# An Efficient Model-Based Clustering via Joint Multiple Sink Placement for WSNs
## 1 Introduction  
Wireless sensor networks (WSNs) have notably increased in popularity over the last few decades. Their success, and the rising demand for them, are reflected in the ever-expanding range of applications in various fields, such as transportation [1; 2; 3; 4; 5], health [6; 7; 8] (human activities in health care), manufacturing [9; 10; 11; 12], military [13; 14] (battleground surveillance by the military), and environment [15; 16; 17] (wildfire early detection, air pollution monitoring, and water monitoring). WSNs are also critical components of the Internet of Things (IoT) [18]. A typical WSN consists of several sensor nodes (SNs) and at least one base station (BS), called the sink. An SN is a small device with limited abilities (energy, processing capacity, and memory) that is placed in the environment to sense and gather the necessary data before sending it directly (single hop) or via other multihop communications to the nearest sink [19]. The sink is in charge of receiving and conveying these gathereddata to the final user and is outfitted with high energy and processing capabilities [20]. Communications consume more than 70% of the battery energy among various nodes. In sparse topology, a WSN with limited node capacities cannot function as intended if one of the network's sensors runs out of energy [21]. In dense topology, the overlapped sensing areas significantly increase unnecessary energy consumption and shorten the network's lifetime. For that reason, it is necessary to construct an energy-efficient WSN to maximize the network's lifetime. The lifetime is the time until the energy of the first sensor node is exhausted [22], and to improve it the flow balance between nodes must be significantly improved. SNs closer to the base station conserve a considerable quantity of energy for extended periods of time, and energy consumption is related exponentially to distance during data transmission. Hence, the distance between communicating nodes determines the quantity of energy used for data transmission. Specifically, the nodes nearest to the sink consume less energy. In contrast, distant nodes may use other nodes to transmit the data to the sink, which causes energy depletion of the SNs that are closest to the base station. Indeed, the sink location impacts the network's lifetime based on its distance from a significant number of sensor nodes. An excellent way to design an energy-efficient WSN is to deploy numerous sinks rather than a single sink [23]. When designing a network with several sinks, we intend to determine how many sinks there should be. However, even more crucially, we need to determine where the sinks should be placed and then select the optimal path for data transmission. Clustering is a promising strategy for managing the WSN structure, since it has the potential to improve network performance. It aims to group nodes based on predetermined criteria, such as ensuring the quality of service, balancing the network load, and optimizing the resource requirements [24]. Resource-constrained nodes no longer need to send data directly to sinks using clustering techniques. Other approaches are proposed to outperform energy efficiency, such as sleeping mechanisms [25], data aggregation algorithms [20] and compressed sensing mechanisms [26]. The sleeping mechanism significantly reduces energy consumption by putting sensors to sleep or waking them up. The data aggregation algorithm is mainly used to process massive data that does not supply meaningful information to its owner in its current inconsistent form. The compressed sensing mechanism takes advantage of the redundancy present in environmental WSN signals to decrease the number of transmitted measurements and, as a result, achieve an appealing reduction in network energy consumption. However, it necessitates significant data preprocessing, which runs counter to Ambient Intelligence domains' processing and energy limitations.