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Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
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We present a computational method for extracting simple descriptions of high dimensional data sets in the form of simplicial complexes. Our method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data. The proposed method is not dependent on any particular clustering algorithm, i.e. any clustering algorithm may be used with Mapper. We implement this method and present a few sample applications in which simple descriptions of the data present important information about its structure.
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Density Estimation for Statistics and Data Analysis
Silverman, B. W. (2018) · Routledge eBooks · doi:10.1201/9781315140919 · Cited by 15,938
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Algorithms for Clustering Data
Sarle, W. S., Jain, A. K., & Dubes, R. C. (1990) · Technometrics · doi:10.2307/1268876 · Cited by 7,893
(2001) · Cited by 5,374
Hierarchical Clustering Schemes
Johnson, S. C. (1967) · Psychometrika · doi:10.1007/bf02289588 · Cited by 4,948
Rusch, D. B., Halpern, A. L., Sutton, G. G., Heidelberg, K. B., Williamson, S. J., Yooseph, S., Wu, D., Eisen, J. A., Hoffman, J., Remington, K., et al. (2007) · PLoS Biology · doi:10.1371/journal.pbio.0050077 · Cited by 2,044
The Sorcerer II Global Ocean Sampling Expedition: Expanding the Universe of Protein Families
Yooseph, S., Sutton, G., Rusch, D. B., Halpern, A. L., Williamson, S. J., Remington, K., Eisen, J. A., Heidelberg, K. B., Manning, G., Li, W., et al. (2007) · PLoS Biology · doi:10.1371/journal.pbio.0050016 · Cited by 925
Becker, O. M., & Karplus, M. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473299 · Cited by 808
Lafon, S., & Lee, A. B. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.184 · Cited by 620
Cited by
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Novak, T. P., & Hoffman, D. L. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3278045 · Cited by 1
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Zhang, Y., Liu, H., Rosen, P., & Hajij, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.09639 · Cited by 1
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Rosen, P., Hajij, M., Tu, J., Arafin, T., & Piegl, L. A. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1807.02921 · Cited by 1
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Hajij, M., & Istvan, K. (2020) · arXiv (Cornell University) · Cited by 1
Steinhaus Filtration and Stable Paths in the MapperPreprint
Arendt, D., Broussard, M., Krishnamoorthy, B., Saul, N., & Thrall, A. (2019) · arXiv (Cornell University) · doi:10.4230/lipics.socg.2025.10 · Cited by 1
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Bello, H. J., Palomar-Ciria, N., Baca‐García, E., & Lozano, C. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.03727 · Cited by 1
TDA parameters in time series analysis
Fraser, B. A. (2017) · TSpace (University of Toronto) · Cited by 1
Quah, S. K. L., Pirzada, S., Madsen, S., Jo, B., Uddin, L. Q., Mumford, J. A., Barch, D. M., Gotlib, I. H., Fair, D. A., Poldrack, R. A., et al. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.10.13.682124 · Cited by 2
Topological Data Analysis of Properties of Four-Regular Rigid Vertex Graphs
Conine, G. M. (2014) · Digital Commons - University of South Florida (University of South Florida)
Exploring data with topological tools
Žitnik, M. (2014) · XRDS Crossroads The ACM Magazine for Students · doi:10.1145/2627814
Maretty, L., Sibbesen, J. A., & Krogh, A. (2014)
Cohomology operations on random spaces
Zabka, M. (2016) · Human Biology
Fréchet Distance-Based Map Construction Algorithm
Ahmed, M., Καραγιώργου, Σ., Pfoser, D., & Wenk, C. (2015) · Springer eBooks · doi:10.1007/978-3-319-25166-0_3
Topological Methods for Data Fusion
Carlsson, G. (2014) · doi:10.21236/ada608839
Self-citationDoyle, J. (2017) · FIU - Digital Commons (Florida International University) · doi:10.25148/etd.fidc001978
Predicting Materials’ Properties by Using Machine Learning
Hyon, Y. (2018) · Physics and High Technology · doi:10.3938/phit.27.001
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Liao, T., Wei, Y., Luo, M., Zhao, G., & Zhou, H. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/396960
The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs
Gasparovic, E., Gommel, M., Purvine, E., Sazdanović, R., Wang, B., Wang, Y., & Ziegelmeier, L. (2018) · Journal of computational geometry · doi:10.20382/jocg.v10i1a16
Satterfield, D. J., Rohde, J. A., Rodriguez, M., Ma, B., Doyle, J., Godwin, A., Potvin, G., Benson, L., & Kirn, A. N. (2020) · ASEE Annual Conference & Exposition · doi:10.18260/1-2--30099
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Charlier, J., Petit, F., Ormazábal, G., State, R., & Hilger, J. (2019) · arXiv (Cornell University)
Topologia computacional para análise de série temporal
Miranda, V. L. D. (2019) · doi:10.11606/d.59.2019.tde-13052019-175021
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Alcaide, D., & Aerts, J. A. (2019) · Lirias (KU Leuven) · doi:10.48550/arxiv.1907.05783
Jones, L., Tynes, M., & Smith, P. (2019) · Acta Crystallographica Section D Structural Biology · doi:10.1107/s2059798319008933
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Ellis, G. J. (2019) · doi:10.1093/oso/9780198832973.003.0006
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Ellis, G. J. (2019) · doi:10.1093/oso/9780198832973.003.0003
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Charlier, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.11573
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Dłotko, P., Rudkin, S., & Qiu, W. (2019) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1911.10476
Ellis, G. J. (2019) · doi:10.1093/oso/9780198832973.003.0004
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Siegrist, K. W., Chagdes, J. R., & Kramer, R. M. (2019) · doi:10.1115/detc2019-98014
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Lazovskis, J. (2021) · Order · doi:10.1007/s11083-021-09568-1
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Mike, J. L., & Perea, J. A. (2019) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2019.00183
Qiu, W., Rudkin, S., & Dłotko, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2004.10318
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Elkin, Y., Liu, D., & Kurlin, V. A. (2021) · Mathematics and visualization · doi:10.1007/978-3-030-83500-2_13
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Jhun, B. (2020) · arXiv (Cornell University)
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Cornell, F. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.03383
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Talukder, A. K. M. K. A., & Deb, K. (2020) · IEEE Symposium Series on Computational Intelligence (SSCI) · doi:10.1109/ssci47803.2020.9308439
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Kamruzzaman, M., Bielskas, M., Krishnamoorthy, B., Marathe, A., Vullikanti, A. K. S., & Kalyanaraman, A. (2021) · Research Square · doi:10.21203/rs.3.rs-470082/v1
Instability of Mapper Type Algorithms for Topological Data Analysis
Wentland, D. (2020)
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Guo, M. (2020) · International Conference on Big Data and Social Sciences (ICBDSS) · doi:10.1109/icbdss51270.2020.00011
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Bednar, A. E. (2021) · doi:10.21079/11681/40943
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Hu, W. P., Chen, J., Sun, C., Tong, X., Luo, W., Ju, Z., Xia, Y., Pei, Z., Xu, M., Xu, X., et al. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3738690
Cawi, E. (2021) · Open Scholarship Institutional Repository (Washington University in St. Louis) · doi:10.7936/k9g6-ps83
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Roy, S. (2019) · Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature · doi:10.3410/f.735362260.793560954
Ellis, G. J. (2019) · doi:10.1093/oso/9780198832973.003.0002
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O'Malley, M. (2022) · doi:10.14418/wes01.3.137
Forés-Martos, J., Suay‐García, B., Bosch-Romeu, R., Sanfeliu-Alonso, M. C., Falcó, A., & Climent, J. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.09.08.507080
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Magnitude, alpha magnitude, and applications.
O'Malley, M. (2023) · doi:10.14418/wes01.3.150
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Heylen, D., Peeters, J., Aerts, J. A., Ertaylan, G., & Hooyberghs, J. (2023) · PLoS ONE · doi:10.1371/journal.pone.0295361
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Macarasig, R. J., Soria, G., Aycardo, J. E., Garcia, A., Nable, J. A., & Go, C. K. (2024) · AIP conference proceedings · doi:10.1063/5.0192149
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Feng, P., Qu, Q., Zhang, H., Yi, S., Yu, Z., Ding, Z., & Zhu, Y. (2026) · Nature Communications · doi:10.21203/rs.3.rs-3978261/v1
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Dłotko, P. (2024) · European Mathematical Society Magazine · doi:10.4171/mag/190
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Ortigossa, E. S. (2024) · Digital Library of Theses and Dissertations (Universidade de São Paulo) · doi:10.11606/t.55.2024.tde-11072024-171752
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Vicuna, M. R. (2024) · doi:10.22215/etd/2024-16106
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Jurek, A., Gault, R., Ahmaderaghi, B., Fahim, M., & Bai, L. (2024) · World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany · doi:10.1007/978-3-031-62502-2_65
Vannoni, S., Tassi, E., Sampaio, I. W., & Maggioni, E. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-73967-5_8
Raith, F., Scheuermann, G., & Heine, C. (2024) · doi:10.1109/topoinvis64104.2024.00007
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Isufi, E., Leus, G. J. T., Beferull‐Lozano, B., Barbarossa, S., & Lorenzo, P. D. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.5043391
Gäfvert, O., Grindrod, P., Harrington, H. A., Higham, C. F., Higham, D. J., & Yim, K. M. (2025) · Engineering Computations · doi:10.1108/ec-06-2024-0508
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Ser, J. D., Martínez-Seras, A., Laña, I., Bilbao, M. N., Fafoutellis, P., & Vlahogianni, E. I. (2024) · IEEE International Conference on Intelligent Transportation Systems (ITSC) · doi:10.1109/itsc58415.2024.10920176
Singh, Y., Hathaway, Q. A., Dinakar, K., Shaw, L. J., Erickson, B. J., López-Jiménez, F. A., & Bhatt, D. L. (2025) · Mayo Clinic Proceedings Digital Health · doi:10.1016/j.mcpdig.2025.100217
Metadata
- Authors
- Singh, G., Memoli, F., & Carlsson, G.
- ORCID
- Carlsson, Gunnar
- Venue
- The Eurographics Association
- Publisher
- The Eurographics Association
- Published
- 2007
- OpenAlex
- W1607787316
- Cited by
- 514
- References
- 18
- Citations by year
- 2026: 9 · 2025: 33 · 2024: 33 · 2023: 37 · 2022: 39 · 2021: 54 · 2020: 73 · 2019: 74 · 2018: 44 · 2017: 29 · 2016: 26 · 2015: 16 · 2014: 18 · 2013: 5 · 2012: 6
- FWCI
- 5.06
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Eurographics
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Keywords
- Mapper algorithm, simplicial complexes, topological data analysis, high-dimensional data, 3D object recognition
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