Graph-based pattern recognition techniques have been in the spotlight for many years, since there is a constant need for faster and more effective approaches. Among them, the Optimum-Path Forest (OPF) framework has gained considerable attention in the last years, mainly due to the promising results obtained by OPF-based classifiers, which range from unsupervised, semi-supervised and supervised learning. In this paper, we consider a deeper theoretical explanation concerning the supervised OPF classifier with k-neighborhood (OPF k), as well as we proposed two different training and classification algorithms that allow OPF k to work faster. The experimental validation against standard OPF and Support Vector Machines also validates the robustness of OPF k in real and synthetic datasets.

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