# Clustering-Based Segmented Regression for Particulate Matter Sensor Calibration
## 4 Discussion  
Theoretically, in this regression calibration problem, the proposed method divides the whole independent variable space into several parts and allocates one multiple linear regression model for each part. It does not rely on prior knowledge of sensor characteristics but is determined by practical sensory data sampling. This method uses a combination of linear regression models to approximate a complex function structure, relieving the underfitting problem caused by a rough global multiple linear regression model. Inspired by this, the sensor's cross-sensitivity calibration problem can also apply the proposed method to divide its independent variable space with more dimensions and simplify calibration model expression. Compared with a complex global regression model or ANN-based learning model, the proposed method makes the calibration model much easier to determine and explain. In evaluation, we find that when factor relative humidity is involved in clustering or regression, the performance improves more obviously than factor temperature. That is because humidity has an influence in the mechanism of sensor response. The output signals of laser particulate matter sensor depend on laser scattering caused by particulate matter in the sensor responding chamber. Thus, when environment humidity is high or increases sharply over a short period, numerous ambient floating micro-liquid drops will form in the chamber together with particulate matter, affecting laser scattering and the sensor's response. This process is hard to model physically; however, data-driven methods can describe the influence of humidity without knowing chamber structure design, laser scattering or other hardware issues. In total, three groups of data crossing different seasons including summer-autumn (Group 1), autumn-winter (Group 2) and winter-spring (Group 3) are involved in evaluation. Data in winter and spring achieved a larger calibration error than those in autumn. That is because for the location our system was deployed, there are more particulate-matter-related weather events or pollution events happening during the period of autumn to spring the next year. Within such pollution processes, the particulate matter concentration in atmosphere environment is greater. According to Figures 2 and 16, there are more difficulties to reducing calibration error. Calibration error and coefficient of determination regarding PM\({}_{2.5}\) are slightly better than that on PM\({}_{10}\). Generally, PM\({}_{10}\) has higher concentration and wider dynamic range than PM\({}_{2.5}\) on the sensor's readings. This may lead to larger calibration error mean value and error variance concerning PM\({}_{10}\) readings. In addition, PM\({}_{10}\) is affected more by humidity than PM\({}_{2.5}\) in PM sensor measurements. When laser scattering is affected by numerous liquid drops, there will be a larger PM\({}_{10}\) measurement deviation, which was observed in practice. This suggests that the in-field calibration model for PM\({}_{10}\) may be more sophisticated than that for PM\({}_{2.5}\). Better \(R^{2}\) of the proposed method than the global linear regression model might be attributed to clustering. The whole independent variable space is divided by clustering and each cluster possesses a number of samples. If each cluster has sufficient and typical enough samples, it can reach a good fitting degree. However on the other hand, clustering may also lead to some disadvantages in using our method. One such disadvantage is extremely unbalanced sizes of clusters. A cluster with few samples cannot obtain a satisfying regression model and will lead to a large error variance. Outliers and incorrect classification will also bring negative influence on calibration performance. These are issues worth further discussion.