Maximum total correntropy-based broad learning system with robust M-estimator.

Although the broad learning system (BLS) and its existing robust variants have been widely applied in various fields due to their excellent performance, they still cannot effectively handle noise present in the input data of training samples, which may lead to a decline in algorithm performance. To address this issue, this paper proposes a maximum total correntropy-based BLS (MTC-BLS), which trains the model using the maximum total correntropy (MTC) criterion. This endows the model with the advantages of both the total least squares (TLS) method and the MCC criterion, enabling it to effectively handle both input and output noise. Furthermore, to mitigate the impact of kernel width selection deviations in the entropy-based criterion, two new robust methods are further proposed, namely MMTC-BLSa and MMTC-BLSb. The former directly incorporates the M-estimator into the algorithm's objective function, using the dual constraints of the M-estimator and MTC to balance model predictive performance while reducing the algorithm's dependence on the kernel width. The latter uses the M-estimator as a weighting factor in the MTC criterion for model training, employing the M-estimator to compensate for model errors caused by kernel width deviations, thereby effectively mitigating the negative effects of such deviations. Moreover, to enable efficient training, fixed-point iteration methods are introduced to provide iterative solution strategies for MTC-BLS, MMTC-BLSa, and MMTC-BLSb, respectively. The effectiveness and superiority of the proposed methods are validated through multiple comparative experiments on time series datasets, regression datasets and image datasets.