Topological data analysis is a mathematical framework that characterizes the global shape of complex data by identifying structural features—such as clusters, loops, or holes—that remain stable despite noise or small variations. We studied how vocal signals, example shown in (a), should be represented so that topology-based algorithms can correctly classify it.

We compared the topological features extracted from several signal representations, including spectrograms (b), spectrogram zeros (c), and Takens’ embeddings (d). Using a publicly available dataset of 11,200 recorded vowel utterances, we conducted an empirical analysis demonstrating that these topological features provide additional discriminative information for both speaker and vowel classification. Moreover, features derived from different signal representations appear to be complementary. Our results suggest that low-persistence topological features, often dismissed as “topological noise”, encode important information about speech.

Guillem Bonafos, Pierre Pudlo, Jean-Marc Freyermuth, Samuel Tronçon, and Arnaud Rey.
2026.
Speech Communication 178 (March): 103363 —  @HAL

In the context of M/EEG source reconstruction, most distributed source models tend to strongly overestimate the spatial extent of brain activity and underestimate its depth and amplitude (Black contour line: boundary of the “aud-rh” region given by MNE-Python).

The top row shows the results of the MNE and eLORETA algorithms (implemented in MNE-Python with the default parameters), which suffer significantly from these limitations (although eLORETA manages to estimate depth). Sparse Bayesian Learning (SBL, bottom left) underestimates the spatial extent while accurately locating the activity. Combining SBL with spectral graph wavelets, as shown in the bottom right panel, correctly locates the activity (red and green lines are level curves corresponding respectively to 1% and 10% source amplitude levels), estimates its spatial extent and depth, and yields a quantitatively relevant amplitude estimate.