Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks

Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules

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...

Image Reconstruction by the Complex-Valued Neural Networks: Design by Using Generalized Projection Rule

Storing gray-scale images with neural networks is a challenging problem and has received much attention in the past two decades. There are four main approaches for storing images with n pixels and K gray levels. The first approach is to encode the gray level of each pixel by R ( 2 log R K = ) binary neurons (Taketa & Goodman, 1986; Cernuschi-Frias, 1989; Lee, 1999). However, this method needs g...

Complex-Valued Neural Networks

The usual real-valued artificial neural networks have been applied to various fields such as telecommunications, robotics, bioinformatics, image processing and speech recognition, in which complex numbers (two dimensions) are often used with the Fourier transformation. This indicates the usefulness of complex-valued neural networks whose input and output signals and parameters such as weights a...

Complex-Valued Neural Networks

A Complex-Valued Hopfield Neural Network: Dynamics and Applications

Drawing important ideas from several sources, the idea of associative memory from psychology (Kohonen, 1977), the idea of Hebbian adaptation from neurophysiology (Hebb, 1949), the idea of neuron as a thresholding device from prior modeling work (McCulloch & Pitts, 1943) etc., Hopfield presented an elegant model of associative memory storage and retrieval in the brain (Hopfield, 1982; Hopfield, ...