Strong Separation of Two Convex polytopes in Machine Learning

The problem of strong separation of two convex disjoint polytopes is considered. This problem is important for many industrial applications using machine learning, image analysis and pattern recognition. An iterative algorithm based on the Fejerian mappings is proposed. This algorithm is based on the Eremin's method. An important property of this method is the robustness of the computational process in presence of dynamic data changes. The two types of Fejerian mappings are investigated: single-valued Fejerian mapping and multi-valued Fejerian mapping. To study the behavior of the proposed algorithm, the computational experiments with scalable Model-n problems and Random problems were performed. The conducted experiments confirmed the effectiveness of the proposed approach.