Iterative Pseudo-Sparse Partial Least Square and Its Higher Order Variant: Application to Inference From High-Dimensional Biosignals

Partial least square (PLS) regression and its (L1 or L2 norm) regularized versions have been proposed to handle the high-dimensionality aspects of the problem at hand and select relevant features. Addressing these issues improves the generalizability of decoding the unseen data, with the severe challenge of high computational complexity. In order to avoid directly solving the L1 norm optimization problem or performing matrix inversion, this article proposes two PLS-based algorithms, pseudo-sparse PLS (PS-PLS) and iterative pseudo-sparse higher order PLS (iPS-HOPLS). In these proposed methods, we add the Pseudo-Sparsity term to reduce the L1 norm of the regression coefficient vector in a selective scheme for better importance interpretation while keeping the algorithm as simple as possible. Regarding the evaluation of the proposed methods, we investigate three critical high-dimensionality regression problems of 1) the prediction of 3-D trajectory from electrocorticography (ECoG) recordings, 2) decoding continuous fluctuation of the electromyography (EMG) powers from recorded magnetoencephalography (MEG) signals, and 3) continuous decoding of the finger forces from the high-density surface electromyogram (HD-sEMG) signals. As well as providing cognitive-relevant interpretations, the experimental results show significant improvements over the generic methods and competitive performance compared to the state-of-the-art regularized PLS approaches.