Synthesis of complex- and hyperbolic-valued Hopfield neural networks

Abstract

A complex-valued Hopfield neural network (CHNN), a multistate Hopfield model, is useful for processing multilevel data, such as image data. Several alternatives of CHNN have been proposed. A hyperbolic-valued Hopfield neural network (HHNN) improves the noise tolerance of CHNN. In this work, we propose a synthetic Hopfield neural network (SHNN), a combination of a CHNN and an HHNN. An SHNN is the first combination of Hopfield models using different algebras. Since a CHNN and an HHNN have different operators, such as addition and multiplication, they are represented by matrices and vectors to compose an SHNN. A CHNN and an HHNN have different global minima. Only the common global minima are the global minima of SHNN. Thus, an SHNN is expected to improve the noise tolerance. In fact, computer simulations support our expectation.