Vol 45, No 5 (2019)

The NP-hard feature selection problem is studied. For solving this problem, a population based algorithm that uses a combination of random and heuristic search is proposed. The solution is represented by a binary vector the dimension of which is determined by the number of features in the data set. New solution are generated randomly using the normal and uniform distribution. The heuristic underlying the proposed approach is formulated as follows: the chance of a feature to get into the next generation is proportional to the frequency with which this feature occurs in the best preceding solutions. The effectiveness of the proposed algorithm is checked on 18 known data sets. This algorithm is statistically compared with other similar algorithms.

The problem of improving structural properties of artificial discrete neural networks is investigated. The structure of the neural network is regarded as a theoretical graph. Cyclical substructures can occur in this structure under certain conditions, e.g., when there is feedback among neural network layers. Some properties of cycles in the graphs corresponding to neural networks have a significant effect not only on the rate of convergence to the (stable) solutions of the problems posed by network users, but also on the very possibility of obtaining these solutions. These properties include the negativity of some circuits (simple cycles) in neural network graphs. We propose an algorithm that makes it possible to eliminate negative circuits from neural network graphs under certain constraints formulated in this paper. It increases the chances of finding correct solutions to the problems for which neural networks were developed. An illustrative example is presented.

This paper presents a graph-based approach to the implementation of complex computational methods. The approach is aimed at providing the researcher or engineer with a set of software tools for the organization of his or her source code, which makes it possible to reduce the cost of its further verification, validation, and support. The proposed approach is based on three levels of abstraction: categorical level (description of algorithm data transformations in algebraic terms of category theory), graphical level (description of the algorithm in the form of a directed graph), and interface level (particular software implementation of tools for algorithm construction based on the introduced concept of graph model for complex computational methods). Some features of the implemented software framework for building and traversing graph models are described. The effectiveness of the graph-based approach is exemplified by the computational methods for micromechanics of composite materials.

The matrices considered in this paper belong to \({\text{Ma}}{{{\text{t}}}_{n}}(\mathbb{K}[\sigma ,{{\sigma }^{{ - 1}}}])\), i.e., to the ring of \(n \times n\)-matrices whose entries are scalar difference operators with the coefficients from the difference field \(\mathbb{K}\) of characteristic 0 with automorphism (“shift”) \(\sigma \). A family of algorithms is discussed that allow one to check whether there exists an inverse matrix for a given matrix from \({\text{Ma}}{{{\text{t}}}_{n}}(\mathbb{K}[\sigma ,{{\sigma }^{{ - 1}}}])\) in this ring and, if exists, to construct it. These algorithms are made to correspond to complexities in terms of the number of arithmetic operations and the number of shifts (i.e., applications of σ and \({{\sigma }^{{ - 1}}}\)) in the field \(\mathbb{K}\). The algorithms are implemented in the form of Maple-procedures. This makes it possible to experimentally compare them in terms of time spent. The selection of the best algorithm based on these experiments does not always coincide with the complexity-based selection. An attempt is made to find out why this happens. A package of procedures for solving the considered problems is suggested, where the main procedure includes a parameter that specifies which algorithm is to be applied. If this parameter is lacking, than an a priori specified algorithm is selected that is relatively good both from the complexity and experimental standpoint compared to the others.