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bib.bib
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@misc{Carlsson2010,
title = {Classifying Clustering Schemes},
author = {Gunnar Carlsson and Facundo Memoli},
year = {2010},
eprint = {1011.5270},
archiveprefix = {arXiv},
primaryclass = {stat.ML}
}
@book{Roman2017,
title = {An introduction to the language of category theory},
author = {Roman, Steven},
publisher = {Birkhauser},
series = {Compact Textbooks in Mathematics},
edition = 1,
month = jan,
year = 2017,
address = {Basel, Switzerland},
language = {en}
}
@inproceedings{Kleinberg2002,
author = {Kleinberg, Jon},
booktitle = {Advances in Neural Information Processing Systems},
editor = {Suzanna Becker and Sebastian Thrun and Klaus Obermayer},
pages = {},
publisher = {MIT Press},
title = {An Impossibility Theorem for Clustering},
url = {https://proceedings.neurips.cc/paper_files/paper/2002/file/43e4e6a6f341e00671e123714de019a8-Paper.pdf},
volume = {15},
year = {2002}
}
@book{Jain1988-en,
title = {Algorithms for Clustering Data},
author = {Jain, Anil K and Dubes, Richard C},
publisher = {Prentice Hall},
series = {Prentice Hall advanced reference series},
month = jan,
year = 1988,
address = {Old Tappan, NJ},
language = {en}
}
@inbook{Scitovski2021,
title = {Cluster Analysis and Applications},
isbn = {9783030745523},
url = {http://dx.doi.org/10.1007/978-3-030-74552-3},
doi = {10.1007/978-3-030-74552-3},
publisher = {Springer International Publishing},
author = {Scitovski, Rudolf and Sabo, Kristian and Mart{\' i}nez-{\' A}lvarez, Francisco and Ungar, {\v S}ime},
year = {2021}
}
@inproceedings{Dasgupta2008,
title = {The hardness of k-means clustering},
author = {Sanjoy Dasgupta},
year = {2008},
url = {https://api.semanticscholar.org/CorpusID:15516130}
}
@book{Hatcher2001,
title = {Algebraic Topology},
author = {Hatcher, Allen},
publisher = {Cambridge University Press},
month = dec,
year = 2001,
address = {Cambridge, England},
language = {en}
}
@book{Everitt2011,
title = {Cluster Analysis},
author = {Everitt, Brian S and Landau, Sabine and Leese, Morven and Stahl,
Daniel},
publisher = {Wiley-Blackwell},
series = {Wiley Series in Probability and Statistics},
edition = 5,
month = jan,
year = 2011,
address = {Hoboken, NJ},
language = {en}
}
@article{Carlsson2014,
title = {Topological pattern recognition for point cloud data},
volume = {23},
issn = {1474-0508},
url = {http://dx.doi.org/10.1017/S0962492914000051},
doi = {10.1017/s0962492914000051},
journal = {Acta Numerica},
publisher = {Cambridge University Press (CUP)},
author = {Carlsson, Gunnar},
year = {2014},
month = may,
pages = {289–368}
}
@book{Lidl1997-kc,
title = {Applied abstract algebra},
author = {Lidl, Rudolf and Pilz, G{\"u}nter},
publisher = {Springer},
series = {Undergraduate Texts in Mathematics},
edition = 2,
month = nov,
year = 1997,
address = {New York, NY},
language = {en}
}
@book{Leinster2014-dc,
title = {Cambridge studies in advanced mathematics: Basic category theory
series number 143},
author = {Leinster, Tom},
abstract = {At the heart of this short introduction to category theory is
the idea of a universal property, important throughout
mathematics. After an introductory chapter giving the basic
definitions, separate chapters explain three ways of expressing
universal properties: via adjoint functors, representable
functors, and limits. A final chapter ties all three together.
The book is suitable for use in courses or for independent
study. Assuming relatively little mathematical background, it is
ideal for beginning graduate students or advanced undergraduates
learning category theory for the first time. For each new
categorical concept, a generous supply of examples is provided,
taken from different parts of mathematics. At points where the
leap in abstraction is particularly great (such as the Yoneda
lemma), the reader will find careful and extensive explanations.
Copious exercises are included.},
publisher = {Cambridge University Press},
month = jul,
year = 2014,
address = {Cambridge, England}
}
@article{Lance1967-ci,
title = {A general theory of classificatory sorting strategies: 1.
Hierarchical systems},
author = {Lance, G N and Williams, W T},
abstract = {It is shown that the computational behaviour of a hierarchical
sorting-strategy depends on three properties, which are
established for five conventional strategies and four measures.
The conventional strategies are shown to be simple variants of a
single linear system defined by four parameters. A new strategy
is defined, enabling continuous variation of intensity of
grouping by variation in a single parameter. An Appendix
provides specifications of computer programs embodying the new
principles.},
journal = {Comput. J.},
publisher = {Oxford University Press (OUP)},
volume = 9,
number = 4,
pages = {373--380},
month = feb,
year = 1967
}
@article{JMLR:v11:carlsson10a,
author = {Gunnar Carlsson and Facundo M{{\'e}}moli},
title = {Characterization, Stability and Convergence of Hierarchical Clustering Methods},
journal = {Journal of Machine Learning Research},
year = {2010},
volume = {11},
number = {47},
pages = {1425-1470},
url = {http://jmlr.org/papers/v11/carlsson10a.html}
}
@book{MacLane1978,
title = {Categories for the Working Mathematician},
isbn = {9781475747218},
issn = {2197-5612},
url = {http://dx.doi.org/10.1007/978-1-4757-4721-8},
doi = {10.1007/978-1-4757-4721-8},
journal = {Graduate Texts in Mathematics},
publisher = {Springer New York},
author = {Mac Lane, Saunders},
year = {1978}
}