Clique topology reveals intrinsic geometric structure in neural correlations.
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 2D 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 nonspatial behaviors such as wheel running and rapid eye movement (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.
Warren Center for Network and Data Science, Departments of Bioengineering and Mathematics, University of Pennsylvania, Philadelphia, PA 19104; Department of Mathematics, University of Nebraska, Lincoln, NE 68588;
Chad
C
Giusti
Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA 20147;
Eva
E
Pastalkova
Department of Mathematics, University of Nebraska, Lincoln, NE 68588; Department of Mathematics, The Pennsylvania State University, University Park, PA 16802.
Carina
C
Curto
Department of Mathematics, University of Nebraska, Lincoln, NE 68588; Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 vladimir.itskov@psu.edu.
Vladimir
V
Itskov
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006624:Hippocampus / Q000166:cytology / Q000502:physiology*; D008959:Models, Neurological; D009043:Motor Activity / Q000502:physiology*; D009434:Neural Pathways / Q000502:physiology; D009482:Neurophysiology / Q000379:methods*; D017966:Pyramidal Cells / Q000502:physiology*; D051381:Rats; D012895:Sleep, REM / Q000502:physiology*
Betti curves; clique topology; neural coding; structure of neural correlation; topological data analysis