Guest Editorial Special Issue on Complex- and Hypercomplex-Valued Neural Networks

C OMPLEX-VALUED neural networks (CVNNs) exhibit very desirable characteristics in their learning, self-organizing, and processing dynamics, which makes them attractive for applications in various areas in science and technology. For example, they are perfectly suited to deal with complex amplitude, composed of amplitude and phase, which is one of the core concepts in physical systems dealing with electromagnetic, light, sonic/ultrasonic, and quantum waves. This, together with the widespread use of analytic signals and phasor representations, gives them a critical advantage in practical applications in diverse fields of engineering, where signals are routinely analyzed and processed in time/space, frequency, and phase domains. Besides, by convenience of representation , many big electromechanical engineering systems such as the electric power system are designed and analyzed in the complex domain. Then it is natural and timely to ask ourselves to which extent do CVNNs outperform standard approaches in various engineering fields. In addition, the bigger picture of CVNNs extends to quaternion and Clifford neural networks, as well as kernel and reservoir approaches; these underpin unique new directions in color-information treatment, robotics, control, and so forth. CVNN-TF has over 40 members and has been successful in promoting this area globally, through regular tutorials and special sessions in conferences within the IEEE CIS remit, and locally through various outreach and industry collaboration activities. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS has recognized the far-reaching theoretical and practical scope of this area and has organized this Special Issue entitled " Complex-and Hypercomplex-Valued Neural Networks. " The special issue has attracted close to 40 manuscripts, and the submissions have been reviewed by over 120 reviewers, with 15 articles accepted. A brief introduction to the papers selected for this special issue is given below. 1) Theory-oriented papers include: Global Stability Criterion for Delayed Complex-Valued Recurrent Neural Networks deals with the stability problem in delayed complex-valued recurrent neural networks. By separating complex-valued networks into real and imaginary parts, forming an equivalent real-valued system, to construct appropriate Lyapunov functionals, the authors present a sufficient condition to ascertain the existence, uniqueness , and globally asymptotical stability of the equilibrium point of complex-valued systems. Further Investigate the Stability of Complex-Valued Recurrent Neural Networks With Time-Delays provides additional arguments and further evidence on two recent results on feasibility of complex-valued recurrent neural networks for neurodynamics applications. This work complements the previous works with new criteria for globally asymptotical stability of equilibria in recurrent …