Study On Riemann Geometry Based Machine Learning In Brain-Computer Interface

Brain-computer interface(BCI)achieves direct control of external equipment through the provision of additional signal pathway,which has broad application prospects in the functional assistance and rehabilitation for the disabled.In motor imagery(MI)BCI,subjects produce various modes of EEG signals by imagining the movement of some body parts,and then the system decodes the subject's EEG as control command to achieve the control of the external equipment.Over the years,the technology has been greatly developed,in which the decoding of MI EEG signals is a key part of its progress.However,the low signal-to-noise ratio,nonstationarities,and individual differences of EEG signals are great obstacles to the commercial application of MI BCI.Therefore,seeking efficient decoding algorithms and reducing training costs are long-term research hotspots in this field.In recent years,some scholars have proposed using the Riemannian geometry to model and analyze the covariance matrix of MI EEG signals,and achieved good results,providing a new tool for decoding EEG signals.However,in practical applications,Riemannian geometric methods often face the curse of dimensionality.It is necessary to design dimensionality reduction algorithms.Based on the Riemannian geometry,this dissertation proposes a new algorithm for decoding MI EEG signals.The algorithm uses the Isomap of manifold learning to reduce the dimension of vectors from the local Riemannian tangent space mapping,and then uses Locally linear embedding to obtain the global coordinates.The algorithm conducts dimensionality reduction and reduces the distortion of edge samples distribution caused by direct use of the Riemannian tangent space mapping,which excels in the BCI Competition dataset.At the same time,aiming at the problem that non-stationarities and individual differences of MI EEG signals lead to the difficulty of training a model,this dissertation designs a new transfer learning algorithm for the MI BCI based on Riemannian geometry and dimensionality reduction method.The algorithm uses the Riemann tangent space mapping to transfer samples of different subjects to the similar feature space,and straighten them into vectors,and then use multidimensional scaling to conduct dimensionality reduction.Finally,efficient linear classifier is used for training and classification in low-dimensional Euclidean space.Experiments show that the algorithm performs better than the existing Riemannian method in the BCI Competition datasets.Finally,the dissertation discusses the non-stationarities and individual differences of the EEG signals based on the distribution of samples on Riemannian manifold.