Cauchy regularized broad learning system for noisy data regression

Abstract

Recently, the Broad Learning System (BLS) has attracted much attention due to its efficiency in clean data regression tasks. However, the conventional BLS performs poorly in the noisy environment, because the least square regression based loss function it used for networking training is noise sensitive. To address this problem, the Cauchy Regularized BLS (CRBLS) is proposed in this paper for noisy data prediction. Specifically, the Cauchy loss function instead of the least square metric is introduced into the system to regularize the residues. Compared to the least square loss, the Cauchy loss can penalize the large noise terms owe to its nonlinearity and bounded influence function. This admits the proposed CRBLS to handle data corrupted by Gaussian noise and outliers with different noise levels. In addition, a new incremental learning algorithm is developed for fast model updating without retraining the whole network when additional training samples are added. To evaluate the feasibility of CRBLS, extensive experiments are conducted, and results show that the proposed CRBLS achieves robustness for noisy data predication.