Topological Data Analysis with Spike Train Metrics
Geometry of spiking patterns in early visual cortex: a
Topological Data Analytic approach
Andrea Guidolin, Mathieu Desroches, Jonathan D. Victor, Keith P. Purpura, and Serafim Rodgrigues
Journal of the Royal Society Interface 19: 20220677 (2022)
Abstract
In the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining
the intrinsic structure of this space presents a theoretical and experimental challenge.
To address this challenge, we introduce a new framework for applying topological data analysis
(TDA) to spike train data and use it to determine the geometry of spiking patterns in the visual
cortex. Key to our approach is a parameterized family of distances based on the timing of
spikes that quantities the dissimilarity between neuronal responses. We applied TDA to visually
driven single-unit and multiple single-unit spiking activity in macaque V1 and V2. TDA across
timescales reveals a common geometry for spiking patterns in V1 and V2 which, among simple
models, is most similar to that of a low-dimensional space endowed with Euclidean or hyperbolic
geometry with modest curvature. Remarkably, the inferred geometry depends on timescale, and
is clearest for the timescales that are important for encoding contrast, orientation, and spatial
correlations.
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