# Early Predictability of Grasping Movements by Neurofunctional Representations: A Feasibility Study
## 2 Methods
### Feature Extraction and Classifiers  
Due to the high complexity and dimensionality of EEG signals, the discrimination accuracy depends heavily on feature extraction methods [35]. Two main extraction methods were chosen in the present study, as follows: the common spatial pattern (CSP) method, which is the most commonly applied filter for band-power feature extractions in hand movements [36]; and the xDAWN spatial filtering with covariance matrix estimation, which has been increasingly used in more recent work, and also allows for time point feature extractions [37]. The former computes spatial filters for signal separation by maximizing variance ratios and the latter computes spatial filters that maximize the ratios between the signals and the signals plus noise. After feature extraction, all classifiers were trained to predict the classes of the considered categorizations (see Section 2.2). The following state-of-the-art matrix and tensor classifiers regarding EEG-based BCIs were compiled and adapted.  
(1) Multinomial arranged logistic regression (LR): This uses variable vectors representing coefficients of the input variables to assume likelihoods [38]. The regression model was adapted to the data using maximum likelihood estimation for regression parameters.  
(2) A linear discriminant analysis (LDA) [39]: Discrimination was achieved by estimating the optimal discriminant function.  
(3) A support vector machine (SVM) classifier: EEG data were separated into their classes using a hyperplane. Since EEG data cannot be linearly separated, the radial basis function kernel was used.  
(4) The LR approach was repeated within the tangent space (TS). Thus, a projection of covariance matrices to TS was performed using Riemannian geometry [25; 40].  
(5) The SVM approach was also repeated within the TS using Riemannian geometry [25; 40].  
(6) A further classifier computing the Riemannian minimum distance to mean (MDM) value [26] was applied. This calculates a geometric mean value for each class from the training data and then assigns an undefined trial to the class corresponding to the closest value [41]. However, class-interesting features within covariance matrices can be obscured by noise.  
(7) To counteract this, the MDM classifier was additionally extended by geodesic filtering (FgMDM) to further maximize the variance between classes and further minimize it within classes [25; 40].  
The LR, SVM, and LDA classifiers were implemented using the Python library scikit-learn with their respective default regularization; the MDM classifier was implemented  
Figure 2: Experimental timeline with the confining events “initial movement” and “object grasped” of the reaching phase lasting at least 800 ms. The MGA of the hand for this phase was between 61 and 65%; therefore, for epoching reasons, it was subdivided into the three time windows, T1 to T3, which lasted 500 ms each. MGA = maximum grip aperture.  
using the Python library pyriemann, which introduces regularization by estimating the shrunk Ledoit-Wolf covariance matrices [42]. Figure 3 shows the compiled classifiers as a function of the two feature extraction methods.