# Unsupervised Text Feature Selection Using Memetic Dichotomous Differential Evolution
## 3 Unsupervised Text Feature Selection Using Memetic Optimization  
The proposed method has four phases. First, the text document's corpus is transformed into numerical data in the pre-processing phase, as was described earlier. Second, the resultant data are fed into the proposed feature selection method. Third, document clustering is performed using the resultant features. Finally, evaluation measures are used to assess the resultant clusters. In this subsection, the main steps of the proposed method of feature selection are described; the main steps are listed as follows:  
1. The population is first randomly initialized, and then the solutions are refined in each generation. Each solution consists of a random subset of features, as shown in Table 2. All solutions are encoded using a binary encoding scheme. As the unsupervised feature selection is a discrete binary-based optimization problem, the range of every solution is limited only to [0,1]. Each solution is represented as a string of random binary values, and the length of each solution represents the number of features. The presence of a feature is represented by one, while the absence of it is represented by 0. Each solution is modified using the differential evolution mutation and crossover operators.
2. The fitness calculation is performed first using the Mean Absolute Distance, MAD, as shown in the Equation (10). \[MAD\Big{(}u_{ijG}\Big{)}=\sum_{i=1}^{m}\sum_{j=1}^{n}\frac{\big{|}u_{ijG}-\overline {u}_{ijG}\big{|}}{n}\] (10) where \(m\) is the number of features (one valued in any particular solution), and \(u_{ijG}\) is the trail vector resulted from the dichotomous crossover, while \(n\) is the number of documents containing feature \(i\). The reason behind using the MAD fitness function is to find the score of each feature and to find its distance from the mean values of that feature in all documents with no consideration of the original class labels using a data-driven scheme.
3. Simulated annealing is used as a local search modifier; it resembles the metaheuristic operators when applied as a local search in the memetic search. Almost the same idea of using mutation and crossover is followed by using the local search. The solution chosen for the local search is the one that has the highest MAD fitness value. Simulated annealing is used to guide the differential evolution search in the search space. The control parameters required for the SA are the initial temperature (T0) and the cooling schedule (T), which were adopted from [17].  
Table 2 shows an illustration of each solution, which is composed of an \(n\) number of features, and each solution is weighted using the MAD objective function.  
The evaluation measures are important to observe for the performance of each feature selection method and its effect on the clustering algorithm. Two types of measurements are used in the experiments, which are the internal and external evaluation measures [24]. The F-macro and F-micro are used as external measures, while the internal measure used is the Average-Document-Distance-to-the-Cluster-Centroid (ADDC) [25; 26] It is noteworthy that the F-micro  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solution** & **Index\({}_{1}\)** & **Index\({}_{2}\)** & **Index\({}_{3}\)** & **Index\({}_{n}\)** & **Fitness** \\ \hline S\({}_{1}\) & 0 & 1 & 1 & 1 & MAD\({}_{1}\) \\ \hline S\({}_{2}\) & 1 & 0 & 1 & 1 & MAD\({}_{2}\) \\ \hline S\({}_{3}\) & 1 & 1 & 1 & 0 & MAD\({}_{3}\) \\ \hline  & & & & &. \\ \hline S\({}_{n}\) & 0 & 0 & 0 & 1 & MAD\({}_{m}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Initial population of features; each row (Si) is a solution, and each column is a feature.