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In this paper, we propose to provide more information to Stacked Denoising Auto-Encoding classifiers in order to increase their performance. Specifically, we use the output of an auxiliary classifier to extend the input to those machines, and carry out the layer-by-layer auto-encoding training considering the input recovering and the label errors by means of a convex combination whose parameter is selected by conventional cross-validation. Extensive experiments support the effectiveness of this proposal, showing that the resulting machines offer better results than standard designs in all the cases, as well as a reduced sensitivity to the design parameters. The main conclusion of this study plus a number of avenues for further research close this contribution.