# Optimizing Cervical Cancer Diagnosis with Feature Selection and Deep Learning
## 2 Materials and Methods
### Feature Selection and Ranking  
[PERSON] and [PERSON] noted that using a large number of features is not always beneficial [36]. They suggested that when classification accuracy is not significantly compromised and the error rate remains relatively stable, it is preferable to use fewer features in the feature vector. In this study, we have embraced this approach to determine the optimal combination of the features proposed for the feature vector in the classification of cervical cancer. To achieve this, we have employed five feature selection methods, as described below. The statistical methods are robust to noise, as they evaluate feature distributions rather than raw data values, reducing the impact of outliers and irrelevant variations. Combined with pre-processing steps, such as median filtering, these feature selection techniques ensure the selection of highly informative and resilient features for classification. * **Kruskal-Wallis Test** This is a non-parametric statistical test used to rank features based on their discriminatory power across diagnostic categories. It determines if the samples originate from the same distribution [37]. It is often regarded as the one-way ANOVA method on ranks or groups. The null hypothesis assumes that the cumulative distribution functions in the populations are equal, for \(k>2\). For this test, we recorded a probability value (\(p\)-value) for the null hypothesis. * **Kormogolov-Smirnov Test** This statistical metric represents characteristics through a distribution associated with a data sample [38; 39]. This test determines whether the samples are drawn from the same distribution. If the samples come from two different distributions, then the KS test returns a value 1, otherwise it returns a value 0. * **Friedman Test** A test proposed by [PERSON] [40] that can be used for feature ranking. It assesses differences between at least three correlated classes. Here, we recorded a probability value (\(p\)-value) for this nonparametric Friedman test. * **Stepwise Feature Selection** This is an iterative approach that adds or removes features to maximize classification performance. Given a set of extracted features, the stepwise feature selection method (SFS) chooses a subset of features that provide the best performance. The method \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **NSIL** & **LSIL** & **HSIL** \\ \hline Nucleus size & Very small & Smaller than 1/2 of cell size & Larger than 1/2 of cell size \\ \hline Cell size & Large cell & Modest decrease & Significant decrease \\ \hline Nucleus/cell ratio & 1:10 & Change in favor of nucleus & Significant change in favor of nucleus \\ \hline Stainability & Normal & Hyper-stainability & Hyper-or-hypo-stainability \\ \hline Brightness around nucleus & None & Can be visible & None \\ \hline \hline \end{tabular}
\end{table} 
Table 1: LSIL and HSIL in comparison to a healthy cell [4]. performs a forward feature selection that in an iterative way adds the best features to the subset of selected features. In every iteration, the best prediction features are used and their significance is estimated with the F-test (see [41]). Here, we use the backward version of this algorithm (SBS), where the assumption is made that initially all features of the original feature set are used. At each iteration, the features with the worst prediction are eliminated. * **Significant Feature Selection** This retains features with statistically significant differences between classes. Significant feature selection (SBS) uses statistical significance to reduce the full vector of features. This method estimates a \(p\)-values for each feature in the feature vector. This calculation is based on the two-sample Student's \(t\)-test for the difference of the population means with unequal variances with the assumption that samples are normally distributed. Usually, we consider a feature being statistically significant if its \(p\)-value is smaller than 0.05 which is a typical significance value in biomedical sciences and elsewhere.