Binary classification based on varying of feature space dimension and choice of effective metric

The tasks of reducing $n$-dimensional feature space to a two-dimensional feature space and construction of both separation function for solving two-class (binary) recognition and it inverse mapping in $n$-dimensional space were considered. The inverse transformation is necessary to solve the problem directly in the initial features system. Suggested approach provides unambiguous transformation due to consistent application of known algorithms, but does not guarantee the reconstruction of the separating hyperplane with the required properties. It is proved that the addition of offset into the hyperplane equation and use of Euclidean–Mahalanobis distance allows to solve the task.