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Two important optimization problems in the analysis of geometric data sets are clustering and sketching.
Theory and applications of distance geometry
L.M. Blumenthal · 1953
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Cluster analysis of multivariate data: efficiency versus interpretability of classifications
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Mathematical taxonomy
Nicholas Jardine and Robin Sibson · 1971
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Slink: An optimally efficient algorithm for the single-link cluster method
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Clustering algorithms
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An efficient algorithm for a complete link method
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Algorithm as 136: A k-means clustering algorithm
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Least squares quantization in pcm
Stuart P Lloyd · 1982
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Clustering to minimize the maximum intercluster distance
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Statistical theory in clustering
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A unified approach to approximation algorithms for bottleneck problems
Dorit S Hochbaum and David B Shmoys · 1986
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Ultrametricity for physicists
R. Rammal, G. Toulouse, and M. A. Virasoro · 1986
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Algorithms for clustering data
Anil K Jain and Richard C Dubes · 1988
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I.J. Schoenberg Selected Papers
I.J. Schoenberg · 1988
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Chapter 2 - a catalog of complexity classes
David S. JOHNSON · 1990
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Model-based gaussian and non-gaussian clustering
Jeffrey D. Banfield and Adrian E. Raftery · 1993
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On the hardness of approximating minimization problems
Carsten Lund and Mihalis Yannakakis · 1994
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A polynomial time primal network simplex algorithm for minimum cost flows
James B. Orlin · 1997
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A threshold of ln n for approximating set cover
Uriel Feige · 1998
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A distribution-based clustering algorithm for mining in large spatial databases
Xiaowei Xu, M. Ester, H. . Kriegel, and J. Sander · 1998
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Improved combinatorial algorithms for the facility location and k-median problems
M. Charikar and S. Guha · 1999
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Metric Structures for Riemannian and Non-Riemannian Spaces:
M. Gromov, J. Lafontaine, and P. Pansu · 1999
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Analysis of a local search heuristic for facility location problems
Madhukar R Korupolu, C Greg Plaxton, and Rajmohan Rajaraman · 2000
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On approximate geometric k-clustering
Jirı Matoušek · 2000
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The earth mover’s distance as a metric for image retrieval
Yossi Rubner, Carlo Tomasi, and Leonidas J Guibas · 2000
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Sparse greedy matrix approximation for machine learning
Alex J Smola and Bernhard Schölkopf · 2000
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A Course in Metric Geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
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Concept decompositions for large sparse text data using clustering
Inderjit S Dhillon and Dharmendra S Modha · 2001
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Efficient svm training using low-rank kernel representations
Shai Fine and Katya Scheinberg · 2001
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Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation
Kamal Jain and Vijay V Vazirani · 2001
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Quick k-median, k-center, and facility location for sparse graphs
Mikkel Thorup · 2001
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Using the nyström method to speed up kernel machines
Christopher KI Williams and Matthias Seeger · 2001
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The hardness of k-means clustering
Sanjoy Dasgupta · 2008
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Sketching information divergences
Sudipto Guha, Piotr Indyk, and Andrew McGregor · 2008
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Simpler analyses of local search algorithms for facility location
Anupam Gupta and Kanat Tangwongsan · 2008
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Kernel methods in machine learning
Thomas Hofmann, Bernhard Schölkopf, and Alexander J Smola · 2008
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Efficient sketches for earth-mover distance, with applications
Alexandr Andoni, Khanh Do Ba, Piotr Indyk, and David Woodruff · 2009
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Np-hardness of euclidean sum-of-squares clustering
Daniel Aloise, Amit Deshpande, Pierre Hansen, and Preyas Popat · 2009
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Kernel independent component analysis
Francis R Bach and Michael I Jordan · 2002
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A local search approximation algorithm for k-means clustering
Tapas Kanungo, David M Mount, Nathan S Netanyahu, Christine D Piatko, Ruth Silverman, and Angela Y Wu · 2002
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On bending invariant signatures for surfaces
A. Elad and R. Kimmel · 2003
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The online median problem
Ramgopal R. Mettu and C. Greg Plaxton · 2003
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Phylogenetics
Charles Semple and Mike Steel · 2003
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Topics in Optimal Transportation
C. Villani · 2003
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Introduction to Algorithms, Third Edition
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein · 2009
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The planar k-means problem is np-hard
Meena Mahajan, Prajakta Nimbhorkar, and Kasturi Varadarajan · 2009
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Characterization, stability and convergence of hierarchical clustering methods
Gunnar Carlsson and Facundo Mémoli · 2010
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On the exact space complexity of sketching and streaming small norms
Daniel M Kane, Jelani Nelson, and David P Woodruff · 2010
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Geometric approximation algorithms
Sariel Har-Peled · 2011
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A 1.488 approximation algorithm for the uncapacitated facility location problem
Shi Li · 2011
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Gromov–Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
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K-means requires exponentially many iterations even in the plane
Andrea Vattani · 2011
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Sampling methods for the nyström method
Sanjiv Kumar, Mehryar Mohri, and Ameet Talwalkar · 2012
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Some properties of Gromov–Hausdorff distances
Facundo Mémoli · 2012
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The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces
Karl-Theodor Sturm · 2012
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Homomorphic fingerprints under misalignments: sketching edit and shift distances
Alexandr Andoni, Assaf Goldberger, Andrew McGregor, and Ely Porat · 2013
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Metric Transforms
Michel Marie Deza and Elena Deza · 2013
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Javaplex: A research software package for persistent (co) homology
Henry Adams, Andrew Tausz, and Mikael Vejdemo-Johansson · 2014
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Sketching and embedding are equivalent for norms
Alexandr Andoni, Robert Krauthgamer, and Ilya Razenshteyn · 2015
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Algorithms and Computation - 26th International Symposium, ISAAC 2015, Nagoya, Japan, December 9-11, 2015, Proceedings
Khaled M. Elbassioni and Kazuhisa Makino, editors · 2015
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On sketching quadratic forms
Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P Woodruff, and Qin Zhang · 2016
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Impossibility of sketching of the 3d transportation metric with quadratic cost
Alexandr Andoni, Assaf Naor, and Ofer Neiman · 2016
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Constructing geodesics on the space of compact metric spaces
Samir Chowdhury and Facundo Mémoli · 2016
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Analysis of farthest point sampling for approximating geodesics in a graph
Pegah Kamousi, Sylvain Lazard, Anil Maheshwari, and Stefanie Wuhrer · 2016
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Computational aspects of the gromov-hausdorff distance and its application in non-rigid shape matching
Felix Schmiedl · 2017
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