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Constructing mesoscale functionomics by neural dynamics subspace clustering.

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  1. [1] § RESULTS › Principle of FRID ↔ FRID/FRID.m, the whole file · a weak match · score 0.64 · spectral cluster, neural activities, affinity matrix, quadratic, anchors, algorithm · Report a mismatch

Paper

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The authors' code

MATLAB · 48 lines · 1.1 KB · Apache-2.0 · 1 match

  1. function [U,labels,Z] = FRID(X,k,alpha,numanchor,ifnorm,nrepanch)
  3. % Input:
  4. % X: The neural activity, size of neuron number x time steps
  5. % k: number of clustering
  6. % alpha: sparisity penalty parameter
  7. % numanchor: anchor number
  8. % ifnorm: bool, if perform normalization
  9. % nrepanch: number of repetitions on finding anchor
  11. % Output:
  12. % U: The embedding of the neurons
  13. % labels: The clustering result of each neuron
  14. % Z: The affinity matrix
  16. num=size(X,1);
  18. % Normalization
  19. if ifnorm
  20. for t = 1:size(X,1)
  21. X(t,:)=X(t,:)./norm(X(t,:),'fro');
  22. end
  23. end
  24. X = double(X);
  26. % Find anchor
  27. [~, H] = litekmeans(X,numanchor,'MaxIter', 100,'Replicates',nrepanch);
  28. [numanchor,~]=size(H);
  30. % Do quadratic optization
  31. options = optimset( 'Algorithm','interior-point-convex','Display','off');
  33. A=2*alpha*eye(numanchor)+2*H*H';
  34. A=(A+A')/2;
  35. B=X';
  36. parfor ji=1:num
  37. ff=-2*B(:,ji)'*H';
  38. Z(:,ji)=quadprog(A,ff',[],[],[],[],-ones(numanchor,1),ones(numanchor,1),[],options);
  39. end
  41. % Get the affinity matrix
  42. Sbar=abs(Z);
  44. % Do spectral clustering
  45. [U,Sig,V] = mySVD(Sbar',k);
  46. labels=litekmeans(U, k, 'MaxIter', 100,'Replicates',10);

FRID.m at commit fd924f8, under Apache-2.0 · at the source

Overview

Authors: Yeyi Cai1,2, Xinhong Xu1,2, Guihua Xiao1,2,3, Huaming Ling4, Zuoqiang Shi4, Minghuan Wang5, Mingrui Wang6, Fenghua Chen2, Jiamin Wu1,2,7, Qionghai Dai1,2,7
ORCID iDs: Zuoqiang Shi, Qionghai Dai
  1. Department of Automation, Tsinghua University, Beijing 100084, China
  2. Institute for Brain and Cognitive Sciences, Tsinghua University, Beijing 100084, China
  3. Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China
  4. Department of Mathematical Science, Tsinghua University, Beijing 100084, China
  5. Department of Neurology, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430074, China
  6. Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518071, China
  7. IDG/McGovern Institute for Brain Research, Tsinghua University, Beijing 100084, China
Institutions: Tsinghua University (China); Beijing National Research Center for Information Science and Technology (China); Tongji Hospital (China); Tsinghua Shenzhen International Graduate School (China); Huazhong University of Science and Technology (China)
Journal: National science review, volume 13, issue 15, article nwag420
Dates: received 27 April 2026; accepted 2 July 2026; published online 11 July 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1093/nsr/nwag420 · PMID 42592399 · PMCID PMC13463643 · OpenAlex W7168051293
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: systems (subfield)
Methods: Machine learning, Single-unit activity, calcium imaging
Keywords: functionomics, subspace clustering, cortical dynamics
Topic: Single-cell and spatial transcriptomics (Molecular Biology, Biochemistry, Genetics and Molecular Biology), according to OpenAlex
Funding: National Natural Science Foundation of China (32400938, 62222508, 62525506, 62088102); Natural Science Foundation of Beijing Municipality (JR25021, Z240011)
Citations: not cited yet (Europe PMC); 77 references in the paper

Abstract

Building a fine-grained functional atlas of the brain is crucial for deciphering bio-intelligence. However, the intricate and non-linear interactions at single-neuron level lead to asynchronous and heterogeneous firing patterns among closely interacting neural populations, thereby challenging correlated-firing-based clustering methods. Here, we present Functional subspace clustering based on sparse Representation of Intrinsic Dynamics (FRID), an unsupervised approach for identifying neurons with shared microcircuit connectivity and information encoding properties (referred to as ‘Functionomics’) from mesoscale neural recordings. FRID significantly outperforms correlated-firing-based methods in both simulated complex networks and empirical calcium recordings. The accuracy and utility of FRID are validated across sensory integration and decision-making tasks to produce functionomic clusters with improved resolution and coding specificity than those defined by anatomical functional areas. As representative findings, we demonstrate single-cell level functional remapping during recovery from ischemic stroke and the learning-induced reorganization of functional modularization. Together with large-scale neural recordings, FRID could serve as a general data-driven paradigm to accelerate the understanding of mesoscale brain functions.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Cai-yy/FRID

License: Apache-2.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: fd924f8590d13a3832387f538c0741fd21b205b2, 18 January 2026
Languages: MATLAB (19)
Size: 25 files, 19 scripts
Software Heritage: not archived
Found in: “DATA AVAILABILITY”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Optimization Toolbox (3 files), Statistics and Machine Learning Toolbox (3 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
21 files
At the source: github.com/Cai-yy/FRID

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 19 scripts, each with its path and the digest of its content;
  • 1 match between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

A demonstration of FRID framework could be found at https://github.com/Cai-yy/FRID. Simulation datasets and GUI codes are all available at GitHub. The calcium dataset is available from the corresponding authors.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 2, 28 September 2026

  • Funding: added National Natural Science Foundation of China: 32400938, 62222508, 62525506, 62088102; Natural Science Foundation of Beijing Municipality: JR25021, Z240011

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 10 authors, 3 keywords, 72 references.

Cite

This paper

Cai, Y., Xu, X., Xiao, G., Ling, H., Shi, Z., Wang, M., Wang, M., Chen, F., Wu, J., & Dai, Q. (2026). Constructing mesoscale functionomics by neural dynamics subspace clustering. National science review, 13(15), nwag420. https://doi.org/10.1093/nsr/nwag420

BibTeX

@article{cai2026constructing,
author = {Cai, Yeyi and Xu, Xinhong and Xiao, Guihua and Ling, Huaming and Shi, Zuoqiang and Wang, Minghuan and Wang, Mingrui and Chen, Fenghua and Wu, Jiamin and Dai, Qionghai},
title = {{Constructing mesoscale functionomics by neural dynamics subspace clustering}},
journal = {National science review},
year = {2026},
month = jul,
volume = {13},
number = {15},
pages = {nwag420},
publisher = {Oxford University Press},
issn = {2095-5138},
doi = {10.1093/nsr/nwag420},
url = {https://doi.org/10.1093/nsr/nwag420},
pmid = {42592399},
pmcid = {PMC13463643}
}

RIS

TY - JOUR
AU - Cai, Yeyi
AU - Xu, Xinhong
AU - Xiao, Guihua
AU - Ling, Huaming
AU - Shi, Zuoqiang
AU - Wang, Minghuan
AU - Wang, Mingrui
AU - Chen, Fenghua
AU - Wu, Jiamin
AU - Dai, Qionghai
TI - Constructing mesoscale functionomics by neural dynamics subspace clustering
T2 - National science review
J2 - Natl Sci Rev
PY - 2026
DA - 2026/07/11
VL - 13
IS - 15
SP - nwag420
SN - 2095-5138
PB - Oxford University Press
DO - 10.1093/nsr/nwag420
UR - https://doi.org/10.1093/nsr/nwag420
LA - en
ER -

CSL-JSON

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"type": "article-journal",
"title": "Constructing mesoscale functionomics by neural dynamics subspace clustering",
"container-title": "National science review",
"author": [
{
"family": "Cai",
"given": "Yeyi"
},
{
"family": "Xu",
"given": "Xinhong"
},
{
"family": "Xiao",
"given": "Guihua"
},
{
"family": "Ling",
"given": "Huaming"
},
{
"family": "Shi",
"given": "Zuoqiang"
},
{
"family": "Wang",
"given": "Minghuan"
},
{
"family": "Wang",
"given": "Mingrui"
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{
"family": "Chen",
"given": "Fenghua"
},
{
"family": "Wu",
"given": "Jiamin"
},
{
"family": "Dai",
"given": "Qionghai"
}
],
"container-title-short": "Natl Sci Rev",
"volume": "13",
"issue": "15",
"page": "nwag420",
"DOI": "10.1093/nsr/nwag420",
"PMID": "42592399",
"PMCID": "PMC13463643",
"ISSN": "2095-5138",
"publisher": "Oxford University Press",
"URL": "https://doi.org/10.1093/nsr/nwag420",
"language": "en",
"issued": {
"date-parts": [
[
2026,
7,
11
]
]
}
}

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