Initialization-Based k-Winners-Take-All Neural Network Model Using Modified Gradient Descent

The k -winners-take-all ( k -WTA) problem refers to the selection of k winners with the first k largest inputs over a group of n neurons, where each neuron has an input. In existing k -WTA neural network models, the positive integer k is explicitly given in the corresponding mathematical models. In this article, we consider another case where the number k in the k -WTA problem is implicitly specified by the initial states of the neurons. Based on the constraint conversion for a classical optimization problem formulation of the k -WTA, via modifying the traditional gradient descent, we propose an initialization-based k -WTA neural network model with only n neurons for n -dimensional inputs, and the dynamics of the neural network model is described by parameterized gradient descent. Theoretical results show that the state vector of the proposed k -WTA neural network model globally asymptotically converges to the theoretical k -WTA solution under mild conditions. Simulative examples demonstrate the effectiveness of the proposed model and indicate that its convergence can be accelerated by readily setting two design parameters.