Clique topology reveals intrinsic geometric structure in neural correlations

TL;DR

Clique topology is a new method for analyzing neural correlation data that detects intrinsic geometric structures invariant under nonlinear transformations, revealing underlying circuit organization beyond position coding.

Contribution

The paper introduces clique topology, a novel matrix analysis technique that identifies geometric structures in neural data regardless of nonlinear monotone transformations.

Findings

Detected geometric organization in hippocampal neurons during spatial and non-spatial behaviors.

Confirmed that neural correlation structures reflect underlying circuit architecture.

Method is robust to nonlinearities in the data.

Abstract

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a two-dimensional environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during non-spatial behaviors such as wheel running and REM sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits, and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.