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We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets.
On the transfer of masses
L.V. Kantorovich · 1942
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e-approximations with minimum packing constraint violation
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Network and discrete location: models, algorithms, and applications
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Atomic decomposition by basis pursuit
S.S. Chen, D.L. Donoho, and M.A. Saunders · 1998
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Mass Transportation Problems: Volume I: Theory
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A constant-factor approximation algorithm for the k-median problem
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Z. Drezner and H.W. Hamacher · 2001
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Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation
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A constant-factor approximation algorithm for the k-median problem
M. Charikar, S. Guha, É. Tardos, and D.B. Shmoys · 2002
Cited alongside, same era.
Topics in optimal transportation
C. Villani · 2003
Decoding by linear programming
E.J. Candes and T. Tao · 2005
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Model selection and estimation in regression with grouped variables
M. Yuan and Y. Lin · 2005
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Convex clustering with exemplar-based models
Danial Lashkari and Polina Golland · 2007
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Optimal transport: old and new
C. Villani · 2008
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From sparse solutions of systems of equations to sparse modeling of signals and images
A.M. Bruckstein, D.L. Donoho, and M. Elad · 2009
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The convex algebraic geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P.A. Parrilo, and A.S. Willsky · 2010
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Mémoire sur la théorie des déblais et des remblais
G. Monge
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Recovery of sparse probability measures via convex programming
M. Pilanci, L. El Ghaoui, and V. Chandrasekaran · 2012
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