Classification methods for planar shapes

Abstract

The goal of this paper is to propose supervised learning methods considering two-dimensional landmarks (planar shapes). We introduce a novel method based on a support vector machine (SVM) algorithm, which had to be adapted to complex vectors. We also propose other novel methods based on density estimation, kernel k-means, and hill-climbing. Combinations between the classifiers using the ensemble method are considered as well. Furthermore, we compared the proposed methods to the existing Bayes discriminant approach. We conducted simulation experiments to evaluate the performance of the proposed methods. The numerical results prove that for low concentrated data sets, the SVM algorithm outperforms the other methods. Moreover, four real-world data sets are considered: gorilla skulls, orangutan skulls, mouse vertebrae, and schizophrenia. These data sets present different configurations, such as several landmarks and variability. The proposed SVM method achieved the best performance in three data sets.