# Clustering-Based Segmented Regression for Particulate Matter Sensor Calibration
## 1 Introduction  
Recently, serious issues concerning air pollution have raised public attention with the development of urbanization and industrialization [1]. It presents a severe threat to not only the ecological environment but also to human health. In order to improve the environmental monitoring and governance capacity, high-precision air pollution monitoring stations are established all over the world to obtain accurate air pollutant concentration information [2]. However, monitoring stations cannot be deployed with a high-spatial density to achieve high resolution because it is limited by large costs associated with high-precision equipment [3, 4].  
For fine-grained monitoring, various forms of wireless sensor networks (WSN) have been applied in air pollution monitoring as a complement [5, 6, 7, 8]. Low-cost gas or particulate sensors make fine-grained air pollution monitoring possible under large-scale deployment.Compared with existing monitoring architecture with high-precision equipment, sensor-based air pollution monitoring has high resolution both spatially and temporally [9] at the expense of accuracy and robustness [10], due to limitations regarding the sensor's characteristics and performance. First, sensor drift [11] and cross-sensitivity [11, 12] inevitably cause measurement deviations after deployment. In addition, environmentalfactors such as temperature and humidity result in response fluctuations increasing measurement deviation further [13]. Therefore to guarantee the performance of a sensor-based air pollution monitoring system and make it closer to ground truth, it is essential to calibrate the sensory data against varied interference.  
In this paper, we focus on in-field calibration problem of particulate matter (PM) sensor for PM\({}_{2.5}\) and PM\({}_{10}\) sensing and propose a clustering-based segmented regression method. Interference from relative humidity and temperature are taken into consideration in the particulate matter concentration calibration model. Instead of a global regression model covering all situations of concentration, and humidity and temperature, samples for modeling are divided into clusters by a clustering algorithm and each cluster has an individual multiple linear regression equation. After the calibration modeling mentioned above is finished, the final calibrated result of one sample is obtained from the regression model of the cluster the sample belongs to. Our method is evaluated under a practical in-field deployment and shown to perform better than a global multiple regression method under different initial error levels. It demonstrates at least 16% and 9% improvement ratio of calibration error on RMSE, respectively, for pollutants PM\({}_{2.5}\) and PM\({}_{10}\) than the baseline, especially when relative humidity is involved.  
The main contributions of the paper are as follows. First, the clustering-based segmented regression method uses a combination of linear regression models to approximate a complex function structure for the in-field sensor calibration problem. It only relies on sensory data sampling with little prior knowledge of sensor characteristics. Second, the proposed method may have lower calculation cost and relieve overfitting problems, since its error is not overly sensitive to the cluster number and the ratio of training set and testing set. Third, it demonstrates better performance with a better fitting degree and a smaller calibration error both in mean value and variance, when compared with the global multiple linear regression model. Furthermore, it is easier to explain than those ANN-based methods.  
This paper is organized as follows: Section 2 introduces the problem background and method design. Section 3 presents an evaluation of the proposed method in practical deployment. Section 4 gives further discussion on the method's potential and Section 5 provides concluding remarks.