Broad learning system based on the quantized minimum error entropy criterion

The broad learning system (BLS) based on the minimum mean square error (MMSE) criterion can achieve outstanding performance without spending too much time in various machine learning tasks. However, when data are polluted by non-Gaussian noise, the stability of BLS may be destroyed because the MMSE criterion is sensitive to outliers. Different from the MMSE criterion, the minimum error entropy (MEE) criterion utilizes the kernel function to capture high-dimensional information and decrease the negative influence of outliers, which will make BLS more discriminative and robust. Nevertheless, the computational complexity of MEE is high due to a double summation of the data size. To solve these issues, this paper proposes a new robust BLS variant based on the quantized minimum error entropy (QMEE) criterion, in which a quantization operation is used to reduce the computational complexity of MEE. The proposed model BLS-QMEE is optimized by the fixed-point iterative method, and a sufficient condition for its convergence is provided. Compared with the standard BLS and other existing robust variants of BLS, BLS-QMEE performs more satisfactorily without consuming too much time. The desirable performance of BLS-QMEE is verified by various experiments on function approximation, several public datasets, and a practical application.