The statistical analysis of compositional data
The statistical analysis of compositional data
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
OPTICS: ordering points to identify the clustering structure
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Cluster analysis: a further approach based on density estimation
Computational Statistics & Data Analysis
Clustering Algorithms
Clustering via nonparametric density estimation
Statistics and Computing
Clustering via nonparametric density estimation
Statistics and Computing
Operator Norm Convergence of Spectral Clustering on Level Sets
The Journal of Machine Learning Research
Density-based Silhouette diagnostics for clustering methods
Statistics and Computing
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Although Hartigan (1975) had already put forward the idea of connecting identification of subpopulations with regions with high density of the underlying probability distribution, the actual development of methods for cluster analysis has largely shifted towards other directions, for computational convenience. Current computational resources allow us to reconsider this formulation and to develop clustering techniques directly in order to identify local modes of the density. Given a set of observations, a nonparametric estimate of the underlying density function is constructed, and subsets of points with high density are formed through suitable manipulation of the associated Delaunay triangulation. The method is illustrated with some numerical examples.