** \\ \hline \multirow{4}{*}{6-class classification} & RF & **0.8369** & **0.8348** & **0.8351** & **0.9450** & **0.9670** \\  & k-NN & 0.6985 & 0.7018 & 0.6932 & 0.9006 & 0.9404 \\  & Ridge & 0.7045 & 0.7096 & 0.7035 & 0.9032 & 0.9419 \\  & DT & 0.7075 & 0.7027 & 0.7036 & 0.9009 & 0.9406 \\ \hline \multirow{4}{*}{2-class hierarchical classification} & RF & **0.9591** & **0.9585** & **0.9585** & **0.9585** & **0.9585** \\  & k-NN & 0.8749 & 0.8736 & 0.8735 & 0.8736 & 0.8736 \\  & Ridge & 0.9423 & 0.9407 & 0.9406 & 0.9407 & 0.9407 \\  & DT & 0.9254 & 0.9240 & 0.9239 & 0.9240 & 0.9240 \\ \hline \multirow{4}{*}{3-class hierarchical classification} & RF & **0.9635** & **0.9633** & **0.9633** & **0.9686** & **0.9764** \\  & k-NN & 0.9341 & 0.9329 & 0.9328 & 0.9424 & 0.9569 \\ \cline{1-1}  & Ridge & 0.9394 & 0.9391 & 0.9390 & 0.9478 & 0.9608 \\ \cline{1-1}  & DT & 0.9219 & 0.9216 & 0.9216 & 0.9328 & 0.9496 \\ \hline \multirow{4}{*}{6-class hierarchical classification} & RF & **0.9110** & **0.9091** & **0.9097** & **0.9697** & **0.9819** \\  & k-NN & 0.8155 & 0.8126 & 0.8104 & 0.9375 & 0.9625 \\ \cline{1-1}  & Ridge & 0.8317 & 0.8333 & 0.8316 & 0.9444 & 0.9666 \\ \cline{1-1}  & DT & 0.8256 & 0.8255 & 0.8250 & 0.9418 & 0.9651 \\ \hline \hline \end{tabular}
\end{table}
Table 6: CRIC classification results.