@Manual{R-TDA,
  title = {TDA: Statistical Tools for Topological Data Analysis},
  author = {Brittany T. Fasy and Jisu Kim and Fabrizio Lecci and Clement Maria and David L. Millman and Vincent Rouvreau.},
  year = {2021},
  note = {R package version 1.7.7},
  url = {https://CRAN.R-project.org/package=TDA},
}

@Article{R-kernlab,
    title = {kernlab -- An {S4} Package for Kernel Methods in {R}},
    author = {Alexandros Karatzoglou and Alex Smola and Kurt Hornik and Achim Zeileis},
    journal = {Journal of Statistical Software},
    year = {2004},
    volume = {11},
    number = {9},
    pages = {1--20},
    url = {https://www.jstatsoft.org/v11/i09/},
}

@Manual{TDAvec,
    title = {TDAvec: Vector Summaries of Persistence Diagrams},
    author = {Umar Islambekov and Alexey Luchinsky},
    year = {2022},
    note = {R package version 0.1.1},
    url = {https://CRAN.R-project.org/package=TDAvec},
}

@Manual{TDAkit,
    title = {TDAkit: Toolkit for Topological Data Analysis},
    author = {Kisung You and Byeongsu Yu},
    year = {2021},
    note = {R package version 0.1.2},
    url = {https://CRAN.R-project.org/package=TDAkit},
}

@Article{R-clue,
    title = {A {CLUE} for {CLUster Ensembles}},
    author = {Kurt Hornik},
    year = {2005},
    journal = {Journal of Statistical Software},
    volume = {14},
    number = {12},
    month = {September},
    doi = {10.18637/jss.v014.i12},
}

@Manual{R-stats,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2021},
    url = {https://www.R-project.org/},
}

@article{PD_means,
author = {Turner, Katharine},
year = {2013},
month = {07},
journal = {arXiv},
title = {Means and medians of sets of persistence diagrams}
}

@article{PD_distributions,
	Author = {Turner, Katharine and Mileyko, Yuriy and Mukherjee, Sayan and Harer, John},
	Journal = {Discrete \& Computational Geometry},
	Number = {1},
	Pages = {44--70},
	Title = {Frechet Means for Distributions of Persistence Diagrams},
	Volume = {52},
	Year = {2014}
}

@Manual{R-TDAstats,
  title = {TDAstats: Pipeline for Topological Data Analysis},
  author = {Raoul Wadhwa and Andrew Dhawan and Drew Williamson and Jacob Scott},
  year = {2019},
  note = {R package version 0.4.1},
  url = {https://github.com/rrrlw/TDAstats},
}

@Manual{Dionysus,
  title = {Dionysus is a C++ library for computing persistent homology},
  author = {Dimitriy Morozov},
  year = {2017},
  url = {https://mrzv.org/software/dionysus2/}
}

@Manual{GUDHI,
  title = {The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding},
  author = {Theo Lacombe and Hind Montassif and Manuel Soriano-Trigueros and Gard Spreeman and Masatoshi Takenouchi},
  year = {2019},
  url = {https://gudhi.inria.fr/}
}

@Manual{PHAT,
  title = {Persistent homology algorithm toolbox},
  author = {Ulrich Bauer and Michael Kerber and Jan Reininghaus},
  year = {2013},
  url = {https://www.sciencedirect.com/science/article/pii/S0747717116300098}
}

@Manual{Ripser,
  title = {Persistent homology algorithm toolbox},
  author = {Ulrich Bauer},
  year = {2015},
  url = {https://github.com/Ripser/ripser}
}

@misc{scikittda2019,
    author       = {Nathaniel Saul and Chris Tralie},
    title        = {Scikit-TDA: Topological Data Analysis for Python},
    year         = 2019,
    doi          = {10.5281/zenodo.2533369},
    url          = {https://doi.org/10.5281/zenodo.2533369}
}

@misc{tauzin2020giottotda,
      title={giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration},
      author={Guillaume Tauzin and Umberto Lupo and Lewis Tunstall and Julian Burella Pérez and Matteo Caorsi and Anibal Medina-Mardones and Alberto Dassatti and Kathryn Hess},
      year={2020},
      eprint={2004.02551},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@Article{TDAstats2018,
  title = {TDAstats: R pipeline for computing persistent homology in topological data analysis},
  author = {Raoul R. Wadhwa and Drew F. K. Williamson and Andrew Dhawan and Jacob G. Scott},
  journal = {Journal of Open Source Software},
  year = {2018},
  volume = {3},
  number = {28},
  pages = {860},
  url = {https://doi.org/10.21105/joss.00860},
  doi = {10.21105/joss.00860},
}

@article{PHoriginal,
  title={Topological Persistence and Simplification},
  author={Herbert Edelsbrunner and David Letscher and Afra Zomorodian},
  journal={Discrete \& Computational Geometry},
  year={2000},
  volume={28},
  pages={511-533}
}

@article{ComputingPH,
author = {Zomorodian, Afra and Carlsson, Gunnar},
year = {2005},
month = {02},
pages = {249-274},
title = {Computing Persistent Homology},
volume = {33},
journal = {Discrete and Computational Geometry},
doi = {10.1007/s00454-004-1146-y}
}

@article{review_of_PH_for_fMRI,
title = {From mathematics to medicine: A practical primer on topological data analysis (TDA) and the development of related analytic tools for the functional discovery of latent structure in fMRI data},
journal = {PLoS ONE},
volume = {16},
number = {8},
year = {2021},
author = {A. Salch et al}
}

@ARTICLE{PHeconomics,
  
AUTHOR={Yen, Peter Tsung-Wen and Cheong, Siew Ann},   
	 
TITLE={Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan},      
	
JOURNAL={Frontiers in Physics},      
	
VOLUME={9},      
	
YEAR={2021},      
	  
URL={https://www.frontiersin.org/article/10.3389/fphy.2021.572216},       
	
DOI={10.3389/fphy.2021.572216},      
	
ISSN={2296-424X}
}

@Article{Robinson_Turner,
author = {Robinson, Andrew and Turner, Katharine},
year = {2017},
title = {Hypothesis testing for topological data analysis},
journal = {Journal of Applied and Computational Topology},
volume = {1},
issue = {2}
}

@inproceedings{persistence_fisher,
 author = {Le, Tam and Yamada, Makoto},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams},
 url = {https://proceedings.neurips.cc/paper/2018/file/959ab9a0695c467e7caf75431a872e5c-Paper.pdf},
 volume = {31},
 year = {2018}
}

@article{kernel_TDA,
  author  = {Genki Kusano and Kenji Fukumizu and Yasuaki Hiraoka},
  title   = {Kernel Method for Persistence Diagrams via Kernel Embedding and Weight Factor},
  journal = {Journal of Machine Learning Research},
  year    = {2018},
  volume  = {18},
  number  = {189},
  pages   = {1-41},
  url     = {https://jmlr.org/papers/v18/17-317.html}
}

@InProceedings{sliced_wasserstein,
  title = 	 {Sliced {W}asserstein Kernel for Persistence Diagrams},
  author =       {Mathieu Carri{\`e}re and Marco Cuturi and Steve Oudot},
  booktitle = 	 {Proceedings of the 34th International Conference on Machine Learning},
  pages = 	 {664--673},
  year = 	 {2017},
  editor = 	 {Precup, Doina and Teh, Yee Whye},
  volume = 	 {70},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {06--11 Aug},
  publisher =    {PMLR}
}

@article{kernel_TDA_original,
author = {Reininghaus, Jan and Huber, Stefan and Bauer, Ulrich and Kwitt, Roland},
year = {2014},
month = {12},
title = {A Stable Multi-Scale Kernel for Topological Machine Learning}
}

@InProceedings{topological_time_and_space,
author="Anderson, Keri L.
and Anderson, Jeffrey S.
and Palande, Sourabh
and Wang, Bei",
editor="Wu, Guorong
and Rekik, Islem
and Schirmer, Markus D.
and Chung, Ai Wern
and Munsell, Brent",
title="Topological Data Analysis of Functional MRI Connectivity in Time and Space Domains",
booktitle="Connectomics in NeuroImaging",
year="2018",
publisher="Springer International Publishing",
address="Cham",
pages="67--77"
}

@article {BrainOrganizationMapperNew,
	Title = {Uncovering Dynamic Brain Reconfiguration in MEG Working Memory n-Back Task Using Topological Data Analysis},
	Author = {Duman, Ali Nabi and Tatar, Ahmet Emin and Pirim, Harun},
	DOI = {10.3390/brainsci9060144},
	Number = {6},
	Volume = {9},
	Month = {June},
	Year = {2019},
	Journal = {Brain sciences},
	ISSN = {2076-3425},
	URL = {https://europepmc.org/articles/PMC6628086},
}

@article {TDA_ADHD,
author = {Gracia-Tabuenca, Zeus and D{\'\i}az-Pati{\~n}o, Juan Carlos and Arelio, Isaac and Alcauter, Sarael},
title = {Topological Data Analysis reveals robust alterations in the whole-brain and frontal lobe functional connectomes in Attention-Deficit/Hyperactivity Disorder},
elocation-id = {751008},
year = {2020},
journal = {eneuro}
}

@article{importance_of_the_whole,
    author = {Sizemore, Ann E. and Phillips-Cremins, Jennifer E. and Ghrist, Robert and Bassett, Danielle S.},
    title = "{The importance of the whole: Topological data analysis for the network neuroscientist}",
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    volume = {3},
    number = {3},
    pages = {656-673},
    year = {2019},
    month = {07},
    issn = {2472-1751},
    doi = {10.1162/netn_a_00073},
    url = {https://doi.org/10.1162/netn\_a\_00073},
    eprint = {https://direct.mit.edu/netn/article-pdf/3/3/656/1092395/netn\_a\_00073.pdf},
}

@article{PHpatches,
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}

@inproceedings{TDA_Alzheimers,
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month = {09},
pages = {297-304},
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volume = {17},
isbn = {978-3-319-10442-3},
doi = {10.1007/978-3-319-10443-0_38}
}

@article{rs_networks,
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year = {2011},
month = {06},
pages = {1125-65},
title = {The organization of the human cerebral cortex estimated by functional correlation},
volume = {106},
journal = {Journal of neurophysiology},
doi = {10.1152/jn.00338.2011}
}

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year = {2008},
month = {02},
pages = {4},
title = {Representational Similarity Analysis – Connecting the Branches of Systems Neuroscience},
volume = {2},
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}

@article{TDA_intro,
author = {Chazal, Frédéric and Michel, Bertrand},
year = {2017},
month = {10},
pages = {},
title = {An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists},
volume = {4},
journal = {Frontiers in Artificial Intelligence},
doi = {10.3389/frai.2021.667963}
}

@article{TDA_chemistry,
author = {Krishnapriyan, Aditi S. et al},
year = {2021},
month = {4},
pages = {},
title = {Machine learning with persistent homology and chemical word embeddings improves prediction accuracy and interpretability in metal-organic frameworks},
volume = {11},
journal = {Nature Scientific Report}
}

@inproceedings{word_embeddings,
    title = "Unsupervised Geometric and Topological Approaches for Cross-Lingual Sentence Representation and Comparison",
    author = "Haim Meirom, Shaked  and
      Bobrowski, Omer",
    booktitle = "Proceedings of the 7th Workshop on Representation Learning for NLP",
    month = may,
    year = "2022",
    address = "Dublin, Ireland",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2022.repl4nlp-1.18",
    doi = "10.18653/v1/2022.repl4nlp-1.18",
    pages = "173--183"
}

@article{statistics_on_landscapes, 
author = {Bubenik, Peter}, 
title = {Statistical Topological Data Analysis Using Persistence Landscapes}, 
year = {2015}, 
issue_date = {January 2015}, 
publisher = {JMLR.org}, 
volume = {16}, 
number = {1}, 
issn = {1532-4435}, 
journal = {J. Mach. Learn. Res.}, 
month = jan, 
pages = {77–102}, 
numpages = {26} 
}

@article{landscapes_toolbox,
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year = {2017},
note = {Algorithms and Software for Computational Topology},
issn = {0747-7171},
doi = {https://doi.org/10.1016/j.jsc.2016.03.009},
author = {Peter Bubenik and Pawel Dlotko}
}

@inproceedings{mapper,
  title={Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition},
  author={Gurjeet Singh and Facundo M{\'e}moli and Gunnar E. Carlsson},
  booktitle={SPBG},
  year={2007}
}

@INPROCEEDINGS{persistent_hom_brain_networks,
author={Lee, Hyekyoung and Chung, Moo K. and Kang, Hyejin and Kim, Bung-Nyun and Lee, Dong Soo},
booktitle={2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro}, 
title={Discriminative persistent homology of brain networks},
year={2011},
pages={841-844},
doi={10.1109/ISBI.2011.5872535}
}

@article{functional_fingerprinting,
author = {Finn, Emily and Shen, Xilin and Scheinost, Dustin and Rosenberg, Monica and Jessica, Huang and Chun, Marvin and Papademetris, Xenophon and Constable, Robert},
year = {2015},
month = {10},
pages = {},
title = {Functional connectome fingerprinting: Identifying individuals using patterns of brain connectivity},
volume = {18},
journal = {Nature neuroscience},
doi = {10.1038/nn.4135}
}

@article{Denoising,
title = "Methods for cleaning the BOLD fMRI signal",
journal = "NeuroImage",
volume = "154",
pages = "128 - 149",
year = "2017",
issn = "1053-8119",
doi = "https://doi.org/10.1016/j.neuroimage.2016.12.018",
url = "http://www.sciencedirect.com/science/article/pii/S1053811916307418",
author = "César Caballero-Gaudes and Richard C. Reynolds"
}

@Article{distance_calc,
author = {Kerber, Michael and Morozov, Dmitriy and Nigmetov, Arnur},
title = {Geometry Helps to Compare Persistence Diagrams},
year = {2017},
issue_date = {2017},
journal = {ACM journal of Experimental Algorithmics},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {22},
issn = {1084-6654},
url = {https://doi.org/10.1145/3064175},
doi = {10.1145/3064175},
month = {sep},
numpages = {20}
}

@Inbook{Cox2008,
author={Cox, Michael A. A.
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bookTitle={Handbook of Data Visualization},
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}

@Article{dependencies,
author = {Abdallah, Hassan et al.},
journal = {Github},
url = {https://github.com/hassan-abdallah/Statistical_Inference_PH_fMRI/blob/main/Abdallah_et_al_Statistical_Inference_PH_fMRI.pdf},
year = {2021}
}

@inproceedings{kernel_test,
author = {Gretton, Arthur and Fukumizu, Kenji and Teo, Choon and Song, Le and Sch\"{o}lkopf, Bernhard and Smola, Alex},
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editor = {J. Platt and D. Koller and Y. Singer and S. Roweis},
pages = {},
publisher = {Curran Associates, Inc.},
title = {A Kernel Statistical Test of Independence},
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}

@inproceedings{kkmeans,
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@ARTICLE{kpca,
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@Manual{R-reticulate,
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}

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}

@article{PH_benchmarking,
  author = {Somasundaram, Eashwar V. and Brown, Shael E. and Litzler, Adam and Scott, Jacob G. and Wadhwa, Raoul R.},
  title = {The R Journal: Benchmarking R packages for Calculation of Persistent Homology},
  journal = {{The R Journal}},
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  note = {https://doi.org/10.32614/RJ-2021-033},
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  volume = {13},
  issue = {1},
  issn = {2073-4859},
  pages = {184-193}
}

@article{PChom,
author = {de Silva, V., Morozov, D., and Vejdemo-Johansson, M.},
title = {Persistent Cohomology and Circular Coordinates},
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volume = {45},
year = {2011},
pages = {737-759}
}

@article{PHom_dualities,
author = {de Silva, V., Morozov, D., and Vejdemo-Johansson, M.},
title = {Dualities in persistent (co)homology},
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issue = {12},
year = {2011}
}

@article{bootstrap,
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month = {03},
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}

@article{HCP,
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@article{topological_feasibility,
author = {Ellis, Cameron and Lesnick, Michael and Henselman, Greg and Keller, Bryn and Cohen, Jonathan},
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title = {Feasibility of topological data analysis for event-related fMRI},
volume = {3},
journal = {Network Neuroscience},
doi = {10.1162/netn_a_00095}
}

@ARTICLE{cohomology_feasability,
  
AUTHOR={Kang, Louis and Xu, Boyan and Morozov, Dmitriy},   
	 
TITLE={Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System},      
	
JOURNAL={Frontiers in Computational Neuroscience},      
	
VOLUME={15},           
	
YEAR={2021},      
	  
URL={https://www.frontiersin.org/articles/10.3389/fncom.2021.616748},       
	
DOI={10.3389/fncom.2021.616748},      
	
ISSN={1662-5188}
}

@book{PON,
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  lccn={2012023071},
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  publisher={McGraw-Hill Education}
}

@article{twos_company,
author = {Giusti, Chad and Ghrist, Robert and Bassett, Danielle},
year = {2016},
month = {01},
pages = {},
title = {Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data},
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journal = {Journal of Computational Neuroscience},
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@article{BrainOrganizationMapper,
  title={Towards a new approach to reveal dynamical organization of the brain using topological data analysis},
  author={Manish Saggar and Olaf Sporns and Javier Gonzalez-Castillo and Peter A. Bandettini and Gunnar E. Carlsson and Gary H. Glover and Allan L. Reiss},
  journal={Nature Communications},
  year={2018},
  volume={9}
}