*2.8. TreeNet Regression*

We used the TreeNet regression algorithm to determine influential features on the positioning accuracy of the u-blox ZED-F9P. Numerous advantages have been reported for TreeNet, in comparison with other machine learning based approaches. In addition to its highly accurate predictions, TreeNet is not sensitive to errors in data or missing data. No data pre-processing (e.g., transformation, normalisation, or reduction) or preselection of the variables is required. TreeNet is strong against overfitting, and the process of growing trees is extraordinarily fast [54,55].

TreeNet begins with an initial model, which consists of a very small tree. This simple model is deliberately weak. The residuals are computed for each data in the first model and are used to grow the second tree. The residuals of the second tree are then computed and used to grow the third tree. Likewise, this process repeats to generate a sequence of hundreds or thousands of trees, in order to achieve an optimal tree. All trees contribute to the optimal model. The final model prediction is based on the total contribution of the individual trees, which is known as score. The accuracy of the TreeNet score will improve steadily by increasing the number of trees until to reach an optimal number of trees [55].

We used a dataset including 2000 sample objects. Twenty percent of the sample objects were randomly assigned as the testing set and the remaining 80% as the learning set. The TreeNet loss function was set on Huber-M. The mean square error (MSE) was chosen as the criterion for determining the number of optimal trees. We set the initial tree size at 10,000 and generated 12 TreeNet models based on the different learning rates and tree complexity levels. The optimal model was selected based on the one that recorded the minimum MSE, and its parameters were tuned for the final TreeNet model. The performance of the model was tested using the area under the receiver operating characteristic (ROC) curve. A value greater than 0.9 represents high performance, while values less than 0.7 indicate low performance [56] of the TreeNet model.

The influence of features on the positioning accuracy of the u-blox ZED-F9P was determined via relative importance [55]. The importance values of the features are ranged between 0 and 100. The most influential feature gains a value of 100 and the remaining features are rescaled to reflect their importance relative to this feature. We produced partial dependence (PD) plots for individual and pairs of features that contributed to the predicted positioning accuracy in the model. The PD plots represent the response of the target variable to individual or pairs of features, as all remaining features are taken into account [57].

**Table 1.** Object features affecting on the accuracy of positioning by u-blox ZED-F9P, derived from different metrics of high-density LiDAR data.


### **3. Results**
