Enhance CCA-based method with modified CP decomposition for SSVEP frequency detection

Recently, the use of brain-computer interface (BCI) systems based on Steady-State Visual Evoked Potentials (SSVEPs) has increased significantly. This increase is attributed to their advantageous features, such as acceptable accuracy and minimal user training requirements. SSVEPs, a crucial pattern in BCI systems, are generated in the occipital region of the brain through visual stimulation within the frequency range of 6 to 60 Hz. In this paper, we propose two novel algorithms based on the Multiway Canonical Correlation Analysis (MCCA) method for frequency detection in SSVEP-based BCI systems. Our goal in the proposed algorithms, namely Sine-Cosine Filtered-CP-CCA (SCF-CP-CCA) and EEG-Filtered-CP-CCA (EF-CP-CCA), is to augment the initial reference signal by using tensor decomposition tools on multidimensional input EEG data. In both algorithms, we perform a modified Canonical Polyadic (CP) decomposition using an Alternating Least Squares (ALS) approach. Similar to the MCCA algorithm, for each stimulation frequency, a higher order array is generated using training data and the resulting tensor is decomposed using the proposed ALS method where loading matrices are filtered in each iteration. The obtained temporal loading matrix and a classic Sine-Cosine signal are then used in a Canonical Correlation Analysis (CCA) model to obtain the reference signal. The way the reference signal is generated, using the canonical scores of the EEG loading matrix or the Sine-Cosine matrix, leads to the proposal of two algorithms: SCF-CP-CCA and EF-CP-CCA. Finally, the Multiple Linear Regression (MLR) algorithm between the EEG test data matrix and the obtained reference signal is used to determine the target frequency. To evaluate the proposed algorithms, we use the real MEMANSSVEP dataset and compare the results of the proposed methods with those of the MCCA one. Compared to the MCCA algorithm, the average accuracy of the proposed SCF-CPCCA and EF-CP-CCA algorithms has improved by $3.2 \%$ and $7.7 \%$, respectively.