Deterministic and randomized methods of entropy projection for dimensionality reduction problems

The work is devoted to development of methods for deterministic and randomized projection aimed at dimensionality reduction problems. In the deterministic case, the authors develop the parallel reduction procedure minimizing Kullback–Leibler cross-entropy target to condition on information capacity based on the gradient projection method. In the randomized case, the authors solve the problem of reduction of feature space. The idea of application of projection procedures for reduction of data matrix is implemented in the proposed method of randomized entropy projection where the authors use the principle of keeping average distances between high- and low-dimensional points in the corresponding spaces. The problem leads to searching of a probability distribution maximizing Fermi entropy target to average distance between points.