EMD-Fuzzy: An Empirical Mode Decomposition Based Fuzzy Model for Cross-Stimulus Transfer Learning of SSVEP

TL;DR

This work tackles calibration time in SSVEP-based BCIs by introducing CSTL in the frequency domain via Empirical Mode Decomposition (EMD) and a fuzzy decoder. The core idea is to reconstruct target-stimulus signals in the Fourier domain using IMF-based frequency exchange, then learn a frequency-mapping with a Takagi–Sugeno–Kang (TSK) fuzzy system featuring Modified-Laplace membership functions and a two-layer MLP. Across two public datasets, the method achieves state-of-the-art offline results (e.g., $ACC=82.75\%$, $ITR=186.56$ bits/min with 4 frequencies) and demonstrates online robustness, with an average accuracy of $86.30\%$ across seven subjects in an AR-based real-time setup. The approach reduces calibration burden by requiring a subset of labeled data while maintaining reliable decoding, indicating strong potential for real-time, user-friendly SSVEP-BCI applications.

Abstract

The Brain-Computer Interface (BCI) enables direct brain-to-device communication, with the Steady-State Visual Evoked Potential (SSVEP) paradigm favored for its stability and high accuracy across various fields. In SSVEP BCI systems, supervised learning models significantly enhance performance over unsupervised models, achieving higher accuracy in less time. However, prolonged data collection can cause user fatigue and even trigger photosensitive epilepsy, creating a negative user experience. Thus, reducing calibration time is crucial. To address this, Cross-Stimulus transfer learning (CSTL) can shorten calibration by utilizing only partial frequencies. Traditional CSTL methods, affected by time-domain impulse response variations, are suitable only for adjacent frequency transfers, limiting their general applicability. We introduce an Empirical Mode Decomposition (EMD) Based Fuzzy Model (EMD-Fuzzy), which employs EMD to extract crucial frequency information and achieves stimulus transfer in the frequency domain through Fast Fourier Transform (FFT) to mitigate time-domain differences. Combined with a Fuzzy Decoder that uses fuzzy logic for representation learning, our approach delivers promising preliminary results in offline tests and state-of-the-art performance. With only 4 frequencies, our method achieved an accuracy of 82.75% (16.30%) and an information transfer rate (ITR) of 186.56 (52.09) bits/min on the 40-target Benchmark dataset. In online tests, our method demonstrates robust efficacy, achieving an averaged accuracy of 86.30% (6.18%) across 7 subjects. This performance underscores the effectiveness of integrating EMD and fuzzy logic into EEG decoding for CSTL and highlights our method's potential in real-time applications where consistent and reliable decoding is crucial.

Figures (11)

• Figure 1: The diagram of three classification scenarios. (A): intra-stimulus classification; (B): inter-stimulus few-shot classification;
• Figure 2: Overview of the online experimental setup and data processing in EMD-Fuzzy system. (A) Training signal from an online experiment, showing a dominant 8 Hz source frequency and its 16 Hz harmonic in the spectrum. (B) Decomposition of channel 1 into $K$ intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). (C) Signal reconstruction in EMD-Fuzzy: Replacement of the target harmonic spectrum $\Omega^p_{[1]}=22Hz$ with the source harmonic set $\Gamma^q$ at 11 Hz, scaled by $g^q$ in each IMF. (D) Averaged reconstruction of IMFs post frequency-matching across channels, displayed alongside the reconstructed spectrum peaks for $P=\{11Hz\}$ before iFFT transformation. After that, sliding windows (blue) are applied among all four seconds data. (E) Setup of the online experiment using Augmented Reality (AR) to display flickers at various frequencies; sensors over the occipital lobe are indicated in pink. (F) Testing signal with target frequency 11 Hz and detection of its 22 Hz harmonic peak in the spectrum. Use only the first window (blue) as the test data. (G) Fuzzy Decoder architecture highlighting the Fuzzy AIC module and a classifier MLP head. (H) Detailed structure of the Fuzzy AIC module: inputs are processed through Fuzzy Consequents and Query Embedding, with subsequent calculations of firing strength and membership degree via Fuzzy Center and Modified-Laplace membership functions (MFs), culminating in model output via TSK Fuzzy Model multiplication. (I) Firing strength measurement from the fuzzy decoder for the testing signal. (J) Learning of the Fuzzy Center from the reconstructed training signal. (K) System design of the online setup, detailing EEG data acquisition, processing, and interface with the AR system and study participants during both training and testing phases; real AR view is shown in the lower sub-figure.
• Figure 3: Schematic representation of the training and testing strategy for EMD-Fuzzy. All frequencies, $P \cup Q$, are initially divided into source frequencies $P$ (randomly selected) and target frequencies $Q$ (remained). $N_{trial}$ denotes the number of trials for each class (frequency).
• Figure 4: Results of model comparisons across various data lengths (from 0.5s to 2s, in increments of 0.25s). (A): Accuracy and ITR of the 12JFPM Dataset. (B): Accuracy and ITR of the Benchmark Dataset. Statistical significance between our proposed EMD-Fuzzy model and baseline models is indicated by * ($p<0.05$) and ** ($p<0.01$).
• Figure 5: Schematic of the real-time experiment design, illustrating the setup for the calibration phase (A) and the real-time testing phase (B). This layout details the sequence of tasks, participant interactions, and data collection points critical for evaluating the real-time performance of the system.