David Boothe | Searcharxiv

arXiv2025

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

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.

math.GN↗

arXiv2022

A Topological Deep Learning Framework for Neural Spike Decoding

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells to determine orientation whereas grid cells consist of layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single head direction or grid. We want to capture this firing structure and use it to decode head direction grid cell data. Understanding, representing, and decoding these neural structures requires models that encompass higher order connectivity, more than the 1-dimensional connectivity that traditional graph-based models provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network. Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the simplicial convolutional neural network is demonstrated on head direction and trajectory prediction via head direction and grid cell datasets.

cs.NE↗