# Clustering-Based Segmented Regression for Particulate Matter Sensor Calibration
## 3 Results
### Evaluation
#### 3.2.3 Dimension of Clustering  
In order to determine the environment variables used in the clustering basis and regression equation, comparative experiments are conducted from two aspects: clustering factor and regression factors. The PM\({}_{2.5}\) concentration, temperature and humidity data used in clustering are all normalized to ensure that the clustering effect will not be affected by different data ranges.  
**Clustering factors**. In order to partition the data set more reasonably and improve the accuracy of the calibration phase, K-means algorithm is used to partition the data set according to different sensor information. Three different dimensions of clustering tests were conducted. The Figure 11 shows the intuitive effect of data samples clustering under two-dimensional and three-dimensional case.  
As shown in Table 1, in the Group 1 data group, regression the divided data set to obtain calibration parameters, and calculate the PM\({}_{2.5}\) concentration after calibration on the test set, after calibration, the RMSE values of the three different division methods and the standard data are 4.63, 4.48 and 4.46, respectively. Compared with the clustering based on concentration and temperature, two-dimensional clustering with concentration and humidity, and three-dimensional clustering with both concentration and temperature and  
Figure 11: The normalized PM\({}_{2.5}\) concentration, temperature and humidity are used as the clustering basis for K-means. As (**a**) shows the result of six clusters based on PM\({}_{2.5}\) concentration and humidity, as (**b**) is the result of six clusters based on PM\({}_{2.5}\) concentration, temperature and humidity.  
Figure 10: Taking RMSE as the evaluation index, the calibration performance of the model is compared when K-means, Fuzzy c-means, and Mean-shift algorithms are used to partition data setshumidity were used. RMSE after regression decreased by 3.24% and 3.67%, which also had the same effect on Group 2 and Group 3. RMSE in Group 2 decreased by 21.82%, 20.58%, and that in Group 3 decreased by 14.39%, 15.62%. It can be seen that whether it is two-dimensional or three-dimensional clustering, introducing humidity as one of the classification criteria can significantly improve calibration performance.  
**Regression factors**. In order to further compare the effects of humidity and temperature on the calibration performance of the sensor, humidity is introduced into the regression equation in the two-dimensional division based on concentration temperature clustering. It is found that the RMSE in the three groups of data decreased by 3.89%, 22.13% and 12.09%, respectively, compared with those before the introduction, and all obtained objective improvement. Then, by comparing the concentration temperature humidity ternary as the training parameter of the regression equation, it is determined that when the concentration humidity is used as the clustering basis and the concentration, temperature and humidity are used as the regression parameters, compared with baseline, the RMSE of the three groups of data after calibration decreased by 16.89%, 17.27% and 20.37%, respectively, the best calibration performance can be achieved in the three groups of data under the existing conditions.  
Based on the above experiments, the PM\({}_{2.5}\) concentration, humidity are used as the classification basis in the three groups of data, and the PM\({}_{2.5}\) concentration, temperature, humidity are used as the training parameters in the regression equation to obtain the best effect. Compared with the three-dimensional K-means clustering, it can also have lower overhead. Therefore, we suggest using the two-dimensional K-means clustering method combined with the multiple linear regression equation.