SSVEP-stCCA

Steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) can deliver high information transfer rate (ITR), but requiring a large amount of subject’s calibration data to learn the class- and subject-specific model parameters (e.g. the spatial filters and SSVEP templates). Among the current calibration-based algorithms, the amount of the calibration data is proportional to the number of classes (or visual stimuli). In addition, the size of calibration data cannot be less than the number of stimuli.

We propose a subject transfer based canonical correlation analysis (stCCA) algorithm that utilizes the intra- and inter-subject knowledge to highly reduce the subject's calibration data. Our experimental results demonstrate that the stCCA method performs well with extremely little calibration data, providing an ITR at 198.18±59.12 bpm with 9 calibration trials in the Tsinghua benchmark dataset and 127.86±60.43 bpm with 9 calibration trials in the BETA dataset.

What is subject transfer CCA (stCCA)?

In the stCCA, it uses the intra-subject spatial filter and inter-subject SSVEP template to compute the correlation coefficient.

Intra-subject spatial filter

According to [1], we find that SSVEPs share a common spatial pattern (or a common spatial filter) across different stimulus frequencies (precisely speaking, from 8Hz to 15.8Hz) and the spatial pattern has very large individual difference. This may imply that each subject has his/her own spatial filter and different subjects cannot share a common spatial filter. This subject-specific spatial filter can be termed the intra-subject spatial filter.

Based on the multi-stimulus CCA, it is possible to learn the intra-subject spatial filter from a subject's SSVEP templates $\bar{\mathbf{X}}_j$ corresponding to only several frequencies (e.g., $K$ frequencies, $1 \le K \le N_f$ and $N_f$ is the number of stimuli):

$$r_{k}=\max_{\mathbf{u},\mathbf{v}}{\frac{\mathbf{u}^\top\mathcal{X}^\top\mathcal{Y}\mathbf{v}}{\sqrt{\mathbf{u}^\top \mathcal{X}^\top\mathcal{X}\mathbf{u}\cdot\mathbf{v}^\top\mathcal{Y}^\top\mathcal{Y}\mathbf{v}}}}=\mathrm{CCA}(\mathcal{X},\mathcal{Y}),$$

where

$$\mathcal{X} = \left[\bar{\mathbf{X}}_{a_1}^\top,\bar{\mathbf{X}}_{a_2}^\top,\cdots,\bar{\mathbf{X}}_{a_K}^\top \right]^\top, \mathcal{Y} = \left[{\mathbf{Y}}_{a_1}^\top,{\mathbf{Y}}_{a_2}^\top,\cdots,{\mathbf{Y}}_{a_K}^\top \right]^\top,$$ $$\mathbf{Y} = \left[\begin{array}{c} \sin (2\pi f_{k} t + \phi_k)\\\ \cos (2\pi f_{k} t + \phi_k)\\\ \sin (2\pi 2f_{k} t + 2\phi_k)\\\ \cos (2\pi 2f_{k} t + 2\phi_k)\\\ \vdots\\\ \sin (2\pi N_h f_{k} t + N_h \phi_k)\\\ \cos (2\pi N_h f_{k} t + N_h \phi_k)\\ \end{array}\right]^\top$$

and $a_1$, $a_1$, ..., $a_K$ are the indices of $K$ stimuli (let's say: $1 \le a_1 < a_2 \cdots < a_K \le N_f$).

Inter-subject SSVEP template

Here we assume that different subjects' spatially filtered SSVEP template share common knowledge. Specifically, a new subject's (or target subject's) spatially filtered SSVEP template is the weighted summation of the existing subjects' (or source subjects') spatially filtered SSVEP templates. In addition, the weight vector is invariant with different stimulus frequencies.

$$\tilde{\mathbf{X}}_k=\frac{1}{M}\sum_{n=1}^{M}{w_{n}\cdot {_{n}\bar{\mathbf{X}}_{k}}\cdot{_{n}{\mathbf{u}}}},$$

where $w_n$ is the weight for the $n$-th source subject, $_{n}\bar{\mathbf{X}}_{k}$ and $_{n}\mathbf{u}$ are the SSVEP template and the spatial filter from the $n$-th source subject. $n=1,2,\cdots, M$.

$$\mathbf{w}=\min_{\mathbf{w}}{\frac{1}{2} ||{\mathbf{b}-\mathbf{A}\mathbf{w}}}||,$$

where $\mathbf{w}=[w_{1},w_{2},\cdots,w_{M}]^\top$, $\mathbf{b}$ is the collection of target subject's $K$ spatially filtered SSVEP templates, and $\mathbf{A}$ is the collection of $K$ spatially filtered SSVEP templates from $M$ source subjects.

$$\mathbf{b}=\left[ \begin{array}{c} \bar{\mathbf{X}}_{a_1}\cdot\mathbf{u} \\\ \bar{\mathbf{X}}_{a_2}\cdot\mathbf{u} \\\ \vdots \\\ \bar{\mathbf{X}}_{a_K}\cdot\mathbf{u} \end{array}\right], \mathbf{A}=\left[ \begin{array}{cccc} {_{1}\bar{\mathbf{X}}_{a_1}}\cdot{_{1}\mathbf{u}}& {_{2}\bar{\mathbf{X}}_{a_1}}\cdot{_{2}\mathbf{u}}&\cdots&{_M\bar{\mathbf{X}}_{a_1}}\cdot {_M}\mathbf{u}\\\ {_{1}\bar{\mathbf{X}}_{a_2}}\cdot{_{1}\mathbf{u}}&{_{2}\bar{\mathbf{X}}_{a_2}}\cdot{_{2}\mathbf{u}}&\cdots&{_M\bar{\mathbf{X}}_{a_2}}\cdot {_M}\mathbf{u}\\\ \vdots& \vdots & \ddots & \vdots\\\ {_{1}\bar{\mathbf{X}}_{a_K}}\cdot{_{1}\mathbf{u}}&{_{2}\bar{\mathbf{X}}_{a_K}}\cdot{_{2}{\mathbf{u}}}&\cdots&{_M\bar{\mathbf{X}}_{a_K}}\cdot {_M}\mathbf{u}\\ \end{array}\right],$$

Two SSVEP datasets

1. Tsinghua benchmark dataset (Dataset I) [2]
2. BETA dataset (Dataset II) [3]

These two datasets can be downloaded from http://bci.med.tsinghua.edu.cn/

In [1], we used the Tsinghua benchmark dataset and UCSD dataset [4].

Matlab code

fun_stcca(f_idx,num_of_trials,TW,dataset_no)
f_idx: the index of the selected frequencies
num_of_trials: number of trials for each selected frequency
TW: data length (unit: sec)
dataset_no: 1-> tsinghua benchmark dataset, 2-> BETA dataset

fun_calculate_ssvep_template(dataset_no)
dataset_no: 1-> tsinghua benchmark dataset, 2-> BETA dataset

itr_bci(p,Nf,T)
p: accuracy Nf: number of stimuli T: data length (same dimensions as p), including the stimulation length and the rest length

Simulation study

In this simulation study, we test the accuracy of the stCCA with only 9 calibration trials. The 9 calibration trials are corresponding to 9 different stimulus frequencies (e.g., 8.2, 9.2, 10.0, 11.0, 11.8, 12.6, 13.6, 14.4, 15.4 Hz, according to the selection strategy A2 as mentioned in [1]) on two different SSVEP datasets.

Dataset I

fun_calculate_ssvep_template(1); % run it if you do not have 'th_ssvep_template_for_stcca.mat'
k=9; tw=0.7;
f_idx=round((40/k*[1:k]+40/k*[0:k-1])/2);
[sub_acc]=fun_stcca(f_idx,1,tw,1);
all_sub_itr=itr_bci(sub_acc/100,40,(tw+0.5)*ones(35,1));
mean(all_sub_itr);

The average ITR is 198.18 bpm, which is exactly the same one in Table IV [1] (this code can be used to reproduce the results as reported in [1], such as the Figure 7 and Figure 9). As mentioned in [1], this ITR is comparable to some of current calibration-based algorithms with minimally required calibration data (i.e., the ms-eCCA with 40 calibration trials and the eTRCA with 80 calibration trials).

Dataset II

fun_calculate_ssvep_template(2); % run it if you do not have 'beta_ssvep_template_for_stcca.mat'
k=9; tw=0.7;
f_idx=round((40/k*[1:k]+40/k*[0:k-1])/2);
[sub_acc]=fun_stcca(f_idx,1,tw,2);
all_sub_itr=itr_bci(sub_acc/100,40,(tw+0.5)*ones(70,1));
mean(all_sub_itr);

The average ITR is 127.86 bpm. I believe that this performance is comparable to some of current calibration-based algorithms with minimally required calibration data (i.e., the eCCA with 40 calibration trials and the eTRCA with 80 calibration trials).

Version

v1.0: (28 Oct 2022)
Test stCCA in two SSVEP datasets

Feedback

If you find any mistakes, please let me know via chiman465@gmail.com.

Reference

[1] Wong, C. M., et al. (2020). Inter-and intra-subject transfer reduces calibration effort for high-speed SSVEP-based BCIs. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 28(10), 2123-2135.
[2] Wang, Y., et al. (2016). A benchmark dataset for SSVEP-based brain–computer interfaces. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 25(10), 1746-1752.
[3] Liu, B., et al. (2020). BETA: A large benchmark database toward SSVEP-BCI application. Frontiers in neuroscience, 14, 627.
[4] Nakanishi, M., et al. (2015). A comparison study of canonical correlation analysis based methods for detecting steady-state visual evoked potentials. PloS one, 10(10), e0140703.

Citation

If you use this code for a publication, please cite the following papers

@article{wong2020learning,
title={Learning across multi-stimulus enhances target recognition methods in SSVEP-based BCIs},
author={Wong, Chi Man and Wan, Feng and Wang, Boyu and Wang, Ze and Nan, Wenya and Lao, Ka Fai and Mak, Peng Un and Vai, Mang I and Rosa, Agostinho},
journal={Journal of Neural Engineering},
volume={17},
number={1},
pages={016026},
year={2020},
publisher={IOP Publishing}
}

@article{wong2020spatial,
title={Spatial filtering in SSVEP-based BCIs: unified framework and new improvements},
author={Wong, Chi Man and Wang, Boyu and Wang, Ze and Lao, Ka Fai and Rosa, Agostinho and Wan, Feng},
journal={IEEE Transactions on Biomedical Engineering},
volume={67},
number={11},
pages={3057--3072},
year={2020},
publisher={IEEE}
}

@article{wong2020inter,
title={Inter-and intra-subject transfer reduces calibration effort for high-speed SSVEP-based BCIs},
author={Wong, Chi Man and Wang, Ze and Wang, Boyu and Lao, Ka Fai and Rosa, Agostinho and Xu, Peng and Jung, Tzyy-Ping and Chen, CL Philip and Wan, Feng},
journal={IEEE Transactions on Neural Systems and Rehabilitation Engineering},
volume={28},
number={10},
pages={2123--2135},
year={2020},
publisher={IEEE}
}