  The Partial Least Square Regression (PLSR) exhibits admirable competence for
predicting continuous variables from inter-correlated brain recordings in the
brain-computer interface. However, PLSR is in essence formulated based on the
least square criterion, thus, being non-robust with respect to noises. The aim
of this study is to propose a new robust implementation for PLSR. To this end,
the maximum correntropy criterion (MCC) is used to propose a new robust variant
of PLSR, called as Partial Maximum Correntropy Regression (PMCR). The
half-quadratic optimization is utilized to calculate the robust projectors for
the dimensionality reduction, and the regression coefficients are optimized by
a fixed-point approach. We evaluate the proposed PMCR with a synthetic example
and the public Neurotycho electrocorticography (ECoG) datasets. The extensive
experimental results demonstrate that, the proposed PMCR can achieve better
prediction performance than the conventional PLSR and existing variants with
three different performance indicators in high-dimensional and noisy regression
tasks. PMCR can suppress the performance degradation caused by the adverse
noise, ameliorating the decoding robustness of the brain-computer interface.
