Rainfall–runoff modelling is at the core of any hydrological forecasting system. The high spatio-temporal variability precipitation patterns, complexity physical processes, and large quantity parameters required to characterize a watershed make prediction runoff rates quite difficult. In this study, hyper-complex artificial neural network in form an octonion-valued (OVNN) proposed estimate rate...

The equalization of digital communication channel is an important task in high speed data transmission techniques. The multipath channels cause the transmitted symbols to spread and overlap over successive time intervals. The distortion caused by this problem is called inter-symbol interference (ISI) and is required to be removed for reliable communication of data over communication channels. I...

Neural networks expanded to complex domains have recently been studied in the field of computational intelligence. Complex-valued neural networks are effective for learning the relationships between complex inputs and outputs, and applications to complex analysis and complex image processing have been studied (Hirose, 2006). In addition, the effectiveness of the computational complexity and the...

At present, the vast majority of building blocks, techniques, and architectures for deep learning are based on real-valued operations and representations. However, recent work on recurrent neural networks and older fundamental theoretical analysis suggests that complex numbers could have a richer representational capacity and could also facilitate noise-robust memory retrieval mechanisms. Despi...

The ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations has been applied to the estimation of optical flows and the generation of fractal images. The complex-valued neural network has the adaptability and the generalization ability as inherent nature. This is the most different point between the ability of the 1-n-1 complex-valued neural network to learn 2D aff...

The advent of arti0cial neural networks has contributed signi0cantly to the 0eld of knowledge engineering. Neural networks belong to a family of models that are based on a learning-by-example paradigm in which problem solving knowledge is automatically generated according to actual examples presented to them. The knowledge, however, is represented at a subsymbolic level in terms of connections ...

Although complex-valued neural networks (CVNNs) – networks which can operate with complex arithmetic – have been around for a while, they have not been given reconsideration since the breakthrough of deep network architectures. This paper presents a critical assessment whether the novel tool set of deep neural networks (DNNs) should be extended to complex-valued arithmetic. Indeed, with DNNs ma...

Frequency domain generalization in complex valued neural networks is analyzed The complex valued neu ral networks consist of variable delay lines neural connection conductance and complex neuron nonlinearity The learning of frequency pro les is realized by adjusting the delay time and the conductance using backprop agation process The information geometry is discussed for obtaining a parameter ...

Many models of neural networks have been extended to complex-valued neural networks. A complex-valued Hopfield neural network (CHNN) is a complex-valued version of a Hopfield neural network. Complex-valued neurons can represent multistates, and CHNNs are available for the storage of multilevel data, such as gray-scale images. The CHNNs are often trapped into the local minima, and their noise to...