Nonlinear sparse partial least squares: an investigation of the effect of nonlinearity and sparsity on the decoding of intracranial data

Abstract

Objective. Partial Least Squares (PLS) regression is a suitable linear decoder model for correlated and high dimensional neural data. This algorithm has been widely used in the application of brain–computer interface (BCI) for the decoding of motor parameters. PLS does not consider nonlinear relations between brain signal features. The nonlinear version of PLS that considers a nonlinear relationship between the latent variables has not been proposed for the decoding of intracranial data. This nonlinear model may cause overfitting in some cases due to a larger number of free parameters. In this paper, we develop a new version of nonlinear PLS, namely nonlinear sparse PLS (NLS PLS) and test it in BCI applications. Approach. In motor related BCI systems, improving the decoding accuracy of both kinetic and kinematic parameters of movement is crucial. To do this, two BCI datasets were chosen to decode the force amplitude and position of hand trajectory using the nonlinear and sparse versions of PLS algorithm. In our new NLS PLS method, we considered a polynomial relationship between the latent variables and used the lasso penalization in the latent space to avoid overfitting and to improve the decoding accuracy. Main results. Some linear and nonlinear based PLS models and our new proposed method, NLS PLS, were applied to the two datasets. According to our results, significant improvement from the NLS PLS method is confirmed over other methods. Our results show that nonlinear PLS outperforms generic PLS in the force decoding but it has lower accuracy in the hand trajectory decoding because of high dimensional feature space. By using lasso penalization, we presented a sparse nonlinear PLS-based model that outperforms generic PLS in both datasets and improves the coefficient of determination, 34% in the force decoding and 10% in the hand trajectory decoding. Significance. We constructed a simple PLS-based model that considers a nonlinear relationship between features and it is also robust to overfitting because of using the lasso penalty in the latent space. This model is suitable for a high dimensional and correlated datasets, like intracranial data and can improve the accuracy of estimation.