No Holes Barred: Using Topological Data Analysis Approaches to Understand the Link Between Neural Population Activity and Behavior

Standard approaches to studying neural data typically rely on making an underlying linear assumption about the data. This approach is useful for its simplicity and the fact that it does not require huge amounts of data to test hypotheses. However, several works have demonstrated that linear methods miss much of the complexity of neuronal population activity. Our preliminary work demonstrates that some of this complexity is important: it strongly related to behavior and can constrain models of the underlying neuronal mechanisms. Because of this observation, we focus on nonlinear approaches to understanding neural data and creating models. We continue the interdisciplinary spirit of successful attempts to quantify and model the brain by drawing on fields including algebraic topology, network control theory, and data science.