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Weighted LS-SVM is normally used for function estimation from highly corrupted data in order to decrease the impact of outliers. However, this method is limited in size and big time series should be segmented in smaller groups. Therefore, border discontinuities represent a problem in the final estimated function. Several methods such as committee networks or multilayer networks of LS-SVMs are used to address this problem, but these methods require extra training and hence the computational cost is increased. In this paper a technique that includes an extra weight vector in the formulation of the cost function for the LS-SVM problem is proposed as an alternative solution. The method is then applied to the removal of some artifacts in biomedical signals.