An analog neural network approach for the least absolute shrinkage and selection operator problem
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This paper addresses the analog optimization for non-differential functions. The Lagrange programming neural network (LPNN) approach provides us a systematic way to build analog neural networks for handling constrained optimization problems. However, its drawback is that it cannot handle non-differentiable functions. In compressive sampling, one of the optimization problems is least absolute shrinkage and selection operator (LASSO), where the constraint is non-differentiable. This paper considers the hidden state concept from the local competition algorithm to formulate an analog model for the LASSO problem. Hence, the non-differentiable limitation of LPNN can be overcome. Under some conditions, at equilibrium, the network leads to the optimal solution of the LASSO. Also, we prove that these equilibrium points are stable. Simulation study illustrates that the proposed analog model and the traditional digital method have the similar mean squared performance.
KeywordsAnalog neural network Neural dynamics LPNN Local competition algorithm
This work is partially supported by the Research Grants Council, Hong Kong, under Grant Number, CityU 115612.
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Conflict of interest
Authors declare that they do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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