## 3 Methodology
### Phase 4: Concept Clustering  
The purpose of the concept clustering phase is to cluster the concepts extracted from documents on the base of their numerical weights calculated through TF-IDF. The terms with the highest weights are selected as important terms for the clustering of concepts [54]. Here, a widely used and popular Fuzzy C-Mean soft clustering algorithm was considered for the formation of clusters, as Fuzzy C-Mean is used in most cluster-based semantic information retrieval systems. This clustering algorithm is used in a large variety of schemes to study the impact of parameter values on performance, dual expression-based fuzzy clustering, image clustering, membership scaling, pattern recognition with objective functions, and other data analysis techniques [54; 55; 56; 57; 58; 59; 60; 61]. Fuzzy C-Mean is used in differentcluster-based sematic information retrieval systems, data analysis methodologies, and cluster formation problems because of its flexibility, strengths, and significant impact on the effectiveness and efficiency of textual document, textual term, and concept clustering. The Fuzzy C-Mean algorithm was first introduced in [62], where it was an enhanced version of an already proposed clustering technique. The Fuzzy C-Mean algorithm represented in Figure 5 has the ability to form clusters of data values represented in multidimensional space [51]. The computation of a membership degree of between 0 and 1 is the major benefit of this soft clustering mechanism. Another of its advantages is that a single data value can be the member of various clusters. This flexibility is provided through the minimization of the objective function, as provided in Equation (5):  
\[J_{m}=\sum_{i=1}^{N}\sum_{j=1}^{C}u_{ij}^{m}\parallel x_{i}-c_{j}\parallel^{2},\ \ 1\leq m<\infty, \tag{5}\]  
where \(m\) represents the fuzzy exponent variable value that is always greater than 1, \(u_{ij}\) represents the membership degree of concept \(x_{i}\) in \(jth\) cluster, and \(c_{j}\) represents the cluster centroid. The calculation of the similarity distance between a concept and the centroid is represented with \(*\) in the equation. In fuzzy partitioning, the objective function is an important task that is achieved by updating the centroid of cluster \(c_{j}\) and the degree of membership \(u_{ij}\) through an optimal number of iterations. A mathematical representation of the membership degree calculation is given in Equation (6). \[u_{ij}=\frac{1}{\sum_{k=1}^{C}\left[\frac{\left\|x_{i}-C_{j}\right\|}{\left\|x _{i}-C_{k}\right\|}\right]^{\frac{2}{m-1}}}, \tag{6}\]  
The calculation of \(C_{j}\) is depicted in Equation (7):  
\[C_{j}=\frac{\sum_{i=1}^{N}u_{ij}^{m}.x_{i}}{\sum_{i=1}^{N}u_{ij}^{m}}, \tag{7}\]  
Figure 5: Fuzzy C-Mean algorithm [51]. where \(N\) represents the total number of concepts in a cluster. This procedure is continuously and iteratively performed until the condition expressed in the following mathematical expression (8) is met:  
\[max_{ij}\{\parallel U^{(k+1)}-U^{(k)}\parallel\}<\mathcal{E}, \tag{8}\]  
where \(k\) represents the iteration count, \(U\) is the centroid of each iteration, and \(\mathcal{E}\) is the exit state between 0 and 1. The sequence of operations performed in concept clustering is represented in Figure 6, which shows a flow chart of the Fuzzy C-Mean algorithm. The procedure starts after textual concepts are converted into numerical values, and various stages are involved. The number of clusters are decided on the basis of key concepts. The degree of the membership value of each key concept is first calculated as the distance between the centroids of each cluster and other concepts. Then, clusters are formed based on the measured distance. From the newly formed clusters, a new centroid is computed to include more relevant concepts. The process of computing a new centroid for each cluster and adding more relevant concepts is continued until new centroids are computed.