Special Issue: Real, Complex and Hypercomplex Number Systems in Data Processing and Representation

The evolution of human society is inevitably associated with the widespread development of computer technologies and methods, and the constant evolution of the theory and practice of data processing, as well as the need to solve increasingly complex problems in computational intelligence, have inspired the use of complex and advanced mathematical methods and formalisms for representing and processing big data sets. At the same time, the range of tasks to be solved has significantly expanded: the implementation of parallel computing with minimal hardware and energy costs, the compression of numerical data, ensuring error-free fractional–rational calculations, error correction as a result of failures and equipment failures, etc. The emergence of new tasks related to the presentation and processing of data in conditions of limited energy and hardware resources (for example, bank cards, biological sensors implanted in the human or animal body, IoT computing, deep space conditions, etc.), neurocomputing, and stream processing of high-precision spatial data (not only images but also control information in mechatronic systems) have required the improvement of data processing methods presented in various number systems. First of all, this concerns the use of real (rational, integer, and natural), complex (elliptic, parabolic, and hyperbolic), and hypercomplex (quaternions, octonions, sedenions, etc.) numbers in the implementation of computations in intelligent systems. In this Special Issue, we collected six articles devoted to the development of some of the topics identified.

The article by D. Majorkowska-Mech and A. Cariow [1] is devoted to the features of the implementation of resource-saving algorithms for small-sized discrete Fourier transform with real-valued input data. In the article by I. Kalmykov et al., issues related to the use of a polynomial residue number system in error-correction coding are considered [2]. W.-D. Richter’s article is devoted to a deep study of hyperbolic complex number systems [3]. The presentation and processing of octonion-valued 3D signals are the subjects of Blaszczyk’s and Snopek’s paper [4]. Two papers by O. Borysenko et al. describe the fundamentals of a new number system, named binomial by the authors, as well as its application to data compression [5,6].

Although applications for this Special Issue are closed, active research in this area continues and allows us to successfully solve the problems facing the scientific world today, namely, increasing the representativeness and processing speed of large data sets in solving problems in deep learning, data mining, machine vision, cryptography, compression, and coding.