# Diagnosis and Prediction of Large-For-Gestational-Age Fetus Using the Stacked Generalization Method
## 3 Materials and Methods
### Preparation of the Principal Feature Vector
#### 3.3.2 Feature Extraction and Dimension Reduction with Stacked Generalization  
Stacked generalization (SG): also known as Stacking is a process that combines multiple classifiers to form an efficient classification system. It was introduced by [PERSON] in 1992 [40]. The stacking process involves output generated from level-0 (base-level) classifiers as an input to level-1 (meta-level) classifier to improve classification performance using the process of cross validation is as follows,  
Let us suppose that \(L\) is the obtained LGA dataset with \(a_{i}\) attributes with an associated \(y_{i}\)-th class label. Thus, \(L=\{(a_{i},y_{i}),i=,...,n\}\) refers to the level-0 of the LGA dataset. Based on K-fold cross-validation \(L\) is divided into \(K\) disjoints parts of \(L_{1},L_{2},...,L_{k}\) where at each \(k\)-th fold \(L_{k}\) is used as test and \(L^{(-k)}=L-L_{k}\) is used as the test part. Later, N learning algorithms \(A_{1},A_{2},...,A_{N}\) are applied at training part \(L^{(-k)}\) to build \(N\) level-0 classifiers \(C_{1},C_{2},...,C_{N}\). The resultant concatenated predictions of each \(k\)-th fold at \(L_{k}\) of \(N\) level-0 classifiers with the actual class label are used to form meta-level vector (\(ML_{k}\)). It will be use during the establishment of level-1 classification. With the development of complete meta-level vector (\(ML_{k}\)) also called level-1 data which is obtained by the union of each of the \(ML_{k}\), where \(k=1,2,3,...,K\) during the cross-validation process, we applied the algorithm \(A_{m}\) to form the meta-level classifier \(C_{m}\). During the development of \(C_{m}\), the \(Am\) could be any of the \(A_{1}\), \(A_{2},...,A_{N}\) or a different one. Based on this procedure, it is foreseen that after forming the meta-level data, the entire data is trained using the learning algorithms \(A_{1}\), \(A_{2},...,A_{N}\) to build final base-level classifiers \(C_{1},C_{2},...,C_{N}\). [PERSON] et al. [41] proposed to use class probabilities instead of just using class labels for the formation of the meta-level feature vector, as it can better improve classification performance with an improved learning rate. Therefore, to classify a new instance predicted probabilities and predicted class labels by all level-0 classifiers are concatenated to form a meta-level classifier which has \(N\) components. Based on this formed meta-level feature vector, level-1 classifiers assign an actual class label to the final classification result of the input instance \(x\). Figure 2. refers to the process of creation of K-fold cross-validation (the left part of the figure) while the right part of the figure represents the stacking process. Feature Extraction and Dimension Reduction with Stacking: represents the above-defined process where the outputs of level-0 classification are combined to form complete meta-level features. It is, in fact, a process to extract discriminant features rather than just classification predictions. Previously, the combination strategy has already benefited different researcher to improve generalization errors during the classification task. On the basis of this, considering the best classification schemes on the said GridSearch-based RFECV + IG feature subsets, we proposed to use Logistic regression (LR) and Random forest (RF) classifiers for the creation of the discriminant meta-level feature subset followed by Support Vector Machine (SVM) classifiers at level-1 to establish a state of the art LGA classification system. The reason to chose LR, RF, and SVM is because of their efficient performance during the sensitivity analysis process. Furthermore, before starting the feature extraction process, we proposed to use the below-defined technique to reduces the size of data to expedite classification speed and performance without further deletion of valuable records.