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 $\mathcal{B}$-projection functions. Broadly speaking, a $\mathcal{B}$-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

Neural Computing in Quaternion Algebra

兵庫県立大学201

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

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

IMU sensing–based Hopfield neuromorphic computing for human activity recognition

Aiming at the self-association feature of the Hopfield neural network, we can reduce the need for extensive sensor training samples during human behavior recognition. For a training algorithm to obtain a general activity feature template with only one time data preprocessing, this work proposes a data preprocessing framework that is suitable for neuromorphic computing. Based on the preprocessing method of the construction matrix and feature extraction, we achieved simplification and improvement in the classification of output of the Hopfield neuromorphic algorithm. We assigned different samples to neurons by constructing a feature matrix, which changed the weights of different categories to classify sensor data. Meanwhile, the preprocessing realizes the sensor data fusion process, which helps improve the classification accuracy and avoids falling into the local optimal value caused by single sensor data. Experimental results show that the framework has high classification accuracy with necessary robustness. Using the proposed method, the classification and recognition accuracy of the Hopfield neuromorphic algorithm on the three classes of human activities is 96.3%. Compared with traditional machine learning algorithms, the proposed framework only requires learning samples once to get the feature matrix for human activities, complementing the limited sample databases while improving the classification accuracy

Existence and exponential stability of solutions for quaternion-valued delayed hopfield neural networks by ξ-Norms

© 2013 IEEE. Recently, with the development of quaternion applications, quaternion-valued neural networks (QVNNs) have been presented and studied by more and more scholars. In this paper, the existence, uniqueness and exponential stability criteria of solutions for the quaternion-valued delayed Hopfield neural networks (QVDHNNs) are mainly investigated by means of the definitions of ξ-norms. In order to construct a ξ-norm, QVDHNNs system are decomposed into four real-number systems according to Hamilton rules. Then, taking advantage of ξ-norms, inequality technique and Cauchy's test for convergence, time-invariant delays and time-varying delays are considered successively to derive ξ-exponential type sufficient conditions. Based on these, several corollaries about the existence, uniqueness and exponential stability of solutions are obtained. Finally, two numerical examples with time-invariant delays and time-varying delays are given respectively. Their simulated images illustrate the effectiveness of the main theoretical results

Stochastic memristive quaternion-valued neural networks with time delays: An analysis on mean square exponential input-to-state stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying Itoˆ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results

Low-power neuromorphic sensor fusion for elderly care

Smart wearable systems have become a necessary part of our daily life with applications ranging from entertainment to healthcare. In the wearable healthcare domain, the development of wearable fall recognition bracelets based on embedded systems is getting considerable attention in the market. However, in embedded low-power scenarios, the sensor’s signal processing has propelled more challenges for the machine learning algorithm. Traditional machine learning method has a huge number of calculations on the data classification, and it is difficult to implement real-time signal processing in low-power embedded systems. In an embedded system, ensuring data classification in a low-power and real-time processing to fuse a variety of sensor signals is a huge challenge. This requires the introduction of neuromorphic computing with software and hardware co-design concept of the system. This thesis is aimed to review various neuromorphic computing algorithms, research hardware circuits feasibility, and then integrate captured sensor data to realise data classification applications. In addition, it has explored a human being benchmark dataset, which is following defined different levels to design the activities classification task. In this study, firstly the data classification algorithm is applied to human movement sensors to validate the neuromorphic computing on human activity recognition tasks. Secondly, a data fusion framework has been presented, it implements multiple-sensing signals to help neuromorphic computing achieve sensor fusion results and improve classification accuracy. Thirdly, an analog circuits module design to carry out a neural network algorithm to achieve low power and real-time processing hardware has been proposed. It shows a hardware/software co-design system to combine the above work. By adopting the multi-sensing signals on the embedded system, the designed software-based feature extraction method will help to fuse various sensors data as an input to help neuromorphic computing hardware. Finally, the results show that the classification accuracy of neuromorphic computing data fusion framework is higher than that of traditional machine learning and deep neural network, which can reach 98.9% accuracy. Moreover, this framework can flexibly combine acquisition hardware signals and is not limited to single sensor data, and can use multi-sensing information to help the algorithm obtain better stability