Abstract
k-nearest neighbor and linear regression in the prediction of the artificial form factor . T he proposal of this study was to test whether the performance of the non parametric approach k -Nearest Neighbor ( k -NN), would improve estimates of individual artificial form factor ( f 1.3 ) of trees of the hybrid Eucalyptus urophylla x Eucalyptus grandis compared to the O rdinary L east S quares method. A total of 149 sample-trees were selected , felled , and diameter was measured along the trunk at 10% (d 0. 1 ), 30% (d 0. 3 ), 50% (d 0. 5 ) and 70% (d 0. 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 adjust ment 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 m ost multiple linear regression models present problems of collinearity or multicollinearity. The use of the covaria te (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 predicti on of the tree form factor , and its use is recommended when classical linear regression models or other simpler methods do not yield good results.
Highlights
In 2016, the total area of planted trees in Brazil increased by 0.5% in relation to the year 2015, totaling 7.84 million hectares
The Pearson correlation coefficients (r) between the dependent and independent variables contained in the artificial form factor models (f1.3), were significant at the level of α = 0.05, except for the correlation between f1.3 and h/d1.3 (r =-0.062ns; FF7)
Severe multicollinearity effects on model coefficient estimates were detected for most multiple linear regression models, except for the models FF4, FF9 and FF10 (VIF < 10); for the models with VIF > 10 there were correlations between predictor variables greater than 80%
Summary
In 2016, the total area of planted trees in Brazil increased by 0.5% in relation to the year 2015, totaling 7.84 million hectares (ha). The genus Eucalyptus occupies 5.7 million hectares of planted trees with a 2.4% annual growth rate during the last five years. In this period, the state of Mato Grosso do Sul had the largest expansion of Eucalyptus culture registering an increase of 400,000 ha, with an average annual growth rate of 1.3%. The volume can be estimated by the equation: vi = g.h.f, where vi = volume of the i-th tree (m3), g = sectional area at 1.30m from the ground (m2), h = tree height (m), and f = tree form factor (ADEKUNLE et al, 2013)
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