title: Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction.
abstract: A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed to be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex-valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages.
authors: Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan. gouhei@sat.t.u-tokyo.ac.jp
authors: Gouhei
authors: G
authors: Tanaka
authors: Kazuyuki
authors: K
authors: Aihara
mesh_terms: D000465:Algorithms; D001245:Association Learning / Q000502:physiology; D003116:Color; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008568:Memory / Q000502:physiology; D011939:Mental Recall / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D010507:Periodicity; D011336:Probability