  As an effective and efficient discriminative learning method, Broad Learning
System (BLS) has received increasing attention due to its outstanding
performance in various regression and classification problems. However, the
standard BLS is derived under the minimum mean square error (MMSE) criterion,
which is, of course, not always a good choice due to its sensitivity to
outliers. To enhance the robustness of BLS, we propose in this work to adopt
the maximum correntropy criterion (MCC) to train the output weights, obtaining
a correntropy based broad learning system (C-BLS). Thanks to the inherent
superiorities of MCC, the proposed C-BLS is expected to achieve excellent
robustness to outliers while maintaining the original performance of the
standard BLS in Gaussian or noise-free environment. In addition, three
alternative incremental learning algorithms, derived from a weighted
regularized least-squares solution rather than pseudoinverse formula, for C-BLS
are developed.With the incremental learning algorithms, the system can be
updated quickly without the entire retraining process from the beginning, when
some new samples arrive or the network deems to be expanded. Experiments on
various regression and classification datasets are reported to demonstrate the
desirable performance of the new methods.
