$k$-Variance: A Clustered Notion of Variance

DOI10.1137/20M1385895zbMath1493.62257arXiv2012.06958OpenAlexW3112942112MaRDI QIDQ5089735

Justin Solomon, Kristjan Greenewald, H. N. Nagaraja

Publication date: 15 July 2022

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.06958

zbMATH Keywords

clusteringvarianceoptimal transportWasserstein

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Order statistics; empirical distribution functions (62G30) Optimal transportation (49Q22)

Cites Work

• Computational Optimal Transport: With Applications to Data Science
• Constructive quantization: approximation by empirical measures
• Asymptotics for transportation cost in high dimensions
• Probability theory of classical Euclidean optimization problems
• Almost sure convergence of the minimum bipartite matching functional in Euclidean space
• Relations, bounds and approximations for order statistics
• Concentration of measure and isoperimetric inequalities in product spaces
• Convergence of asymptotic costs for random Euclidean matching problems
• Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
• Finer estimates on the \(2\)-dimensional matching problem
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Euclidean random matching in 2D for non-constant densities
• On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
• Combinatorial Optimization Over Two Random Point Sets
• The mean difference and the mean deviation of some discontinuous distributions
• Order Statistics
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• On the theory of order statistics
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