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We propose an autonomous access point selection algorithm for user-centric radio resource usage optimization in distributed wireless networks. We introduce the optimization algorithm based on the mutually connected neural network, which minimizes a given objective function by distributed update of each neuron. In order to improve the quality of services for each user, we apply such an algorithm to optimization of the balance of the available throughput among the users with keeping higher average throughput per user. The mutually connected neural network to minimize the objective function is realized by calculating the connection weights and the thresholds from the coefficients of the energy function and the target objective function. By computer simulations, we show that the proposed algorithm improves the available throughput for each user in large-scale wireless networks. Furthermore, we implement the proposed algorithm on an experimental wireless network, and verify that each user terminal selects a most appropriate access point to optimize the total radio resource usage based on the state of neurons distributively updated at each user terminal.