# Diagnosis and Prediction of Large-For-Gestational-Age Fetus Using the Stacked Generalization Method
## 3 Materials and Methods
### Preparation of the Principal Feature Vector
#### 3.3.1 GridSearch-Based RFECV + IG Feature Selection Scheme  
**Recursive Feature Elimination (RFE)** is a scheme that excludes features based on its irrelevancy and low data integrity to a specified class distribution [25; 35]. The elimination process is a continuous process until a complete list of deterministic feature subset is reached. The elimination process takes a classification model, and based on the classification weights, selects the weighted features with the elimination of noisy features. In addition, for a better elimination and selection process, the parameters for the classification model are required to be tuned. In this research, GridSearch, a popular technique for parameter tuning, is also accompanied by RFE to improve classification performance. Moreover, in the case of Recursive feature elimination with cross-validation (RFECV), the fitting is accompanied by testing, it uses training and test splits provided with a given folding parameter that helps in minimizing generalization errors. Support Vector Machine (SVM) with linear and rbf kernels [36; 37], Logistic Regression (LR) [38], and Decision Tree (DT) [39] classifiers are used in RFECV feature selection scheme with the parameters tuned with GridSearch with five-fold cross validation. During the tuning of GridSearch, for SVM (with linear kernel) and LR classifiers, 'C' is tuned in the range of \(2^{-8}\) to \(2^{8}\); whereas, SVM with rbf kernel, 'C' is tuned in the range of \(2^{-8}\) to \(2^{8}\) and gamma is tuned in the range of \([1,0.1,0.01,0.001,0.00001,10]\). DT attributes are tuned for maximum depth: \([1,2,3,4,5]\), criterion: \([^{\prime}gini^{\prime},entropy^{\prime}]\), and maximum features: \([^{\prime}sqrt^{\prime},log2^{\prime},auto^{\prime}]\). The complete result of the selected features with discussed LGA classifier are presented in Table 2. All of the corresponding feature subsets are given to specified machine learning classifier for the establishment of first experimental setup. Furthermore, the IG feature selection scheme is used as an ensemble of feature selection process to rank above-induced feature subsets which are discussed as follows,  
Information Gain (IG): is an extensively used feature selection scheme in a variety of machine learning problems, especially related to the medical domain. IG feature selection scheme works with an objective of uncertainty reduction in a feature vector. Once the level of uncertainty is known, the larger the uncertainty can be reduced, and more the information the feature can bring to the classification system. Thus, ultimately, we have a larger information gain that is brought to the system for the development of an efficient LGA classification model. In IG feature selection scheme, \"information entropy\" is used to measure the amount of information which is later calculated as the difference between dataset (B)'s information entropy including with and without LGA features \(x_{i}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**RFECV \(\star\) Machine Learning Classifier** & **Selected Features** & **Time (s)** \\ \hline SVM (Linear kernel) & 53 & 25537 \\ SVM (RBF kernel) & 99 & 201331 \\ Logistic Regression & 38 & 40386 \\ Decision Tree & 270 & 118 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Features selected with GridSearch-based Recursive Feature Elimination with Cross-validation feature selection scheme with execution time using various machine learning classifiers for tuning parameters. Furthermore, while training dataset B with I class labels, \(\varrho(B)\) represents the information entropy of the LGA class distribution in B, which can be expressed as follows,  
\[\varrho(B)=-\sum_{i=1}^{I}p_{i}\ log_{2}\ p_{I} \tag{1}\]  
where \(P_{i}\) represents the probability of i-th class in the training dataset B. Moreover, \(x_{i}\) features with D distinct values can be used to partition dataset B into D distinct groups.