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We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli.
The construction of hierarchic and non-hierarchic classifications
Nicholas Jardine and Robin Sibson · 1968
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Mathematical Taxonomy
Nicholas Jardine and Robin Sibson · 1971
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k k -blocks and ultrablocks in graphs
David W. Matula · 1978
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Weak hierarchies associated with similarity measures: An additive clustering technique
Hans-Jürgen Bandelt and Andreas W. M. Dress · 1989
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A canonical decomposition theory for metrics on a finite set
Hans-Jürgen Bandelt and Andreas W. M. Dress · 1992
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An order theoretic framework for overlapping clustering
Hans-Jürgen Bandelt and Andreas W. M. Dress · 1994
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One-to-one correspondence between indexed cluster structures and weakly indexed closed cluster structures
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Topological methods for the analysis of high dimensional data sets and 3D object recognition
Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson · 2007
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Enhanced topology-sensitive clustering by Reeb graph shattering
W Harvey, O Rübel, V Pascucci, P-T Bremer, and Y Wang · 2012
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Finding maximal k k -edge-connected subgraphs from a large graph
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Linear-time enumeration of maximal k k -edge-connected subgraphs in large networks by random contraction
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Obtaining splits from cut sets of tight spans
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Weak hierarchies: A central clustering structure
Patrice Bertrand and Jean Diatta · 2014
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