期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 112, 期 44, 页码 13455-13460出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1506407112
关键词
structure of neural correlation; neural coding; Betti curves; clique topology; topological data analysis
资金
- National Science Foundation [DMS 1122519, DMS 1225666/1537228]
- Sloan Research Fellowship
- Defense Advanced Research Projects Agency Young Faculty Award [W911NF-15-1-0084]
- Howard Hughes Medical Institute
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1122519, 1537228] Funding Source: National Science Foundation
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 non-linear 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.
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