# Framework for the Ensemble of Feature Selection Methods
## 3 Results
### Conceptual Framework  
According to the qualitative method described in [29], a literature revision was conducted to select the data sources and understand the main concepts related to featureselection, ensemble learning, and consensus. Figure 2 shows the concepts and relationships identified from the data sources selected. Figure 2: Conceptual framework. The literature about relevance analysis, feature selection, and dimensionality reduction allowed the identification of the three types of methods to determine the features with higher differentiation power. Thus, the types of algorithms were analyzed considering their design, objective, and performance, which permitted the identification of the main concepts and relationships that describe the framework. Considering the FS theory, the datasets contain three types of features: relevant, redundant, and noise. Also, some authors state that the relevant features have either solid or weak relevance [32]. All types of features can be identified by filters, wrappers, or embedded methods. According to the method, the focus can be on identifying features with low differentiation power, the dependence of features, and relevant features. For instance, to identify segments with low relevance, the algorithms analyze columns with low variance. In general, the methods of FS use measures to evaluate the relevance of the features through statistical tests or cross-validation. The results obtained in these evaluations define the following: a ranking of feature relevance in the case of the filter-based methods, a subset of relevant features in the case of wrappers, or a subset of features with a learning model in the case of the embedded methods. In the wrappers or embedded methods, the FS is based on searching a subset of features by evaluating \(\mathbf{n}\) subsets and selecting the one that achieves the best performance in the classification. The outputs of the FS methods are evaluated from several perspectives. Considering the problem to solve, some criteria can be more or less relevant. Because of this, the framework establishes the evaluation of algorithms by reviewing either their performance or their design. In terms of performance, efficiency and effectiveness are evaluated by testing the subset of features selected in a classification process. In terms of design, simplicity and scalability are evaluated by the designers of the algorithms. Following ensemble learning, the consensus of several experts improves the creation of a decision in a context [31]. Thereby, the conceptual framework considers the pooling of several FS algorithms through the consensus of a set of subsets of features selected by each method. This scheme is defined in [33] as a heterogeneous centralized ensemble, where \(\mathbf{n}\) FS methods generate \(\mathbf{n}\) models using the same data. The main objective of reaching a consensus among several FS methods is to generate a subset of relevant features capable of representing the advantages and disadvantages of all used methods and facing the biases of single methods. The design built in Figure 2 describes the results of applying the qualitative analysis shown in Figure 1. The process describes a set of data sources to read and analyze to define the concepts related to the topic. Our study selected the concepts by highlighting the relevant concepts that explain implementing the ensemble feature selection. According to phase four of the methodology, the final list of concepts was analyzed to categorize them and identify EFS roles. This phase defines the constraints and special considerations of an EFS method, which are described below:  
* Instances must have values in all their columns. * Instances must not have outliers. * Values cannot be negative to avoid problems with statistical tests. Considering the above, datasets must be preprocessed before applying EFS to handle their problems and avoid additional biases in the EFS process. In data mining and machine learning, these constraints are related to preprocessing and preparing data.