Clique topology reveals intrinsic geometric structure in neural correlations

Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov

Research output: Contribution to journalArticle

52 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)13455-13460
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume112
Issue number44
DOIs
StatePublished - Nov 3 2015

Fingerprint

Pyramidal Cells
REM Sleep
Running
Hippocampus
Sleep

All Science Journal Classification (ASJC) codes

  • General

Cite this

@article{48a35ae325f24c09b2f9dd3d14e548a7,
title = "Clique topology reveals intrinsic geometric structure in neural correlations",
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.",
author = "Chad Giusti and Eva Pastalkova and Carina Curto and Vladimir Itskov",
year = "2015",
month = "11",
day = "3",
doi = "10.1073/pnas.1506407112",
language = "English (US)",
volume = "112",
pages = "13455--13460",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
number = "44",

}

Clique topology reveals intrinsic geometric structure in neural correlations. / Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 112, No. 44, 03.11.2015, p. 13455-13460.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Clique topology reveals intrinsic geometric structure in neural correlations

AU - Giusti, Chad

AU - Pastalkova, Eva

AU - Curto, Carina

AU - Itskov, Vladimir

PY - 2015/11/3

Y1 - 2015/11/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84946594591&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946594591&partnerID=8YFLogxK

U2 - 10.1073/pnas.1506407112

DO - 10.1073/pnas.1506407112

M3 - Article

C2 - 26487684

AN - SCOPUS:84946594591

VL - 112

SP - 13455

EP - 13460

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 44

ER -