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Edited by William Bialek, Princeton University, Princeton, NJ, and approved September 23, 2015 (received for review April 28, 2015)
Significance
Detecting structure in neural activity is critical for understanding the function of neural circuits. The coding properties of neurons are typically investigated by correlating their responses to external stimuli. It is not clear, however, if the structure of neural activity can be inferred intrinsically, without a priori knowledge of the relevant stimuli. We introduce a novel method, called clique topology, that detects intrinsic structure in neural activity that is invariant under nonlinear monotone transformations. Using pairwise correlations of neurons in the hippocampus, we demonstrate that our method is capable of detecting geometric structure from neural activity alone, without appealing to external stimuli or receptive fields.
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 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.
Footnotes
↵1C.C. and V.I. contributed equally to this work.
- ↵2To whom correspondence should be addressed. Email: vladimir.itskov{at}psu.edu.
Author contributions: C.G., C.C., and V.I. designed research; C.G., E.P., C.C., and V.I. performed research; C.G., C.C., and V.I. analyzed data; and C.G., C.C., and V.I. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1506407112/-/DCSupplemental.
Freely available online through the PNAS open access option.
Clique topology of neural correlations
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