Classification of Epileptic iEEG using Topological Machine Learning

Electroencephalography (EEG) is a critical tool for monitoring brain activity and diagnosing neurological disorders such as epilepsy. However, learning meaningful representations from raw EEG signals remains challenging due to limited annotations, substantial inter-subject variability, and complex temporal dynamics. Recent EEG foundation models (FMs) have demonstrated promising performance through transformer-based architectures and large-scale self-supervised pretraining, yet they often incur substantial computational costs and exhibit diminishing returns with increasing model and dataset scale, limiting their practicality in clinical settings. To address these challenges, we propose EEGDM, a diffusion-based EEG representation learning framework. Specifically, EEGDM introduces a Structured State-Space Model for Diffusion Pretraining (SSMDP) that effectively captures long-range temporal dependencies through generative diffusion training on unlabeled EEG data. The representations are subsequently leveraged for downstream tasks via our Latent Fusion Module (LFM), which integrates multi-layer latent features of SSMDP. We evaluate EEGDM on three EEG benchmarks spanning EEG event classification (TUEV), seizure detection (CHB-MIT), and seizure classification (IIIC). Compared with existing state-of-the-art methods, including EEG FMs, EEGDM achieves competitive performance across diverse tasks and datasets, exceeding existing methods in most cases while requiring substantially fewer samples for both pretraining and downstream adaptation. These results demonstrate that diffusion-based learning can unlock more discriminative EEG representations, with direct implications for epilepsy diagnosis and management. Our source code and pretrained checkpoints are publicly available at: https://github.com/jhpuah/EEGDM.

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic ($χ$) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On $\textit{ECG5000}$, our single-feature ECS classifier achieves $98\%$ accuracy with $O(n+R\cdot T)$ complexity, compared to $62\%$ reported by a recent PH-based method. An AdaBoost extension raises accuracy to $98.6\%$, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on $\textit{TwoLeadECG}$ ($94.1\%$) and $\textit{Epilepsy2}$ ($92.6\%$).

Deep learning for EEG-based seizure detection faces critical challenges: severe annotation scarcity and extreme class imbalance, where ictal events comprise less than 10% of clinical recordings. We present DiffEEG, a 9.6M-parameter self-supervised foundation model that addresses both limitations through denoising diffusion pre-training and reinforcement learning (RL)-based fine-tuning. Pre-trained on 1.3M unlabeled segments from the Temple University Hospital Seizure Corpus (TUHSZ), DiffEEG learns generic neural representations via a 1D U-Net with multi-head self-attention. For downstream adaptation, a reinforced decision layer employs policy gradient optimization to directly maximize F1-score, prioritizing sensitivity to rare seizure events over overall accuracy. Under strict patient-wise evaluation (279 patients, Leave-One-Fold-Out), DiffEEG achieves 61% accuracy and 59% F1 for 4-class seizure subtyping, and 81% accuracy with 85% weighted F1 for binary detection, maintaining clinically viable seizure recall (59%) despite extreme imbalance (6.7% prevalence). Segment-level evaluation establishes an upper bound of 97.6% accuracy, confirming strong architectural capacity. DiffEEG demonstrates that diffusion-based pre-training combined with metric-aware reinforcement learning enables clinically deployable seizure monitoring with minimal labeled data requirements.