On the limits of clustering in high dimensions via cost functions

DOI10.1002/sam.10095OpenAlexW2115817918MaRDI QIDQ4969748

Hoyt A. Koepke, Bertrand S. Clarke

Publication date: 14 October 2020

Published in: Statistical Analysis and Data Mining: The ASA Data Science Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sam.10095

zbMATH Keywords

VC-dimensioncost functionhigh dimensionsclustering impossibility

Mathematics Subject Classification ID

Statistics (62-XX) Computer science (68-XX)

Cites Work

• Estimating the Number of Clusters in a Data Set Via the Gap Statistic
• The remarkable simplicity of very high dimensional data: application of model-based clustering
• Refinement of the upper bound of the constant in the central limit theorem
• Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
• Weak convergence and empirical processes. With applications to statistics
• Nemirovski's Inequalities Revisited
• Impossibility of successful classification when useful features are rare and weak
• On the Performance of Clustering in Hilbert Spaces
• Matrix Analysis
• Uniform Central Limit Theorems
• Geometric Representation of High Dimension, Low Sample Size Data
• A graph-based estimator of the number of clusters
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