# A Two-Phase Approach for Semi-Supervised Feature Selection
## 3 Preliminaries of the Methods Used in the Proposed Approach  
The basics of some methods used in this paper are outlined below for a quick reference. **Classification:** The process of separating data into groups based on some given labels or similarities. Much has been described before. In supervised classification, the training data contain the labels; the knowledge of these labels will be used to determine the label of the testing data. **Clustering:** When the labels are not tagged with the patterns in advance. Similarity among the patterns is used to group (cluster) the datasets. A common approach is to start with a random set of centroids (some or all of them can even be taken as different existing patterns of the dataset),which represent their respective clusters, and then bring the closest patterns (i.e., nearest to the centroid) in a cluster. After a repetitive exercise, we obtain a set of centroids such that the patterns belonging to the clusters represented by these centroids do not shift from one cluster to the other even after repeating the exercise further. This approach is known commonly as K-means clustering [43]. The K-means algorithm has some defects: (1) Algorithm is sensitive to the initial cluster center. The selection of initial centers of the pros and cons will affect the clustering results, and then influence the efficiency of the algorithm performance; (2) the algorithm is sensitive to outlier data and will result in a local optimal solution [44]. **Fuzzy C-Means (FCM):** FCM is a clustering method that allows one point to belong to two or more clusters, unlike K-means where only one cluster is assigned to each point. This method was developed by [PERSON] in 1973 [45] and improved by [PERSON] in 1981 [46]. The FCM provides a broader and soft assignment of a point to a cluster, which is why it is preferred over K-means. For more detail about the clustering techniques, refer to the article by [PERSON] et al. [47]. Some semi-supervised FCM clustering algorithms are available in the literature; for an overview, refer to [48]. [PERSON] et al. [49] proposed an algorithm where they apply an effective feature enhancement procedure to the entire dataset to obtain a single set of features or weights by weighting and discriminating the information provided by the user. By taking pair-wise constraints into account, they proposed a semi-supervised fuzzy clustering algorithm with feature discrimination (SFFD) incorporating a fully adaptive distance function. Although there can be other methods for semi-supervised feature selection, the objective of the present work is to apply a mechanism to obtain a subset of influential features with MRmr in Phase-1. Then, the reduced dataset due to the presence of only influential features will be clustered. In Phase-2, clustering of the reduced dataset is required and, for this purpose only, any clustering algorithm could be applied. For its flexibility in deciding a pattern for affiliation to a cluster (against K-means clustering), the FCM has been used. **Correlation:** These methods are used to find a relationship among attributes (or columns) in a dataset. The most common method to determine the correlation between two column vectors is achieved by computing [PERSON]'s correlation (RRPC) coefficient. For any two column vectors \(X\) and \(Y\), [PERSON]'s correlation coefficient \(\rho\) is calculated as follows:  
\[\rho\ =\ \frac{\sum_{i}(x_{i-x^{*}})\left(y_{i}-y^{*}\right)}{\sqrt{\sum_{i}(x_{i }-x^{*})^{2}\sum_{i}(y_{i}-y^{*})^{2}}} \tag{1}\]  
where \(x_{i}\) and \(y_{i}\) are the \(i\)-th values of the two feature vectors \(X\) and \(Y\) with their means as \(x^{*}\) and \(y^{*}\), respectively. When the value of \(\rho\) is close to 1 (one), the two constituent column vectors are said to be highly correlated. On the other hand, \(\rho\) closeto 0 (zero) indicates a very poor or no similarity between the two vectors.