Correntropy-Driven Nonparallel Least Squares Support Matrix Machine for Matrix Data Classification with Noisy Labels

The non-parallel least squares support matrix machine (NPLSSMM), extending the original model with a non-parallel one, provides an enhanced framework to utilize the structural information of matrix data. However, its least squares loss makes it sensitive to imperfectly labeled data. To address this limitation, this paper proposes a correntropy-based non-parallel least squares support matrix machine (C-NPLSSMM). By incorporating correntropy, a symmetric and bounded similarity measure, into the loss function design, C-NPLSSMM adaptively adjusts the classification model to match the underlying structure of matrix data while mitigating the impact of mislabeled samples. Theoretical analysis is conducted to reveal the intrinsic relationship between C-NPLSSMM and the original NPLSSMM. Specifically, when the kernel size of correntropy loss is large enough, C-NPLSSMM degenerates into NPLSSMM, ensuring consistency with the original formulation. Experimental results on publicly available image and electroencephalogram datasets demonstrate that C-NPLSSMM achieves higher classification accuracy than other competitive methods in most cases.