k-Nearest Neighbor Regression in the Estimation of TectonaGrandis Trunk Volume in the State of Pará, Brazil

ABSTRACT

Models constructed from machine learning are a potential non-parametric alternative for the prediction of biometric variables in opposition to traditional regression modeling. The hypothesis of this study was that the non-parametric approach with the k-Nearest-Neighbor algorithm (k-NN) has the possibility of presenting better accuracy with lower demand for predictor variables in the estimates of T. grandis trunk volume than the traditional volumetric models applied in forest sciences. Ten volumetric models were adjusted. In the regression k-NN was defined as maximum of 25 (25-NN), but with learning only for the odd neighbors starting at 3-NN. The optimal k nearest neighbor for two variations of predictors was obtained through repeated cross-validations. Spurr (ln) and Schumacher-Hall were the most accurate linear models that meet the linear regression assumptions. The optimal k nearest neighbor for the algorithm was k = 5 for the two variations of predictors. The use of the k-NN estimator may be a more general approach to linear regression especially when the assumptions made about the errors are not satisfied. However, its use should be considered only when traditional linear regression models or other simpler methods do not show good results.

KEYWORDS:

• Machine learning
• nearest neighbor
• linear regression
• statistical environment R

Acknowledgments

The authors thank Empresa Brasileira de Pesquisa Agropecuária (Embrapa) for granting the experimental area of T. grandis for the accomplishment of this scientific experiment.

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