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

Continuous-valued quaternionic Hopfield neural network for image retrieval: a color space study

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOContinuous-valued quaternionic Hopfield neural network (CV-QHNN) generalizes the traditional Hopfield network for the storage and retrieval of vectors whose components are unit quaternions. In this paper, we investigate the performance of the CV-QHNN for the retrieval of color images using three different color spaces: RGB, HSV, and CIE-HCL. We point out that a direct conversion from the RGB to unit quaternions may result distortions in which visually different colors are mapped into close quaternions. Preliminary computational experiments reveal that the CV-QHNN based on the HSV color space can be more effective for the removal of noise from a corrupted color image.186191CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO305486/2014-46th Brazilian Conference on Intelligent Systems (BRACIS)2 a 5 de Outubro de 2017Uberlândia, MGSociedade Brasileira Computação, NVIDIA, Banco Itaú, Algar Telecom, Google, IBM Research Brasil, Techmob, SEBRAE, Sankhya, Click PerformanceCenter Convention Uberlândi