Quantifying instability in neurological disorders EEG based on phase space DTM function.

Classifying individuals with neurological disorders and healthy subjects using EEG is a crucial area of research. The current feature extraction approach focuses on the frequency domain features in each of the EEG frequency bands and functional brain networks. In recent years, researchers have discovered and extensively studied stability differences in the electroencephalograms (EEG) of patients with neurological disorders. Based on this, this paper proposes a feature descriptor to characterize EEG instability. The proposed method starts by forming a signal point cloud through Phase Space Reconstruction (PSR). Subsequently, a pseudo-metric space is constructed, and pseudo-distances are calculated based on the consistent measure of the point cloud. Finally, Distance to Measure (DTM) Function are generated to replace the distance function in the original metric space. We calculated the relative distances in the point cloud by measuring signal similarity and, based on this, summarized the point cloud structures formed by EEG with different stabilities after PSR. This process demonstrated that Multivariate Kernel Density Estimation (MKDE) based on a Gaussian kernel can effectively separate the mappings of different stable components within the signal in the phase space. The two average DTM values are then proposed as feature descriptors for EEG instability.In the validation phase, the proposed feature descriptor is tested on three typical neurological disorders: epilepsy, Alzheimer's disease, and Parkinson's disease, using the Bonn dataset, CHB-MIT, the Florida State University dataset, and the Iowa State University dataset. DTM values are used as feature inputs for four different machine learning classifiers, and The results show that the best classification accuracy of the proposed method reaches 98.00 %, 96.25 %, 96.71 % and 95.34 % respectively, outperforming commonly used nonlinear descriptors. Finally, the proposed method is tested and analyzed using noisy signals, demonstrating its robustness compared to other methods.