###### Abstract
The most common properties used for this decision are the location of the node within the sensing area and the residual energy of each node. The first one is not always available in all the applications because nodes usually cannot afford GPS equipment or similar hardware. * Distributed Clustering. The nodes are completely autonomous and decide by themselves if they become CH or not. This decision is supported by the properties that the node can know/estimate by itself. Then, that information is weighted by some methods that indicate whether to become CH or not. Finally, those nodes that selected themselves as CH send a message to the network so that the other nodes can join them to their clusters. Centralized and distributed clustering can also be subdivided into different categories depending on the method used to choose the CHs. There are stochastic approaches, geometric algorithms, methods based on fuzzy logic (Type-1 or Type-2), or techniques supported by other artificial intelligence. The most relevant stochastic and distributed algorithms is Low-Energy Adaptive Clustering Hierarchy  
Figure 1: Illustration of a clustering procedure in a wireless sensor network. (LEACH) [5]. LEACH employs a random number that is generated by each node. This number is compared with a parameter representing the probability of becoming CH. The generated value increases with the number of rounds if the sensor has not been chosen as a CH, and it is determined by a system configuration parameter (\(p\)). If the random number is greater than this value, then the node becomes a CH. An adaptation of this method is detailed in [6], where the nodes add different thresholds depending on the distance or the remaining energy. Other stochastic method is the Hybrid, Energy-Efficient, Distributed clustering approach for ad hoc sensor networks (HEED) [7], a multi-hop clustering algorithm in which the probability of being a CH depends on the residual energy. Normal nodes use the inter-cluster communication cost as a metric to decide which cluster it should join. In an Energy Efficient Clustering Scheme (EECS) [8], the authors propose a clustering method based on a competition among a fixed number of CH candidates. The CH candidates are selected with a probability \(T\). This probability is set empirically in a similar way to parameter \(p\) in LEACH. Other types of approaches are those that combine stochastic and geometrical methods like Voronoi Tessellation. The work in [9] follows this approach for a mobile WSN in which the CH corresponds to the seeds of the cells. Clustering can also be supported by artificial intelligence. Particularly, Fuzzy Rule-Based Systems (FRBS) outstand as a convenient mechanism to decide which nodes will play the role of the CHs. The applications and research scores that use these types of expert systems are very numerous in areas such as image classification [10], performance improvement in wind turbines [11], image fusion field [12], software error identification [13], or wireless sensor networks [14]. As for clustering, the work in [15] describes a particle optimization algorithm based on LEACH. The authors of [16] use a fuzzy logic Type-1 distributed algorithm with two outputs. The first output defines the sending radius of the announcement message and the second one determines whether a node will be CH or not. One of the first relevant centralized methods that employs an expert system is the Cluster-head Election using fuzzy logic (CHEF) [17]. The BS implements a fuzzy logic Type-1 algorithm to decide which node will be cluster head in each round. In [18], the BS selects the best nodes based on a fuzzy Type-2 system. The inputs of this system are the residual energy, the distance to the BS, and the number of neighbors of each node. In the proposal presented in [19], the BS receives information about the energy and the location of the nodes. Then, the BS decides through a simulated annealing algorithm which node configures itself as a CH.