2.3 | CCA, FBCCA, and TRCA Methods
In this research endeavor, we delve into the application and consequences of the advanced ERLLP algorithm on the precision of SSVEP target identification by employing Canonical Correlation Analysis (CCA), Filter Bank Canonical Correlation Analysis (FBCCA), and Task-Related Component Analysis (TRCA) as exemplar methods. The ensuing sections elucidate the mechanisms behind these three target identification methodologies.
CCA Method: Given the acquired EEG dataset denoted asand the reference signals symbolized by,where and, the objective of Canonical Correlation Analysis (CCA) is to deduce a pair of linear transformationsandsuch that the correlation between the transformed variables and, is augmented to its zenith. The mathematical representation is:
Whererepresents the correlation coefficient, whileandare the eigenvectors corresponding to the largest eigenvalue.
For every stimulus frequency, denoted(whereand I represents the total number of stimulus frequencies), the reference signal can be constructed based on:
Whererepresents the number of harmonics, anddenotes the sampling rate. By computing the canonical correlation coefficient ofwith the reference signal under all stimulus frequencies, the stimulus frequency corresponding to the maximum correlation coefficient is identified as the target stimulus frequency.
FBCCA Method: The signalis decomposed into n sub-band signals through a filter bank, and the canonical correlation coefficientof each sub-band signalis calculated. The final discriminant coefficient is then determined by integrating the correlations of the n sub-bands as follows:
Where represents the weight corresponding to the correlation coefficient of the kth sub-band signal, and can be computed using:
In this context,is set to 1.25 andis set to 0.25, as per reference [15]. By comparing the integral coefficients of all the acquired stimulus frequencies, the stimulus frequency corresponding to the maximum correlation coefficient is selected as the target stimulus frequency
TRCA Method: This is a training-based method that requires the collection of user data through multiple experimental sessions. The collected user training data is represented as, wheredenotes the number of sampling points,indicates the number of electrode channels,represents the number of stimulus frequencies, andsignifies the number of blocks. TRCA aims to extract task-related components by spatially filtering the training data. The spatial filterfor stimulus frequencyand residing incan be expressed by the following equation:
In the above equationembodies the multi-channel EEG recordings for theblock subjected to a stimulus frequency.The concluding step involves the computation of the Pearson correlation coefficient between the spatially refined signal and the evaluation signal, which acts as the discriminating coefficient. Upon determining these coefficients for all stimulus frequencies, the target that resonates with the preeminent coefficient is recognized as the focal target. The depiction is as:
| Implementation
3.1 | Dataset
This investigation is grounded upon a benchmark SSVEP dataset introduced and curated by Wang et al. [21]. This dataset was meticulously compiled from a 40-target based BCI speller application, encapsulating the intricate nuances of Brain-Computer Interaction (BCI) paradigms. In particular, the dataset encompasses EEG recordings from a total of 35 healthy participants, spanning an eclectic mix of 8 seasoned participants with prior BCI experience and 27 novices. These recordings were obtained during dedicated target selection exercises steered by visual cues. Elaborating on the BCI speller, its virtual keyboard is intricately designed with 40 distinct visual flickers. These flickers are encoded employing the advanced Joint Frequency and Phase Modulation (JFPM) method, a testament to the rigorous scientific approach applied. The spectrum of stimulus frequencies extends from 8 Hz, reaching up to 15.8 Hz, and is demarcated at regular intervals of 0.2 Hz. Notably, there exists a phase disparity of 0.5between consecutively mapped frequencies.
For every participant in the study, the dataset archives a total of 240 trials (40 targets juxtaposed across 6 blocks). These trials are organized in a stochastic sequence, ensuring that the 40 flickers, guided by visual cues, appear in a randomized order. Each distinct trial has been structured to span a duration of 5 seconds. This dataset has been recognized as a pivotal reference point for scholars and researchers, aiding in the comparative analysis of diverse methods aimed at stimulus encoding and target identification within the realm of SSVEP-based BCI. This invaluable resource has been made accessible to the global research community and can be procured from http://bci.med.tsinghua.edu.cn/download.html. Encoded in MATLAB’s MAT file format, the dataset is disaggregated into 35 distinct files, corresponding to individual participants. Cumulatively, this data amasses a size of approximately 3.3GB. Each of these files, meticulously labeled from S01.mat to S35.mat, encapsulates the EEG readings as double-precision floating-point representations. When decoded in MATLAB, each file unravels into a four-dimensional matrix termed ”data” with demarcations across ”electrode index,” ”time point,” ”target index,” and ”block index.” Specifically, every trial encompasses 1500 data reference points from a 64-channel setup. An astute analysis reveals that the data length, which accumulates to 6 seconds (equivalent to 6 × 250 = 1500 time points), integrates a 0.5-second interval preceding stimulus initiation, 5 seconds post-initiation, and an additional 0.5 seconds post-stimulus cessation. For the sake of meticulous SSVEP signal scrutiny, the channels selected for this investigation are O1, O2, Oz, PO3, PO4, POZ, PO5, and PO6.