Regularized Partial Least Square Regression for Continuous Decoding in Brain-Computer Interfaces.

Continuous decoding is a crucial step in many types of brain-computer interfaces (BCIs). Linear regression techniques have been widely used to determine a linear relation between the input and desired output. A serious issue in this technique is the over-fitting phenomenon. Partial least square (PLS) is a well-known and popular method which tries to overcome this problem. PLS calculates a set of latent variables which are maximally correlated to the output and determines a linear relation between a low-rank estimation of the input and output data. However, this method has shown its potential to overfit the training data in many cases. In this paper, a regularized version of PLS (RPLS) is proposed which tries to determine a linear relation between the latent vector of the input and desired output using the regularized least square instead of the ordinary one. This approach is able to control the effect of non-efficient and non-generalized latent vectors in prediction. We have shown that the proposed method outperforms Ridge regression (RR), PLS, and PLS with regularized weights (PLSRW) in estimating the output in two different real BCI datasets, Neurotycho public electrocorticogram (ECoG) dataset for decoding trajectory of hand movements in monkeys and our own local field potential (LFP) dataset for decoding applied force performed by rats. Furthermore, the results indicate that RPLS is more robust against the increase in the number of latent vectors compared to PLS and PLSRW. Next, we evaluated the resistance of our proposed method against the presence of different noise levels in a BCI application and compared it to other techniques using a semi-simulated dataset. This approach revealed that RPLS offered a higher performance compared with other techniques in all levels of noise. Finally, to illustrate the usability of RPLS in other type of data, we presented the application of this method in predicting relative active substance content of pharmaceutical tablets using near-infrared (NIR) transmittance spectroscopy data. This application showed a superior performance of the proposed method compared to other decoding methods.