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.