Decoding of neural data using cohomological learning

Rybakken, Erik; Baas, Nils A.; Dunn, Benjamin

doi:10.1101/222331

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…The application of persistent (co)homology to neuroscience data is still in its developing stages. Notable lines of work include: dimensionality reduction for manifold decoding in head direction cells [29,30]; simulations of hippocampal place cells in spatial environments with nontrivial topology [31,32,33,34,35];…”

Section: Discussionmentioning

confidence: 99%

Evaluating state space discovery by persistent cohomology in the spatial representation system

Kang

Xu²,

Morozov

2020

Preprint

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Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We explore the application of persistent cohomology to the brain’s spatial representation system. We simulate populations of grid cells, head direction cells, and conjunctive cells, each of which span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures and demonstrate its robustness to various forms of noise. We identify regimes under which mixtures of populations form product topologies can be detected. Our results suggest guidelines for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

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Section: Discussionmentioning

confidence: 99%

Evaluating state space discovery by persistent cohomology in the spatial representation system

Kang

Xu²,

Morozov

2020

Preprint

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“…Although a number of methods have been developed to assess the dynamics of thalamo-cortical HD signals (e.g., Rybakken et al, 2018;Viejo et al, 2018;Fresno et al, 2019), few studies have conducted a quantitative comparison of neural decoding. Statistical model-based approaches have generally been favored with respect to studying population activity of the HD cell system, however recent advances have stimulated new interest in using machine learning approaches for neural decoding.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Neural Decoding Methods and Population Coding Across Thalamo-Cortical Head Direction Cells

Winter

et al. 2019

Front. Neural Circuits

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Head direction (HD) cells, which fire action potentials whenever an animal points its head in a particular direction, are thought to subserve the animal's sense of spatial orientation. HD cells are found prominently in several thalamo-cortical regions including anterior thalamic nuclei, postsubiculum, medial entorhinal cortex, parasubiculum, and the parietal cortex. While a number of methods in neural decoding have been developed to assess the dynamics of spatial signals within thalamo-cortical regions, studies conducting a quantitative comparison of machine learning and statistical model-based decoding methods on HD cell activity are currently lacking. Here, we compare statistical model-based and machine learning approaches by assessing decoding accuracy and evaluate variables that contribute to population coding across thalamo-cortical HD cells.

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“…Is the system time varying with either unweighted (Botnan & Lesnick, 2016; Carlsson & De Silva, 2010) or weighted edges (Cohen-Steiner, Edelsbrunner, & Morozov, 2006; Munch, 2013; Yoo, Kim, Ahn, & Ye, 2016)? Would one perhaps wish to obtain circular coordinates for the data (De Silva, Morozov, & Vejdemo-Johansson, 2011; Rybakken, Baas, & Dunn, 2017)? Would equivalence classes of paths instead of cycles be useful (Chowdhury & Mémoli, 2018)?…”

Section: Resultsmentioning

confidence: 99%

The importance of the whole: Topological data analysis for the network neuroscientist

Sizemore

Phillips-Cremins

Ghrist

et al. 2019

Network Neuroscience

175

139

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Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems.

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Decoding of neural data using cohomological learning

Cited by 6 publications

References 27 publications

Evaluating state space discovery by persistent cohomology in the spatial representation system

Evaluating state space discovery by persistent cohomology in the spatial representation system

A Comparison of Neural Decoding Methods and Population Coding Across Thalamo-Cortical Head Direction Cells

The importance of the whole: Topological data analysis for the network neuroscientist

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