This paper presents a cooperative coevolutive approach for designing neural network ensembles. Cooperative coevolution is a recent paradigm in evolutionary computation that allows the effective modeling of cooperative environments. Although theoretically, a single neural network with a sufficient number of neurons in the hidden layer would suffice to solve any problem, in practice many real-world problems are too hard to construct the appropriate network that solve them. In such problems, neural network ensembles are a successful alternative. Nevertheless, the design of neural network ensembles is a complex task. In this paper, we propose a general framework for designing neural network ensembles by means of cooperative coevolution. The proposed model has two main objectives: first, the improvement of the combination of the trained individual networks; second, the cooperative evolution of such networks, encouraging collaboration among them, instead of a separate training of each network. In order to favor the cooperation of the networks, each network is evaluated throughout the evolutionary process using a multiobjective method. For each network, different objectives are defined, considering not only its performance in the given problem, but also its cooperation with the rest of the networks. In addition, a population of ensembles is evolved, improving the combination of networks and obtaining subsets of networks to form ensembles that perform better than the combination of all the evolved networks. The proposed model is applied to ten real-world classification problems of a very different nature from the UCI machine learning repository and proben1 benchmark set. In all of them the performance of the model is better than the performance of standard ensembles in terms of generalization error. Moreover, the size of the obtained ensembles is also smaller.

This paper presents COVNET, a new cooperative coevolutionary model for evolving artificial neural networks. This model is based on the idea of coevolving subnetworks that must cooperate to form a solution for a specific problem, instead of evolving complete networks. The combination of this subnetworks is part of a coevolutionary process. The best combinations of subnetworks must be evolved together with the coevolution of the subnetworks. Several subpopulations of subnetworks coevolve cooperatively and genetically isolated. The individual of every subpopulation are combined to form whole networks. This is a different approach from most current models of evolutionary neural networks which try to develop whole networks. COVNET places as few restrictions as possible over the network structure, allowing the model to reach a wide variety of architectures during the evolution and to be easily extensible to other kind of neural networks. The performance of the model in solving three real problems of classification is compared with a modular network, the adaptive mixture of experts and with the results presented in the bibliography. COVNET has shown better generalization and produced smaller networks than the adaptive mixture of experts and has also achieved results, at least, comparable with the results in the bibliography.

The k-nearest neighbor (k-NN) classifier is one of the most widely used methods of classification due to several interesting features, including good generalization and easy implementation. Although simple, it is usually able to match and even outperform more sophisticated and complex methods. One of the problems with this approach is fixing the appropriate value of k. Although a good value might be obtained using cross validation, it is unlikely that the same value could be optimal for the whole space spanned by the training set. It is evident that different regions of the feature space would require different values of k due to the different distributions of prototypes. The situation of a query instance in the center of a class is very different from the situation of a query instance near the boundary between two classes. In this brief, we present a simple yet powerful approach to setting a local value of k. We associate a potentially different k to every prototype and obtain the best value of k by optimizing a criterion consisting of the local and global effects of the different k values in the neighborhood of the prototype. The proposed method has a fast training stage and the same complexity as the standard k-NN approach at the testing stage. The experiments show that this simple approach can significantly outperform the standard k-NN rule for both standard and class-imbalanced problems in a large set of different problems.

In this paper, we approach the problem of constructing ensembles of classifiers from the point of view of instance selection. Instance selection is aimed at obtaining a subset of the instances available for training capable of achieving, at least, the same performance as the whole training set. In this way, instance selection algorithms try to keep the performance of the classifiers while reducing the number of instances in the training set. Meanwhile, boosting methods construct an ensemble of classifiers iteratively focusing each new member on the most difficult instances by means of a biased distribution of the training instances. In this work, we show how these two methodologies can be combined advantageously. We can use instance selection algorithms for boosting using as objective to optimize the training error weighted by the biased distribution of the instances given by the boosting method. Our method can be considered as boosting by instance selection. Instance selection has mostly been developed and used for k -nearest neighbor (k -NN) classifiers. So, as a first step, our methodology is suited to construct ensembles of k -NN classifiers. Constructing ensembles of classifiers by means of instance selection has the important feature of reducing the space complexity of the final ensemble as only a subset of the instances is selected for each classifier. However, the methodology is not restricted to k-NN classifier. Other classifiers, such as decision trees and support vector machines (SVMs), may also benefit from a smaller training set, as they produce simpler classifiers if an instance selection algorithm is performed before training. In the experimental section, we show that the proposed approach is able to produce better and simpler ensembles than random subspace method (RSM) method for k-NN and standard ensemble methods for C4.5 and SVMs.