Data Approximation for Time Series Data in Wireless Sensor Networks

Introduction

Data suppression of time series data is an important issue in many fields (Wang, Sun, & Yang, 2010). In recent years, data approximation is widely used to obtain approximations of original values according to a portion of original values (Wang, Zheng, Sun, Zou, & Yang, 2011).

Many prior efforts adopt data prediction approaches¹ to approximate data by building prediction functions on the basis of historical data. Linear (Palpanas, Vlachos, Keogh, & Gunopulos, 2007), non-linear (Silberstein, Puggioni, Gelfand, Munagala, & Yang, 2007; Wang, Fan, Hsu, & Sun, 2014) and correlation (Wang, Ma, He, & Xiong, 2012) data predictions are established in recent years. These approaches build approximate functions of original data and use the parameters of these functions instead of original values. A simple example is shown in Figure 1 (b), the original data originates from Life Under Your Feet (LUYF) project². On the other hand, multiple data prediction approaches (Edara, Limaye, & Ramamritham, 2008), (Sinha & Lobiyal, 2015), (Wu, Tan, & Xiong, 2015) are proposed as well. As illustrated in Figure 1 (c), these approaches only find critical data points with high prediction errors to control the error of prediction. Furthermore, Hung, Jeung, & Aberer, (2013) re-implement several data prediction methods and evaluates various performance metrics with the same benchmark. The study concludes that constant and linear prediction functions outperform the others in the presence of small variations in data. In line with these results, Raza, Camerra, Murphy, Palpanas, & Picco, (2015) use a linear data prediction approach named Derivative-Based Prediction (DBP) to collect data in Wireless Sensor Networks. Through this approach, both parameters of prediction function and critical data are transmitted to the sink.

Figure 1.

Transmitted values in WSNs through different approaches

All the prior approaches find/build critical values of original data or/and function information to represent original time series data (the red-colored points in Figure 1 (b) and (c)). Then there exist two limitations: (1) Both the original values (16-bit (Raza et al., 2015)) and the parameters of prediction functions (32-bit (Edara et al., 2008) or 64-bit (Hung et al., 2013)) are long codes which is a waste of space and unnecessary. (2) The performance of these approaches is strongly dependent on data variations. If the data variation does not follow the supposed manner within some time interval, they have to use more values to represent the original time series values to ensure that the prediction error is within the preset bound. This paper presents a lightweight data approximation approach in a totally original way. According to the data range and the precision requirement, Binary codes are used as abstract data to directly shorten data length. Figure 1 (d) shows an example of our approach with the temperature data of range (20°C, 27°C) and precision requirement 0.5°C. In this example, a 3-bit binary code can represent one value. Based on this approach, two types of application layer messages and their transmission scheme are implemented in the WSN scenario. The scheme can significantly reduce transmissions and timely report critical data. In addition, the proposed approaches are independent on environmental variations. The performance of our approach is verified by comparison with works from Information Sciences (Wu et al., 2015) and IEEE Transactions on Knowledge & Data Engineering (Raza et al., 2015). The details are shown in the section of Performance Evaluation.