Importance of Balance: Lightweight Transformer via Signed Graph Algorithm Unrolling for EEG Signal Denoising

Components of a typical EEG signal exhibit anti-correlations that are best modeled by signed graph edges. However, frequencies of a general signed graph are not well understood, complicating the design of a low-pass (LP) filter for denoising. Leveraging recent progress in spectral theory for balanced signed graphs, we first learn a balanced signed graph ${{\mathcal{G}}^B}$ directly from observed EEG data, where graph balance is enforced via a clever interpretation of the Cartwright-Harary Theorem (CHT). Frequencies of ${{\mathcal{G}}^B}$ are then mapped to those of a corresponding positive graph ${{\mathcal{G}}^ + }$ via a linear transform. This allows an ideal LP filter to be efficiently implemented via Lanczos approximation, where the cutoff frequency is learned. Pairing the unrolled LP graph filter with a graph learning module (acting as a self-attention mechanism) during unrolling results in a lightweight transformer-like neural net. Experiments show superior denoising performance for our balanced signed graph filter over positive and unbalanced signed graph implementations, and comparable to popular deep learning denoisers while reducing parameters drastically.