16 research outputs found
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time
hypercomplex-valued Hopfield-type neural networks. To ensure the neural
networks belonging to this class always settle down at a stationary state, we
introduce novel hypercomplex number systems referred to as real-part
associative hypercomplex number systems. Real-part associative hypercomplex
number systems generalize the well-known Cayley-Dickson algebras and real
Clifford algebras and include the systems of real numbers, complex numbers,
dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as
particular instances. Apart from the novel hypercomplex number systems, we
introduce a family of hypercomplex-valued activation functions called
-projection functions. Broadly speaking, a
-projection function projects the activation potential onto the
set of all possible states of a hypercomplex-valued neuron. Using the theory
presented in this paper, we confirm the stability analysis of several
discrete-time hypercomplex-valued Hopfield-type neural networks from the
literature. Moreover, we introduce and provide the stability analysis of a
general class of Hopfield-type neural networks on Cayley-Dickson algebras
An Introduction to Quaternion-Valued Recurrent Projection Neural Networks
Hypercomplex-valued neural networks, including quaternion-valued neural
networks, can treat multi-dimensional data as a single entity. In this paper,
we introduce the quaternion-valued recurrent projection neural networks
(QRPNNs). Briefly, QRPNNs are obtained by combining the non-local projection
learning with the quaternion-valued recurrent correlation neural network
(QRCNNs). We show that QRPNNs overcome the cross-talk problem of QRCNNs. Thus,
they are appropriate to implement associative memories. Furthermore,
computational experiments reveal that QRPNNs exhibit greater storage capacity
and noise tolerance than their corresponding QRCNNs.Comment: Accepted to be Published in: Proceedings of the 8th Brazilian
Conference on Intelligent Systems (BRACIS 2019), October 15-18, 2019,
Salvador, BA, Brazi
Learning Schemes for Recurrent Neural Networks
兵庫県立大学大学院202
Selected aspects of complex, hypercomplex and fuzzy neural networks
This short report reviews the current state of the research and methodology
on theoretical and practical aspects of Artificial Neural Networks (ANN). It
was prepared to gather state-of-the-art knowledge needed to construct complex,
hypercomplex and fuzzy neural networks.
The report reflects the individual interests of the authors and, by now
means, cannot be treated as a comprehensive review of the ANN discipline.
Considering the fast development of this field, it is currently impossible to
do a detailed review of a considerable number of pages.
The report is an outcome of the Project 'The Strategic Research Partnership
for the mathematical aspects of complex, hypercomplex and fuzzy neural
networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland,
organized in September 2022.Comment: 46 page
Instantaneously trained neural networks with complex and quaternion inputs
Neural network architectures such as backpropagation networks, perceptrons or generalized Hopfield networks can handle complex inputs but they require a large amount of time and resources for the training process. This thesis investigates instantaneously trained feedforward neural networks that can handle complex and quaternion inputs. The performance of the basic algorithm has been analyzed and shown how it provides a plausible model of human perception and understanding of images. The motivation for studying quaternion inputs is their use in representing spatial rotations that find applications in computer graphics, robotics, global navigation, computer vision and the spatial orientation of instruments. The problem of efficient mapping of data in quaternion neural networks is examined. Some problems that need to be addressed before quaternion neural networks find applications are identified
Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach
In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples