k-Nearest Neighbor And Linear Regression In The Prediction Of The Artificial Form Factor

Abstract

The proposal of this study was to test whether the performance of the nonparametric approach k-Nearest Neighbor (k-NN), would improve estimates of individual artificial form factor (f1.3) of trees of the hybrid Eucalyptus urophylla x Eucalyptus grandis compared to the Ordinary Least Squares method. A total of 149 sample-trees were selected, felled, and diameter was measured along the trunk at 10% (d0.1), 30% (d0.3), 50% (d0.5) and 70% (d0.7) of commercial height and posteriorly at 2m intervals. Mathematical models recognized in the literature for predicting the form factor were adjusted for comparison. The hyperparameter k of optimum adjustment for the k-NN estimator was obtained by repeated cross-validation. The training data of the k-NN regression model were identical to those used in the adjustment of the linear regression models since most multiple linear regression models present problems of collinearity or multicollinearity. The use of the covariate (d0.3.d0.7)/d1.32 and k = 15 made it possible to construct k-NN models with better generalization capacity. The potential of the k-NN estimator to predict the artificial form factor and thus to obtain less biased estimates of individual tree volumes was demonstrated and considered to be superior to the use of linear regression and average form factors. The k-NN approach can be considered more generic for prediction of the tree form factor, and its use is recommended when classical linear regression models or other simpler methods do not yield good results.