title: A new class of multi-stable neural networks: stability analysis and learning process.
abstract: 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.
authors.affiliation: Institute of Neural Information Processing, Ulm University, Ulm, Germany; Computer Engineering & Information Technology Department, Amirkabir University of Technology, Tehran, Iran. Electronic address: elham.bavafaye@uni-ulm.de.
authors.forename: E
authors.initials: E
authors.lastname: Bavafaye Haghighi
authors.affiliation: Institute of Neural Information Processing, Ulm University, Ulm, Germany.
authors.forename: G
authors.initials: G
authors.lastname: Palm
authors.affiliation: Computer Engineering & Information Technology Department, Amirkabir University of Technology, Tehran, Iran.
authors.forename: M
authors.initials: M
authors.lastname: Rahmati
authors.affiliation: Control & Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.
authors.forename: M J
authors.initials: MJ
authors.lastname: Yazdanpanah
mesh_terms: D000465:Algorithms; D002965:Classification / Q000379:methods; D016571:Neural Networks, Computer
keywords: Classification; Exponential number of attractors; Lyapunov stability; Multi-stable neural network; Sinusoidal dynamic