Detecting Functional States of the Rat Brain with Topological Data Analysis
One of the cutting-edge methods for analyzing large sets of data involves looking at their “shape”, namely their geometry and topology. In this paper, we apply topological analysis to data arising from a neuroscience experiment involving multichannel voltage measurements of brain activity in awake rats. Data points are viewed as a point cloud, with distance defined using channel correlations or a Euclidean metric. Exploratory data analysis reveals that the topological structure defined in terms of a Euclidean metric can distinguish between a coherent oscillatory brain state and the desynchronized awake state, by associating different Betti numbers to the different brain states.
KeywordsTopological data analysis mu rhythm alpha rhythm Rat brain Persistent homology Betti numbers Local field potentials Spike-and-wave
The authors would like to thank the Wellesley College Science Center Summer Research Program and the Brachman-Hoffman Fellowship. Ismar Volić would also like to thank the Simons Foundation for its support. Michael Wiest’s work was supported by National Science Foundation Integrative Organismal Systems grants 1121689 and 1353571.
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