Incremental Classification for High-Dimensional EEG Manifold Representation Using Bidirectional Dimensionality Reduction and Prototype Learning

In brain-computer interface (BCI) systems, symmetric positive definite (SPD) manifold within Riemannian space has been frequently utilized to extract spatial features from electroencephalogram (EEG) signals. However, the intrinsic high dimensionality of SPD matrices introduces too much computational burden to hinder the real-time applications of such BCI, especially in handling dynamic tasks, like incremental learning. Directly reducing the dimensionality of SPD matrices with conventional dimensionality reduction (DR) methods will alter the fundamental properties of SPD matrices. Moreover, current DR methods for incremental learning always necessitate retaining old data to update their representations under new mapping. To this end, a bidirectional two-dimensional principal component analysis for SPD manifold (B2DPCA-SPD) is proposed to reduce the dimensionality of SPD matrices, in such way that the reduced matrices remain on SPD manifold. Afterwards, the B2DPCA-SPD is extended to adapt to incremental learning tasks without saving old data. The incremental B2DPCA-SPD can be seamlessly integrated with the matrix-formed growing neural gas network (MF-GNG) to achieve an incremental EEG classification, where the new low-dimensional representations of the prototypes in old classifiers can be easily recalculated with the updated projection matrix. Extensive experiments are conducted on two public datasets to perform the EEG classification. The results demonstrate that our method significantly reduces computation time by 38.53% and 35.96%, and outperforms conventional methods in classification accuracy by 4.21% to 19.59%.