Neural network ensembles based on copula methods and Distributed Multiobjective Central Force Optimization algorithm

•Employ copula theory to generate the combining weights.•Apply the gravitational kinematics theory to the proof of the CFO algorithm convergence.•Implement the CFO algorithm using distributed multiobjective architecture.•Use the DMCFO to train the component network.

Copula is a function with multivariate distribution. It has uniformly distributed marginals. Central Force Optimization is a new algorithm which is based on kinematics. It has been illustrated that this algorithm is better than other heuristic methods, when these techniques are applied to the classification problems. This paper proposes a technique of neural network ensembles which use the distributed Central Force algorithm to optimize each individual component network, simultaneously. The distributed Central Force algorithm incorporates an additional regularization term and utilizes the multiobjective architectures to design component networks. Furthermore it proposes that a new method of combining the component networks is to use Copula function theory as an effective design tool which generates the combining weights. The experimental results show that the copula-based ensemble network achieves better performance than other ensemble methods and that Distributed Multiobjective Central Force Optimization is capable of achieving better solutions in the light of converging speed and local minima. In the experimental discussion, the paper gives several reasons why the proposed method outperforms others.

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