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Volume 2018, Article ID 4075656, 14 pages
Research Article

Predicting Facial Biotypes Using Continuous Bayesian Network Classifiers

1Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2640, Peñalolén, Santiago, Chile
2Center of Applied Ecology and Sustainability (CAPES), Santiago, Chile
3Departamento del Niño y Adolescente, Área de Ortodoncia, Facultad de Odontología, Universidad Andrés Bello, Santiago, Chile

Correspondence should be addressed to Gonzalo A. Ruz; lc.iau@zur.olaznog

Received 29 June 2018; Revised 7 November 2018; Accepted 15 November 2018; Published 2 December 2018

Guest Editor: Panayiotis Vlamos

Copyright © 2018 Gonzalo A. Ruz and Pamela Araya-Díaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Bayesian networks are useful machine learning techniques that are able to combine quantitative modeling, through probability theory, with qualitative modeling, through graph theory for visualization. We apply Bayesian network classifiers to the facial biotype classification problem, an important stage during orthodontic treatment planning. For this, we present adaptations of classical Bayesian networks classifiers to handle continuous attributes; also, we propose an incremental tree construction procedure for tree like Bayesian network classifiers. We evaluate the performance of the proposed adaptations and compare them with other continuous Bayesian network classifiers approaches as well as support vector machines. The results under the classification performance measures, accuracy and kappa, showed the effectiveness of the continuous Bayesian network classifiers, especially for the case when a reduced number of attributes were used. Additionally, the resulting networks allowed visualizing the probability relations amongst the attributes under this classification problem, a useful tool for decision-making for orthodontists.