부산대학교 도서관

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.