CliqueTop is a collection of matlab scripts for doing topological analysis of symmetric matrices. The syntax for using the package is: ompute_clique_topology(A) for any symmetric matrix A. Options and details can be found in the documentation for the compute_clique_topology function. CliqueTop currently relies on the following software packages, which are included in this repository for convenience and should function automatically without installation: For persistent homology computations, we make use of Perseus by Vidit Nanda. As of this writing, the current version can be found at vnanda/perseus/index.html. We recommend using the snapshot provided in this repository, as the input/output format for Perseus may change in the future. Cliquer, for the clique splitting version of the clique enumeration algorithm, a C package by Sampo Niskanen and Patric R. J. Östergård, available at pat/cliquer.html. The code was written by Chad Giusti, and the underlying ideas are the result of joint work with Vladimir Itskov and Carina Curto. The work was supported by NSF DMS-1122519. More details can be found in Giusti, Pastalkova, Curto and Itskov, ”Clique topology reveals instrinsic geometric structure in neural correlations.” (arXiv:1502.06172 [q-bio.NC] and arXiv:1502.06173 [q-bio.NC])

References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Belton, Robin Lynne; Fasy, Brittany Terese; Mertz, Rostik; Micka, Samuel; Millman, David L.; Salinas, Daniel; Schenfisch, Anna; Schupbach, Jordan; Williams, Lucia: Reconstructing embedded graphs from persistence diagrams (2020)
  2. Bergomi, Mattia G.; Ferri, Massimo; Zuffi, Lorenzo: Topological graph persistence (2020)
  3. Bubenik, Peter; Hull, Michael; Patel, Dhruv; Whittle, Benjamin: Persistent homology detects curvature (2020)
  4. Hernández Serrano, Daniel; Sánchez Gómez, Darío: Centrality measures in simplicial complexes: applications of topological data analysis to network science (2020)
  5. Jaquette, Jonathan; Schweinhart, Benjamin: Fractal dimension estimation with persistent homology: a comparative study (2020)
  6. Naitzat, Gregory; Zhitnikov, Andrey; Lim, Lek-Heng: Topology of deep neural networks (2020)
  7. Nie, Chun-Xiao: Nonlinear correlation analysis of time series based on complex network similarity (2020)
  8. Schaub, Michael T.; Benson, Austin R.; Horn, Paul; Lippner, Gabor; Jadbabaie, Ali: Random walks on simplicial complexes and the normalized Hodge 1-Laplacian (2020)
  9. Wang, Dong; Zhao, Yi; Leng, Hui; Small, Michael: A social communication model based on simplicial complexes (2020)
  10. Ding, Li; Hu, Ping: Contagion processes on time-varying networks with homophily-driven group interactions (2019)
  11. Monod, Anthea; Kališnik, Sara; Patiño-Galindo, Juan Ángel; Crawford, Lorin: Tropical sufficient statistics for persistent homology (2019)
  12. Buchet, Mickaël; Escolar, Emerson G.: Realizations of indecomposable persistence modules of arbitrarily large dimension (2018)
  13. Chowdhury, Samir; Mémoli, Facundo: A functorial Dowker theorem and persistent homology of asymmetric networks (2018)
  14. Mulder, Daan; Bianconi, Ginestra: Network geometry and complexity (2018)
  15. Sizemore, Ann E.; Giusti, Chad; Kahn, Ari; Vettel, Jean M.; Betzel, Richard F.; Bassett, Danielle S.: Cliques and cavities in the human connectome (2018)
  16. Curto, Carina: What can topology tell us about the neural code? (2017)
  17. Curto, Carina; Gross, Elizabeth; Jeffries, Jack; Morrison, Katherine; Omar, Mohamed; Rosen, Zvi; Shiu, Anne; Youngs, Nora: What makes a neural code convex? (2017)
  18. Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir: Clique topology reveals intrinsic geometric structure in neural correlations (2015)