Generalized Maximum Correntropy Broad Learning System With Robust M-Estimator

Haiquan Zhao, Xin Lu, C. L. Philip Chen

Abstract: The sensitivity of the broad learning system (BLS) based on the minimum-mean-square error (MMSE) criterion to non-Gaussian noise limits the application of this system. In order to solve this problem, this article proposes robust BLS (GC-BLS) based on generalized maximum correntropy criterion (GMCC). GMCC has a more general kernel function, which can effectively extract high-dimensional features of the data. In the non-Gaussian noise environment, GC-BLS shows excellent robustness. However, if the kernel width deviates from its optimal value, the performance of the system constructed based on the entropy criterion may fluctuate or even degrade. Since robust regression methods can improve robustness and are independent of kernel width, this motivates us to further construct MGC-BLS based on M-estimator functions. MGC-BLS can effectively suppress the performance degradation caused by kernel width deviation and has better robustness when selecting an appropriate M-estimator function. The two algorithms are optimized by fixed-point iteration, the update strategy in the iterative process is analyzed, and the sufficient conditions for the convergence of the algorithms are given. Compared with other BLS variants, GC-BLS and MGC-BLS can show better performance in the tests. Experiments on University of California Irvine (UCI) regression datasets and time-series datasets show the effectiveness of the two new algorithms.