# Clustering-Based Segmented Regression for Particulate Matter Sensor Calibration
## 5 Conclusions  
In general, we design a method using a clustering algorithm to realize segmented regression for in-field sensor calibration. It can compensate for humidity and temperature interference on PM sensor with statistical characteristics of samples and less prior knowledge, using a combination of linear regression models. Samples for modeling are divided into clusters via clustering algorithm and each cluster has its own individual multiple linear regression model calculated from least square fitting. The final calibrated result of one sensory sample is calculated from the regression model of the cluster the sample itself belongs to. Theoretically, the proposed method divides the whole independent variable space into several parts and allocates one multiple linear regression model for each part. This provides a more meticulous function for sensory data calibration and to some extent, can overcome the underfitting problem of using a global multiple linear regression model. The proposed method is evaluated on a practical deployed air pollution sensing system using official monitoring station as calibration reference, and a global multiple linear regression model as the baseline. An evaluation on the data set of different initial error levels indicates that the clustering-based calibration method produces a better performance. It works on the sensory data of both PM\({}_{2.5}\) and PM\({}_{10}\), and provides at least 16% and 9% improvement ratio of calibration error on RMSE, respectively, for pollutants PM\({}_{2.5}\) and PM\({}_{10}\) compared with the baseline. Regarding error statistics, the error of our method has both a smaller mean value and variance than the global linear regression model meaning that our method produces superior stability among numerous random tests. Besides both on PM\({}_{2.5}\) and PM\({}_{10}\), our method has a better fitting degree due to a better determination coefficient than the baseline. Our experiments consider different combinations of clustering factors and regression factors. It is found that under existing conditions the best calibration effect is achieved when clustering factors include PM concentration and humidity, and regression factors include PM concentration, humidity and temperature. Relative humidity has an appreciable influence and corresponds with usage experience and mechanism of the laser particulate matter sensor. The evaluation also shows that the proposed method may have a lower calculation cost. Because the calibration error is not quite sensitive to cluster number and the ratio of training set and testing set, this means that a moderate number of clusters is sufficient, and the training data can be reduced to relieve over-fitting problem. These benefits can improve the efficiency of post-deployment sensor calibration. Furthermore, there are several aspects for future research regarding the proposed method. In practical sensor deployment, calibration model updating warrants further attention because the proposed method has seasonal limitation based on limited sampling. The updating involves clustering updating and regression parameters updating, both on accuracy and efficiency. Optimization on clustering algorithms is another attractive issue and the selection of clustering algorithms may be related to multiple-dimension sensory data distribution. In addition, the existing evaluation only involves the current status of variables and does not consider delay items of the variables. If reflecting the changing process of some environmental factors in the model, e.g., humidity, it can improve calibration performance, delay items such as \(P(n-1)\), \(H(n-1)\) and \(H(n-2)\) require to be added in regression models. Last but not least, since the method works on PM\({}_{2.5}\) and PM\({}_{10}\) calibration against temperature and humidity, it also has potential value in assisting the sensor's cross-sensitivity calibration problem and may be more efficient than pre-deployment laboratory calibration. Conceptualization, S.L. and X.L. ; methodology, S.L. and X.L.