Fetching the paper…
Reading the bibliography…
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm.
The Speed of Mean Glivenko-Cantelli Convergence
R. M. Dudley · 1969
Earlier work this paper cites.
Probability Measures on Metric Spaces
K.R. Parthasarathy · 1972
Earlier work this paper cites.
SLINK: An optimally efficient algorithm for the single-link cluster method
Robin Sibson · 1973
Earlier work this paper cites.
Clustering algorithms
John A. Hartigan · 1975
Earlier work this paper cites.
General Topology
Ákos Császár · 1978
Earlier work this paper cites.
Consistency of single linkage for high-density clusters
J. A. Hartigan · 1981
Earlier work this paper cites.
Classification of olive oils from their fatty acid composition
M. Forina, C. Armanino, S. Lanteri, and E. Tiscornia · 1983
Earlier work this paper cites.
Density Estimation for Statistics and Data Analysis
B. W. Silverman · 1986
Earlier work this paper cites.
Real analysis and probability , volume 74 of Cambridge Studies in Advanced Mathematics
R. M. Dudley · 1989
Earlier work this paper cites.
A density-based algorithm for discovering clusters in large spatial databases with noise
Martin Ester, Hans-Peter Kriegel, Jörg Sander, and Xiaowei Xu · 1996
Earlier work this paper cites.
Convergence of Probability Measures, Second Edition
Patrick Billingsley · 1999
Earlier work this paper cites.
Estimating the number of clusters
Antonio Cuevas, Manuel Febrero, and Ricardo Fraiman · 2000
Earlier work this paper cites.
A Course in Metric Geometry , volume 33 of Graduate Studies in Mathematics
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
Earlier work this paper cites.
Topological persistence and simplification
Herbert Edelsbrunner, David Letscher, and Afra Zomorodian · 2002
Earlier work this paper cites.
On choosing and bounding probability metrics
Alison L. Gibbs and Francis Edward Su · 2002
Earlier work this paper cites.
Persistent homotopy theory, 2020
J. F. Jardine · 2002
Earlier work this paper cites.
Optimal matching between reduced size functions
M d’Amico, P Frosini, and C Landi · 2003
Earlier work this paper cites.
On boundary estimation
Antonio Cuevas and Alberto Rodríguez-Casal · 2004
Earlier work this paper cites.
Afra Zomorodian and Gunnar Carlsson · 2005
Earlier work this paper cites.
Vines and vineyards by updating persistence in linear time
David Cohen-Steiner, Herbert Edelsbrunner, and Dmitriy Morozov · 2006
Earlier work this paper cites.
Comparing clusterings—an information based distance
Marina Meilă · 2006
Earlier work this paper cites.
A graph-based estimator of the number of clusters
Gérard Biau, Benoît Cadre, and Bruno Pelletier · 2007
Earlier work this paper cites.
Multidimensional size functions for shape comparison
Silvia Biasotti, Andrea Cerri, Patrizio Frosini, Daniela Giorgi, and Claudia Landi · 2008
Earlier work this paper cites.
Barcodes: The persistent topology of data
Robert Ghrist · 2008
Cited alongside, same era.
The theory of multidimensional persistence
Gunnar Carlsson and Afra Zomorodian · 2009
Cited alongside, same era.
Multidimensional persistent homology is stable, 2009
Andrea Cerri, Barbara Di Fabio, Massimo Ferri, Patrizio Frosini, and Claudia Landi · 2009
Cited alongside, same era.
Proximity of persistence modules and their diagrams
Frédéric Chazal, David Cohen-Steiner, Marc Glisse, Leonidas J. Guibas, and Steve Y. Oudot · 2009
Cited alongside, same era.
Tessellations of random maps of arbitrary genus
Grégory Miermont · 2009
Cited alongside, same era.
A generalized single linkage method for estimating the cluster tree of a density
Werner Stuetzle and Rebecca Nugent · 2009
The structure and stability of persistence modules
Frédéric Chazal, Vin de Silva, Marc Glisse, and Steve Oudot · 2016
Later among the works it cites.
Statistical inference for cluster trees
Jisu Kim, Yen-Chi Chen, Sivaraman Balakrishnan, Alessandro Rinaldo, and Larry Wasserman · 2016
Later among the works it cites.
Topological consistency via kernel estimation
Omer Bobrowski, Sayan Mukherjee, and Jonathan E. Taylor · 2017
Later among the works it cites.
Accelerated hierarchical density based clustering
Leland McInnes and John Healy · 2017
Later among the works it cites.
hdbscan: Hierarchical density based clustering
Leland McInnes, John Healy, and Steve Astels · 2017
Later among the works it cites.
The fiber of the persistence map for functions on the interval
Justin Curry · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
One-dimensional reduction of multidimensional persistent homology
Francesca Cagliari, Barbara Di Fabio, and Massimo Ferri · 2010
Cited alongside, same era.
Characterization, stability and convergence of hierarchical clustering methods
Gunnar Carlsson and Facundo Mémoli · 2010
Cited alongside, same era.
Multiparameter hierarchical clustering methods
Gunnar Carlsson and Facundo Mémoli · 2010
Cited alongside, same era.
Rates of convergence for the cluster tree
Kamalika Chaudhuri and Sanjoy Dasgupta · 2010
Cited alongside, same era.
Generalized density clustering
Alessandro Rinaldo and Larry Wasserman · 2010
Cited alongside, same era.
Stability of density-based clustering
Alessandro Rinaldo, Aarti Singh, Rebecca Nugent, and Larry Wasserman · 2012
Cited alongside, same era.
Formigrams: Clustering summaries of dynamic data
Woojin Kim and Facundo Mémoli · 2018
Later among the works it cites.
The rank invariant stability via interleavings
Claudia Landi · 2018
Later among the works it cites.
DTM-Based Filtrations
Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage, and Yuhei Umeda · 2019
Later among the works it cites.
A kernel for multi-parameter persistent homology
René Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, and Bei Wang · 2019
Later among the works it cites.
Stable components and layers
J. F. Jardine · 2019
Later among the works it cites.
Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
U. Bauer, M. Botnan, S. Oppermann, and J. Steen · 2020
Closest in time.
Elder-Rule-Staircodes for Augmented Metric Spaces
Chen Cai, Woojin Kim, Facundo Mémoli, and Yusu Wang · 2020
Closest in time.
Multiparameter persistence images for topological machine learning
Mathieu Carrière and Andrew J. Blumberg · 2020
Closest in time.
Locally Persistent Categories And Metric Properties Of Interleaving Distances
Luis Scoccola · 2020
Closest in time.
Multiparameter persistence landscapes
Oliver Vipond · 2020
Closest in time.
Essential Mathematics for Undergraduates: A Guided Approach to Algebra, Geometry, Topology and Analysis
Simon G. Chiossi · 2021
Closest in time.
Flattening multiparameter hierarchical clustering functors, 2021
Dan Shiebler · 2021
Closest in time.
Stability of 2-parameter persistent homology
Andrew J. Blumberg and Michael Lesnick · 2022
Closest in time.
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions
Magnus Bakke Botnan, Steffen Oppermann, and Steve Oudot · 2022
Closest in time.
Computational Topology for Data Analysis
Tamal Krishna Dey and Yusu Wang · 2022
Closest in time.
Persistable: persistent and stable clustering
Luis Scoccola and Alexander Rolle · 2023
Closest in time.