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Topological data analysis involves the statistical characterization of the shape of data.
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Edelsbrunner, H. and Harer, J. (2008), “Persistent Homology - a Survey,” Contemporary mathematics
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Carlsson, G. (2009), “Topology and data,” Bulletin of the American Mathematical Society
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Talabi, O., AlSayari, S., Iglauer, S., and Blunt, M. J. (2009), “Pore-scale simulation of NMR response,” Journal of Petroleum Science and Engineering
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Bourgon, R., Gentleman, R., and Huber, W. (2010), “Independent filtering increases detection power for high-throughput experiments,” Proceedings of the National Academy of Sciences
2010
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2012
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Genovese, C. R., Perone-Pacifico, M., Verdinelli, I., and Wasserman, L. (2012), “Manifold estimation and singular deconvolution under Hausdorff loss,” Annals of Statistics
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Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smola, A. (2012), “A Kernel Two-sample Test,” Journal of Machine Learning Research
2012
Cited alongside, same era.
Mason, L. J. and McDonough, M. (2012), “Biology, behavior, and ecology of stored grain and legume insects,” Stored product protection
Cang, Z. and Wei, G.-W. (2017), “TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions,” PLOS Computational Biology
2017
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Chazal, F., Fasy, B., Lecci, F., Michel, B., Rinaldo, A., Rinaldo, A., and Wasserman, L. (2017), “Robust Topological Inference: Distance to a Measure and Kernel Distance,” Journal of Machine Learning Research
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2017
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Kerber, M., Morozov, D., and Nigmetov, A. (2017), “Geometry helps to compare persistence diagrams,” Journal of Experimental Algorithmics
2017
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2012
Cited alongside, same era.
2012
Cited alongside, same era.
Chazal, F., Fasy, B. T., Lecci, F., Rinaldo, A., and Wasserman, L. (2014), “Stochastic convergence of persistence landscapes and silhouettes,” Proceedings of the thirtieth annual symposium on Computational geometry
2014
Cited alongside, same era.
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2014
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Fasy, B. T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S., and Singh, A. (2014), “Confidence sets for persistence diagrams,” Annals of Statistics
2014
Cited alongside, same era.
Marron, J. S. and Alonso, A. M. (2014), “Overview of object oriented data analysis,” Biometrical Journal
2014
Cited alongside, same era.
Bubenik, P. (2015), “Statistical Topological Data Analysis Using Persistence Landscapes,” Journal of Machine Learning Research
2015
Cited alongside, same era.
Chen, Y.-C., Wang, D., Rinaldo, A., and Wasserman, L. (2015), “Statistical Analysis of Persistence Intensity Functions,” arXiv e-prints
2015
Cited alongside, same era.
Kusano, G., Fukumizu, K., and Hiraoka, Y. (2017), “Kernel method for persistence diagrams via kernel embedding and weight factor,” The Journal of Machine Learning Research
2017
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Robinson, A. and Turner, K. (2017), “Hypothesis testing for topological data analysis,” Journal of Applied and Computational Topology
2017
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Stevens, J. R., Al Masud, A., and Suyundikov, A. (2017), “A comparison of multiple testing adjustment methods with block-correlation positively-dependent tests,” PLOS ONE
2017
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Cericola, C., Johnson, I. J., Kiers, J., Krock, M., Purdy, J., and Torrence, J. (2018), “Extending hypothesis testing with persistent homology to three or more groups,” Involve: A Journal of Mathematic
2018
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Hommel, J., Coltman, E., and Class, H. (2018), “Porosity–Permeability Relations for Evolving Pore Space: A Review with a Focus on (Bio-)geochemically Altered Porous Media,” Transport in Porous Media
2018
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Jiang, F., Tsuji, T., and Shirai, T. (2018), “Pore geometry characterization by persistent homology theory,” Water Resources Research
2018
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Kimura, M., Obayashi, I., Takeichi, Y., Murao, R., and Hiraoka, Y. (2018), “Non-empirical identification of trigger sites in heterogeneous processes using persistent homology,” Scientific reports
2018
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Obayashi, I., Hiraoka, Y., and Kimura, M. (2018), “Persistence diagrams with linear machine learning models,” Journal of Applied and Computational Topology
2018
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2018
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Herring, A. L., Robins, V., and Sheppard, A. P. (2019), “Topological persistence for relating microstructure and capillary fluid trapping in sandstones,” Water Resources Research
2019
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Kališnik, S. (2019), “Tropical coordinates on the space of persistence barcodes,” Foundations of Computational Mathematics
2019
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Kusano, G. (2019), “On the expectation of a persistence diagram by the persistence weighted kernel,” Japan Journal of Industrial and Applied Mathematics
2019
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Lawson, P., Sholl, A., Brown, J., Fasy, B. T., and Wenk, C. (2019), “Persistent homology for the quantitative evaluation of architectural features in prostate cancer histology,” Scientific Reports
2019
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Monod, A., Kalisnik, S., Patino-Galindo, J. Á., and Crawford, L. (2019), “Tropical sufficient statistics for persistent homology,” SIAM Journal on Applied Algebra and Geometry
2019
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Moon, C., Mitchell, S. A., Heath, J. E., and Andrew, M. (2019), “Statistical inference over persistent homology predicts fluid flow in porous media,” Water Resources Research
2019
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Sauerwald, N., Shen, Y., and Kingsford, C. (2019), “Topological data analysis reveals principles of chromosome structure in cellular differentiation,” in 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)
2019
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Aguilar, A. and Ensor, K. (2020), “Topology data analysis using mean persistence landscapes in financial crashes,” Journal of Mathematical Finance
2020
Closest in time.
Berry, E., Chen, Y.-C., Cisewski-Kehe, J., and Fasy, B. T. (2020), “Functional summaries of persistence diagrams,” Journal of Applied and Computational Topology
2020
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Maroulas, V., Nasrin, F., and Oballe, C. (2020), “A Bayesian framework for persistent homology,” SIAM Journal on Mathematics of Data Science
2020
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Townsend, J., Micucci, C. P., Hymel, J. H., Maroulas, V., and Vogiatzis, K. D. (2020), “Representation of molecular structures with persistent homology for machine learning applications in chemistry,” Nature Communications
2020
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2021
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Edelsbrunner, H. and Harer, J. L. (2022), Computational topology: an introduction
2022
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