Sunia Tanweer

Sunia Tanweer, Narayan Puthanmadam Subramaniyam, Firas A. Khasawneh

Epileptic seizure detection from EEG signals remains challenging due to the high dimensionality and nonlinear, potentially stochastic, dynamics of neural activity. In this work, we investigate whether features derived from topological data analysis (TDA) can improve the classification of brain states in preictal, ictal and interictal iEEG recordings from epilepsy patients using multichannel data. We analyze data from 55 patients, significantly larger than many previous studies that rely on patient-specific models. Persistence diagrams derived from iEEG signals are vectorized using several TDA representations, including Carlsson coordinates, persistence images, and template functions. To understand how topological representations interact with modern machine learning pipelines, we conduct a large-scale ablation study across multiple iEEG frequency bands, dimensionality reduction techniques, feature representations, and classifier architectures. Our experiments show that dimension-reduced topological representations achieve up to 80\% balanced accuracy for three-class classification. Interestingly, classical machine learning models perform comparably to deep learning models, achieving up to 79.17\% balanced accuracy, suggesting that carefully designed topological features can substantially reduce model complexity requirements. In contrast, pipelines preserving the full multichannel feature structure exhibit severe overfitting due to the high-dimensional feature space. These findings highlight the importance of structure-preserving dimensionality reduction when applying topology-based representations to multichannel neural data.

Sunia Tanweer, Firas A. Khasawneh

We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems for continuous semimartingales, which correlates number $N_\varepsilon$ of excursions of magnitude at least $\varepsilon$ with the quadratic variation $[X]_T$ of the process. The scaling law holds universally for all continuous semimartingales with finite quadratic variation, including general Ito diffusions with nonlinear or state-dependent volatility, but fails sharply for deterministic systems -- thereby providing a theoretically-certfied method of distinguishing between these dynamics, as opposed to the subjective entropy or recurrence based state of the art methods. We construct a robust data-driven diffusion test. The method compares the empirical excursion counts against the theoretical expectation. The resulting ratio $K(\varepsilon)=N_{\varepsilon}^{\mathrm{emp}}/N_{\varepsilon}^{\mathrm{theory}}$ is then summarized by a log-log slope deviation measuring the $\varepsilon^{-2}$ law that provides a classification into diffusion-like or not. We demonstrate the method on canonical stochastic systems, some periodic and chaotic maps and systems with additive white noise, as well as the stochastic Duffing system. The approach is nonparametric, model-free, and relies only on the universal small-scale structure of continuous semimartingales.

Vicente Bosca, Tatum Rask, Sunia Tanweer et al.

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regression task -- to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.