# Distributed Global Function Model Finding for Wireless Sensor Network Data
## 1 Introduction  
Progress in wireless communication and microelectronic devices has led to the development of low-power sensors and the deployment of large-scale sensor networks [1]. Wireless sensor networks (WSNs) have been developed and applied to many fields, such as smart grid [2], agriculture [3; 4], environment monitoring [5; 6], and the military [7]. In these applications, because of the large number and wide distribution of sensors, the data from sensors is characterized by high dimension, large amount, and wide distribution [8; 9]. How to find useful knowledge from high dimensional, massive and distributed data has become a key issue of data mining in wireless sensor networks [8; 9]. Recently, all kinds of approaches, including clustering [10; 11], association rules [12] and classification [13; 14], have been successfully applied in wireless sensor networks. Function model finding is also an important branch of data mining. The function finding technique for all kinds of application data from WSNs can reveal the essence and phenomenon in the application. However, in the existing references, function finding is rarely mentioned in WSNs. The existing function model discovery algorithms mainly include the regression, the evolution algorithms, and so on. Generally, traditional regression methods assumed that the function type was known, and then the least squares method or its improved methods for parameter estimation were used to determine the functional model [15]. These traditional regression methods needed to depend on _a priori_ knowledge and a lot of subjective factors. Moreover, these methods have high time complexity and low computation efficiency for complex and high-dimensional datasets from WSNs. To solve these problems, [PERSON] _et al._ and [PERSON] _et al._ used genetic programming (GP) for mathematical modeling and obtained good experimental results [16; 17]. [PERSON] _et al._ proposed a method which dealt with smooth fitting problem by GP [18]. In order to fit data points to curves in CAD (Computer Aided Design)/CAM (Computer Aided Manufacturing), [PERSON] _et al._ present a new hybrid evolutionary approach (GA-PSO) for B-spline curve reconstruction [19]. Meanwhile, GP, genetic algorithm (GA) or hybrid evolutionary algorithms also avoid the defect of traditional statistical methods' selected function models in advance. However, the efficiency of function model mined by GP, GA or hybrid evolutionary algorithms was low. Thus, a new algorithm called gene expression programming (GEP) was proposed [20]. Compared with GP, the efficiency of complex functions mined based on GEP was improved 4-6 times. Therefore, in order to reveal the inherent nature of the sensor data, this paper proposes a function finding algorithm using gene expression programming (FF-GEP). In FF-GEP, an adaptive population generation strategy is put forward. The strategy avoids the local optimum of GEP population. However, thousands of distributed sensor nodes, and the unstable wireless communication environment make traditional centralized function mining algorithms difficult to meet the needs of function mining in wireless sensor networks. Traditional centralized FF-GEP is unable to meet the requirement of function finding in wireless sensor networks. In order to better find functions for complex, massive and high-dimensional sensor data, on the basis of FF-GEP, this paper presents distributed global function model finding for wireless sensor networks data (DGFMF-WSND).