A new class of multi-stable neural networks: Stability analysis and learning process

• Published in: Neural networks Vol. 65; pp. 53 - 64
• Main Authors: Bavafaye Haghighi, E., Palm, G., Rahmati, M., Yazdanpanah, M.J.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.05.2015
• Subjects: Algorithms; Classification; Classification - methods; Classifiers; Dynamical systems; Dynamics; Exponential number of attractors; Learning; Lyapunov stability; Multi-stable neural network; Neural networks; Neural Networks (Computer); Sinusoidal dynamic; Specifications; Stability; Topology; Sinusoidal dynamic; Lyapunov stability; Multi-stable neural network; Exponential number of attractors; Classification
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/j.neunet.2015.01.010

Recently, multi-stable Neural Networks (NN) with exponential number of attractors have been presented and analyzed theoretically; however, the learning process of the parameters of these systems while considering stability conditions and specifications of real world problems has not been studied. In this paper, a new class of multi-stable NNs using sinusoidal dynamics with exponential number of attractors is introduced. The sufficient conditions for multi-stability of the proposed system are posed using Lyapunov theorem. In comparison to the other methods in this class of multi-stable NNs, the proposed method is used as a classifier by applying a learning process with respect to the topological information of data and conditions of Lyapunov multi-stability. The proposed NN is applied on both synthetic and real world datasets with an accuracy comparable to classical classifiers.