# Missing Data Imputation in the Internet of Things Sensor Networks
## 6 Conclusion and Future Work  
In this work, we explored various missing value imputation strategies for LCS deployed to generate data for air quality monitoring stations. We investigated imputation techniques such as \(k\)NN, RI, EM, missForest and proposed the BFMVI technique for handling missing data. In this study, the BFMVI technique shows the most promising performance for estimating univariate missing data when compared with other imputation techniques. From our analysis, the concentrations of other auxiliary sensor variables such as \(CO,NMHC,NO_{x}\) and \(O_{3}\) exhibiting strong correlation with the target variable \(C_{6}H_{6}\) were added to the imputation model, which had strong effects on the predictions, while it is unfeasible to evaluate the accuracy of imputation techniques when the true values are not known, the authors took the fully observed dataset and introduced artificial missing values using two patterns to test the accuracy of the imputation methods. Overall, our proposed BFMVI method showed promising results when compared to the other competing algorithms when applied to a real world Air Quality monitoring dataset. Furthermore, we took the dataset imputed at 30% for all the imputation techniques and evaluated their effect on the sensor calibration process. The authors evaluated the efficiency of various calibration models (DT, MLR, and RF) when trained on various imputed datasets. Results showed improvements when the MLR model was trained on our proposed BFMVI approach with an RMSE of 0.0310 as opposed to other techniques.  
Due to time constraint, this study could not consider other gas/electrochemical sensor data with multivariate missing values. Future research could concentrate on other types of gas sensor data, including Non-Dispersive Infrared (NDIR) sensor data.  
The work described in this article is a collaborative effort from all of the authors. Conceptualisation: B.A., H.A.-A. and R.H.; Methodology: B.A.; Design, implementation, and generation of results: B.A.; Analysis and interpretation of results: B.A., H.A.-A. and T.A.; Preparing the draft, review, and editing: B.A., H.A.-A., R.H. and T.A.; visualization: B.A., H.A.-A., R.H. and T.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Data Availability Statement:** Not Applicable, the study does not report any data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Imputation Method** & **Performance Measure** & **MLR** & **DT** & **RF** \\ \hline Original Data & RMSE & 1.105198 & 2.675627 & 1.307132 \\  & R\({}^{2}\) & 0.977588 & 0.852582 & 0.967482 \\  & MAE & 0.782843 & 1.924280 & 0.941910 \\ \hline KNN & RMSE & 0.921755 & 1.831899 & 1.443856 \\  & R\({}^{2}\) & 0.983985 & 0.939847 & 0.961877 \\  & MAE & 0.711107 & 0.694035 & 0.703279 \\ \hline RI & RMSE & 0.85446 & 1.630087 & 1.28414 \\  & R\({}^{2}\) & 0.985646 & 0.949827 & 0.968328 \\  & MAE & 0.656718 & 0.61114 & 0.622812 \\ \hline EM & RMSE & 2.529208 & 5.450468 & 4.118277 \\  & R\({}^{2}\) & 0.757888 & 0.403799 & 0.530481 \\  & MAE & 1.928332 & 2.196589 & 2.132884 \\ \hline MissForest & RMSE & 0.823423 & 1.631028 & 1.287602 \\  & R\({}^{2}\) & 0.986708 & 0.949937 & 0.968244 \\  & MAE & 0.634978 & 0.60595 & 0.61483 \\ \hline BFMVI & RMSE & 0.031015 & 0.201528 & 0.195777 \\  & R\({}^{2}\) & 0.999982 & 0.999268 & 0.999308 \\  & MAE & 0.023258 & 0.006227 & 0.010485 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of Imputation Techniques on \(C_{6}H_{6}\) Sensor Calibration.