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The exceptional capabilities of the much celebrated Real Adaboost ensembles for solving decision and classification problems are universally recognized. These capabilities come from progressively constructing unstable and weak learners that pay more attention to samples that oppose more difficulties to be correctly classified, and linearly combine them in a progressive manner. However, the corresponding emphasis can be excessive, especially when there is an intensive noise or in the presence of outliers. Although there are many modifications to control the emphasis, they show limited success for imbalanced or asymmetric problems. In this paper, we use the neighborhood concept to design a simple modification of the emphasis mechanisms that is able to deal with these situations. It can also be combined with other emphasis control mechanisms. Experimental results confirm the potential of the proposed modification by itself and also when combined with a previously tested mixed emphasis algorithm. The main conclusions of our work and some suggestions for further research along this line close the paper.