A novel quaternion optimization model for imagined speech classification

Abstract

Imagined speech, characterized by its extensive vocabulary and diverse applications, is a highly promising paradigm in BCI. Multi-channel EEGs are utilized for imagined speech classification. While low rank and sparse representation (LRSR) models have proven useful for EEG processing, they overlook the inter-channel correlations, leading to potential information loss. To address this issue, this paper proposes a quaternion valued LRSR (QLRSR) model for processing the EEGs. Quaternion algebra is a hypercomplex number system extending complex numbers with one real component and three orthogonal imaginary units(i,j,k). Since quaternion can excavate the potential connection of multi-dimensional signals, it is adopted in our QLRSR algorithm for processing muti-channel EEGs. The proposed QLRSR model for imagined speech classification involves two key steps. First, it models sampling points in four-channel EEGs as quaternion-valued numbers, exploiting cross-channel correlations during quaternion operations. Second, the model formulates the QLRSR problem as a quaternion-valued optimization problem. To validate the model's effectiveness, two public datasets are used: Track 3 of the BCI Competition 2020 and the Kara One dataset. By finding the solution of the quaternion valued optimization problem, it is found that the average classification accuracies of our proposed QLRSR model are 64.05 % and 75.46 %, which is higher than the existing models including low rank, sparse, LRSR-based model. Also, the required computational time for performing the classification of the imagined speech via our proposed QLRSR model is 5.12-17.33 % lower than of the aforementioned models. Since QLRSR integrates quaternion algebra into the LRSR-based method, which is more suitable for processing muti-channel signal than LRSR-based method. Hence, our proposed QLRSR model is efficient. Our work in the QLRSR is helpful for the researchers who work on finding a mathematical solution of the quaternion optimization problem. Furthermore, our proposed QLRSR model provides new directions and ideas for BCI and medical rehabilitation field.