MapperEEG: A Topological Approach to Brain State Clustering in EEG Recordings

TL;DR

MapperEEG introduces a topological approach that fuses traditional EEG spectral features with the Mapper algorithm to unsupervisedly cluster brain states. By evaluating gamma-band power and constructing Mapper graphs, the method yields high clustering accuracy on a tapping task and reveals meaningful brain-state connectivity, even when standard clustering fails on a go/no-go task. The work demonstrates the value of spectral-domain inputs for Mapper-based brain-state analysis and discusses practical limitations and future directions, including real-time deployment and broader task coverage. Overall, MapperEEG contributes a novel, structure-aware lens for EEG data that complements conventional clustering and opens avenues for exploring brain-state transitions and connectivity.

Abstract

Background: Topological data analysis (TDA) has exploded as a tool for analyzing and making sense of high dimensional datasets across a variety of fields. Mapper is a tool from TDA that captures low-dimensional structure from high-dimensional data, precisely the approach needed to capture relevant information from high-dimensional neural time series. Electrical potential scalp recording, or electroencephalography (EEG), is routinely used in clinical applications and research studies thanks to its noninvasive nature, relatively inexpensive equipment, and high temporal resolution. But, it is prone to contamination, exhibits low spatial resolution, and has a non-stationary nature. Thus, it requires advanced signal processing and mathematical analysis methods for tasks requiring unsupervised brain state clustering. New Method: We introduce MapperEEG, an approach to unsupervised brain state clustering that uses tools from classical EEG analysis combined with Mapper to cluster and connect brain states. Results: We show that MapperEEG can serve as a clustering algorithm in the spectral domain and provide additional information about the underlying brain state connectivity in a tapping task. Additionally, we use a go/no-go shooting task to explore how MapperEEG can still provide insight into the underlying structure and clusters of brain states even when it and other clustering methods fail. Comparison with Existing Methods: We demonstrate that it outperforms six other clustering algorithms such as hierarchical clustering, Hidden Markov Models, and basic autoencoders on identifying states in a tapping task. Conclusions: MapperEEG offers a novel and effective approach to analyzing EEG data, showing promise for brain state clustering and analysis.

Figures (7)

• Figure 1: An example of the Mapper algorithm applied to a toy dataset. Note, the structure of the Mapper graph captures the shape of the dataset.
• Figure 2: The tappers were isolated from each other and participated in two sessions: a synchronized session where the tappers matched the beat and a syncopated session where the tappers tapped between the beat. During each session, the pairs experienced three runs of each of the four trial types: no lead, left lead, right lead, and bidirectional. No lead: both tappers tapped independently, with no feedback from the other tapper. Left lead: the left tapper was instructed to synchronize/syncopate with the metronome and then keep the beat while the right tapper was instructed to synchronize/syncopate with the leader via a visual representation of the left tapper's tap on the screen. Right lead: identical to left lead except the rolls were reversed. Bidirectional: each tapper was given visual feedback from the other tapper and the two tappers were told to synchronize/syncopate with each other's tapping.
• Figure 3: Screengrabs from the Go/No-Go Shooting task, with the left grab showing a target and the right showing no target. The low stress condition had longer target exposure time whereas the high stress condition had shorter target exposure time.
• Figure 4: The MapperEEG pipeline. First (light blue arrow), we preprocess the data using well-established methods from EEG research. Next, we apply the Mapper algorithm (yellow arrows) as described in Subsection \ref{['subsec:Mapper']}. Finally, we apply our clustering mechanism (dark purple arrow) that allows the Mapper algorithm to be used as a clustering tool. For additional information, see Section \ref{['sec:Methods']}.
• Figure 5: For illustration purposes, we show the distribution of power values for each band calculated for one subject in one channel for each of the two datasets.