## 1 Introduction
### Common EEG Feature Extraction Methods for ERP Classification  
At present, one common category of methods is to use temporal characteristics to extract ERP features from EEG. In the year of 1988, [PERSON] and [PERSON] proposed stepwise discriminant analysis (SWDA) [4] to extract P300 ERP component from EEG. For multi-channel EEG data, the SWDA method simply combines it to a matrix, without analysis of spatial characteristics. Then, Independent Component Analysis (ICA) was proposed for ERP feature extraction, to overcome the disadvantages of SWDA. ICA can extract the distribution of EEG signals on the brain cortex, and then find the classification features related to ERP. [PERSON] et al. first used ICA to perform spatial analysis on ERP, using the spatial locations to find independent components that can represent ERP, and using them to obtain a more obvious waveform from a single trial [5]; [PERSON] et al. used ICA and the Hilbert-Huang Transform (HHT) [6] combined method to filter artifacts such as the ocular electrogram from the single-channel EEG, and improved the signal-to-noise ratio of ERP [7]. [PERSON] et al. used one-unit ICA with a reference, a variant of ICA for single-trial ERP extraction [8]. By analyzing the spatial distribution difference of each ERP waveform, a more significant difference between the deviation stimulus and the standard stimulus was obtained. [PERSON] et al. used global optimal constrained ICA to search for movement-related cortical potential in single-trial EEG data, and reached a higher accuracy rate in a motor-imaging classification experiment [9]. The major shortcoming of the ICA-based methods is that ICA requires separating components to be statistically independent. ICA also needs multi-channel EEG signals for accuracy, which also limits its application in BCI. Another widely used category of method is based on the statistical characteristics of ERP waveform and noise. Among these methods, component estimation methods based on statistical principles, such as Kalman filtering and Bayesian estimation, can separate ERP waveforms from interference noise, and therefore are used to extract ERP classification features from EEG. [PERSON] et al. used ICA and Kalman in combination to reduce the interference of white noise on ICA [10] and improve the performance of ICA and ERP extraction; [PERSON] et al. used Particle Filter to extract P300 waveforms [11], and obtained more accurate delay estimation and P300 component amplitude estimation; [PERSON] et al. used Kalman filter to extract ERP, by adding the EM algorithm to Kalman filter to achieve a more accurate amplitude estimation [12]; [PERSON] et al. used Bayesian estimation to study semantic understanding in the process of learning--the trial by trial change of the N400 component in the ERP waveform cannot be achieved by the superimposed average method [13]. [PERSON] et al. used Bayesian ranks to analyze and calculate the Event related potential scores of each trial, and use event-related potential scores as the time domain features to improve the accuracy of the P300-based speller [14]. This kind of method can handle delay estimation and amplitude estimation on a single-signal frame and improve the classification accuracy. However, there is a main disadvantage that the non-stationary characteristics of the EEG signals have a negative impact on the performance, so that ERP waveform estimation error cannot be guaranteed. The third category is feature extraction methods based on sparse modeling. Sparse modeling is an efficient representation method for high-dimensional data, especially for the EEG data [15]. The purpose is to approximate the input data with a linear combination of sparse dictionary atoms. On the other hand, atoms must have data adaptability--that is, atoms can describe certain essential characteristics of the data. At the same time, the linear combination coefficient, also called the sparse representation vector, can also be used as a classification feature. [PERSON] et al.