# Building Tree Allometry Relationships Based on TLS Point Clouds and Machine Learning Regression
## 4 Discussion
In the same way, [PERSON] [41] reported that a DL model with 100 neurons and nine hidden layers was the best network model compared to ANN, nonlinear regression, and nonlinear mixed-effect models to predict the relationships between H and DBH in stands of even aged and pure Anatolian Crimean Pine. Even fewer studies have addressed tree height and diameter allometry relative to machine learning methods other than ANN and DL. In this sense, [PERSON] et al. [42] tested four machine learning algorithms (k-nearest neighbors, RFR, support vector regression [SVR], and ANN) for modeling the height-diameter relationship of _Pinus taeda_ L. stands at different ages, comparing the results to those obtained by linear regression models. They reported that the machine learning models showed statistical indicators similar to the linear regression models when only H was included as an explanatory variable, which fully agrees with the results obtained in this work. They did not test including CD as an additional explanatory variable. In the same research line, [PERSON] et al. [43] evaluated the accuracy of predictions of annual periodic increment in diameter of individual trees in the Atlantic Forest using three machine learning techniques (ANN, SVR, and RFR), finding that ANN was the technique that presented the highest efficiency to predict the diameter increment of trees. In a recent work published by the authors, a traditional regression univariate model based on robust least squares fitting was proposed to express DBH as a function of H [14]. In this case, the inclusion of CD as an additional explanatory variable (multivariate model) did not significantly improve the accuracy of the predicted DBH values. In this way, the present work represents a step forward, aiming at testing the potential of machine learning regression models as an alternative to traditional linear regression methods to fit highly nonlinear allometric relationships in teak trees. Indeed, our study has demonstrated that allometric models involving both H and CD to estimate DBH performed better than those based solely on H. In addition, easy-to-apply boosting machine learning regression methods such as GBoost or CatBoost outperformed LR models (traditional linear regression) both in terms of goodness-of-fit (R\({}^{2}\)) and stability (variations in training and testing samples). When quantitatively comparing multivariate GBoost, one of the best machine learning methods tested in this work, and multivariate LR, both showed a low systematic error, slightly overestimating the observed values of DBH with a mean bias of 1.57% (ranging from 0.05% to 3.35%) and 1.84% (ranging from \(-\)0.04% to 3.65%), respectively. Multivariate GBoost and LR also provided reasonably low values of random error, predicting the observed values of DBH with mean RMSE figures of 1.45 cm (RMSE\({}_{\text{relative}}\) = 11.95%) and 1.62 cm (RMSE\({}_{\text{relative}}\) = 13.34%), respectively. In any case, the techniques used in this work should be adapted in order to be applied to other forest areas and species, since the height-diameter models not only depend on the species, but also on the characteristics of the stand and edaphoclimatic factors. In this regard, the authors of this study are currently testing machine learning regression algorithms to model tree allometric relationships in Mediterranean forest species such as Aleppo pine (_Pinus halepensis_ Mill.). It is worth underlining that the TLS-based method applied in this study to extract some dendrometric variables at tree level could be applied even to natural forests with mixed species. However, the two following drawbacks should be considered. First, the total height of the trees could probably be underestimated depending on the density and 3D structure of the forest stand, the phenological conditions, and the design of the TLS scan positions [44]. Note that the main reason of the underestimation of tree height by TLS is that the top of the tree crown is occluded by itself or a neighboring tree [45].