A population background for nonparametric density-based clustering

DOI10.1214/15-STS526zbMath1426.62181arXiv1408.1381MaRDI QIDQ1790301

José E. Chacón

Publication date: 2 October 2018

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1381

zbMATH Keywords

Morse theoryHausdorff distancemodal clusteringclustering consistencydistance in measure

Mathematics Subject Classification ID

Density estimation (62G07) Classification and discrimination; cluster analysis (statistical aspects) (62H30)

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Cites Work

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• Confidence sets for persistence diagrams
• Local equivalences of distances between clusterings -- a geometric perspective
• Maximum transfer distance between partitions
• An advancement in clustering via nonparametric density estimation
• CLUES: a non-parametric clustering method based on local shrinking
• On the path density of a gradient field
• On weak convergence and optimality of kernel density estimates of the mode
• One-sided inference about functionals of a density
• Strong consistency of k-means clustering
• The complexity of computing metric distances between partitions
• Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
• On nonparametric estimation of density level sets
• Estimating the cluster tree of a density by analyzing the minimal spanning tree of a sample
• Data-driven density derivative estimation, with applications to nonparametric clustering and bump hunting
• Classifying clustering schemes
• On Morse theory for piecewise smooth functions
• Foundations of quantization for probability distributions
• The topography of multivariate normal mixtures
• Comparing clusterings -- an information based distance
• Asymptotic normality of plug-in level set estimates
• Transfer distance between partitions
• Multidimensional scaling of measures of distance between partitions
• Cluster Analysis
• Modern Multivariate Statistical Techniques
• Assignment Problems
• Smoothing of Multivariate Data
• Topology and data
• Morse Theory. (AM-51)
• The estimation of the gradient of a density function, with applications in pattern recognition
• Model-Based Clustering, Discriminant Analysis, and Density Estimation
• Estimating the number of clusters
• Data‐driven choice of the smoothing parametrization for kernel density estimators
• Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation
• Estimation of density level sets with a given probability content
• A Sober Look at Clustering Stability
• Persistence-Based Clustering in Riemannian Manifolds
• Stability of Density-Based Clustering
• Riemannian geometry and geometric analysis
• Cluster analysis: a further approach based on density estimation.

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