A Comparison between Optimum-Path Forest and k-Nearest Neighbors Classifiers

This paper presents a comparison between the k-Nearest Neighbors, with an especial focus on the 1-Nearest Neighbor, and the Optimum-Path Forest supervised classifiers. The first was developed in the 1960s, while the second was recently proposed in the 2000s. Although, they were developed around 40 years apart, we can find many similarities between them, especially between 1-Nearest Neighbor and Optimum-Path Forest. This work shows that the Optimum-Path Forest classifier is equivalent to the 1-Nearest Neighbor classifier when all training samples are used as prototypes. The decision boundaries generated by the classifiers are analysed and also some simulations results for both algorithms are presented to compare their performances in real and synthetic data.