  A novel correction algorithm is proposed for multi-class classification
problems with corrupted training data. The algorithm is non-intrusive, in the
sense that it post-processes a trained classification model by adding a
correction procedure to the model prediction. The correction procedure can be
coupled with any approximators, such as logistic regression, neural networks of
various architectures, etc. When training dataset is sufficiently large, we
prove that the corrected models deliver correct classification results as if
there is no corruption in the training data. For datasets of finite size, the
corrected models produce significantly better recovery results, compared to the
models without the correction algorithm. All of the theoretical findings in the
paper are verified by our numerical examples.
