## 3 Cluster Formation
### Optimal Clustering
#### 3.1.2 Balanced Energy Expenditure  
The authors of [80] propose a centralized clustering approach to partition the network into an optimal number of sectors and to balance the energy distribution. In partition-based LEACH (pLEACH) [80], the BS is located in the centre of a network field to which each node sends its location and its remaining energy in initialization stage. The BS considers the network as a circular field where every node is marked with the sequence number of its sector according to its central angle. When the amount of data transmission in a sector outstrips other sectors, the BS rotates the partition circle a given angle for the next round to balance the energy dissipation among the sensor nodes. In the Energy Residue Aware (ERA) clustering algorithm [81], the main goal is to prolong the network lifetime by balancing the energy consumption of the entire network. According to the algorithm, remaining energy and residual energy of each node are two distinct notions. The paper defines the residual energy of a node as its current remaining energy level minus the cost of transmission to the next hop. Therefore, in cluster formation and data transmission phases, each node, either non-CHs or CHs, chooses the next hop not to minimize its power consumption, but rather for forming a route with the maximum sum of the calculated residue energy. In other words, ERA cluster formation scheme emphasizes on even distribution of energy consumption between all nodes rather than the reduction of the average energy consumption of the network. A dynamic clustering algorithm is presented in Cluster Head Load Balanced Clustering (CHLBC), which considers relay traffic of CHs in clustering stage. In the presented algorithm [82], each CH calculates the relay traffic of a CH either generated by the cluster members or relayed by other CHs in the current round and broadcasts a message containing its ID and level of its relay traffic load across the network area. Therefore, Ordinary nodes decide to join a CH not only based on the distance metric but also difference of the relay traffic load of CHs. The result is that the CHs with a heavier relay traffic load will have smaller numbers of cluster members for the next round than the CHs not actively participating in the procedure of relaying data, and hence the energy consumption of CHs is evenly distributed across the network. The papers [30,83] define confidence value for CHs according to their characteristics such as remaining energy of the node and CH, distance of CH to the BS and distance of the node to the CH. Each node calculates the confidence value of the CHs in its transmission range and joins the one with the highest confidence value. The confidence value in [30] is calculated by the nodes, using the Equation (16), and is defined in [83] in the form of the summation of three weighted factors, seen in Equation (17). In both Equations (16) and (17), \(\mathrm{E_{r}}\) is the remaining energy of the node, \(\mathrm{E_{r-CH}}\) is the remaining energy of CH, \(\mathrm{D_{N-CH}}\) is distance of the node to CH and \(\mathrm{D_{CH-BS}}\) is the distance between CH and BS. In Equation (17), MAX\({}_{\mathrm{CH-BS}}\) and MIN\({}_{\mathrm{CH-BS}}\) are the farthest and shortest distance from all the CHs to the BS, respectively and MAX\({}_{\mathrm{N-CH}}\) is the distance of the farthest CH in transmission range of node:  
\[\mathit{Confident}\ _{-}\mathit{value}_{CH} = \frac{E_{r}+E_{r-CH}}{\left(\mathrm{D}_{N-CH}+\mathrm{D}_{CH-BS} \right)^{2}} \tag{16}\] \[\mathrm{F} = \mathrm{W_{I}}\times\frac{E_{i-CH}-E_{r-CH}}{E_{i-CH}}+\mathrm{W_{ 2}}\times\frac{\mathrm{D}_{N-CH}}{\mathrm{MAX}_{N-CH}}+\mathrm{W_{3}}\times \frac{\mathrm{D}_{CH-BS}\cdot\mathrm{MIN}_{CH-BS}}{\mathrm{MAX}_{CH-BS}\cdot \mathrm{MIN}_{CH-BS}} \tag{17}\]  
As the main objective of clustering is to implement data aggregation within the cluster and thus save energy, the Data Correlation and Data Aggregation LEACH (DCDA-LEACH) [84] algorithm considersdata correlation in the cluster formation phase.