## 2 Literature Review  
In many articles, ensemble-learning-based methods are used for prediction and defect diagnosis. For example, in [7] and [8] they were used to find bridge defects and software defects, respectively. In [7], ensemble methods were used to predict bridge defect conditions to help bridge managers make more rational and informed steel-bridge-maintenance decisions. For this purpose, six ensemble-learning models, namely, random forest, ExtraTree, AdaBoost, GBDT, XGBoost, and LightGBM were used. In [8], random forest, ExtraTree, AdaBoost, gradient boosting, histogram-based gradient boosting, XGBoost and CatBoost methods were used for the prediction of software defects and the automatic identification of defective parts of the software.  
Ensemble-learning algorithms are not only used in machine learning but are also widely used in deep leaning. For instance, in [9], a combination model of CNN and SVM was presented, which used the SVM as an ensemble method to aggregate the CNNs. In [10], six algorithms, namely, ANNS, ANNN, ridge regression, lasso regression, MLR, and elastic-net regression were used to build a model that can be used to predict rock tensile strength. In [11], the least absolute shrinkage and selection operator (Lasso) and ridge regression in conjunction with the logistic-regression (LR) method were employed for feature selection. Then, classification algorithms such as KNN, random forest (RF), and logistic regression were used for predicting the results. This study presented a novel hybrid model for the diagnosis and prediction of liver cancer.  
Figure 1: Flowchart of ECAPRAF. A dataset undergoes clustering in order to identify homogeneous subsets of data and assign them to similar groups. Then, trees are extracted as predictors by random forest and reduced by shrinkage methods. Therefore, elimination through the shrinkage methods as a means of reduction leads to a decrease in error and an increase in the model accuracy. In the last part, the remaining trees are ensembled to improve the performance of the model.  
Researchers in various fields have recently focused on the combination of shrinkage methods and machine learning to improve the performance of traditional algorithms. In [12], clustering and coefficient estimation were simultaneously performed using cluster correlation-network support vector machine, in which clusters were penalized by Lasso, SCAD, and MCP. Previously, the combination of elastic net and SVM [13], elastic net and RF [14], as well as SVM with lasso, ridge, and SCAD [15; 16] were used. In [17; 18], a combination of variable clustering and feature selection was also used to reduce the dimension. In addition, hierarchical clustering and variable selection of the main variables were used to evaluate the performance of RF. [PERSON] and [PERSON] [19] enhanced nearest-neighbor classifiers by using selection methods such as lasso or boosting. The relevant nearest neighbors were automatically selected. [PERSON] and [PERSON] [20] proposed a method that adapted the traditional mixture model for modeling and classifying data in a latent discriminative subspace. To generate the proposed discriminative latent mixture (DLM) model, the model-based clustering goals and the discriminative criterion, introduced by [PERSON], were combined. [PERSON] et al. [21], by using shrinkage methods such as lasso, ridge, and elastic net on simple linear regression showed that elastic net had better performance even though it was not combined with machine-learning algorithms. In the present paper, we show that elastic net in combination with machine-learning algorithms has a better performance compared to other shrinkage methods.