Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Asymptotically optimal balloon density estimates
Journal of Multivariate Analysis
Kernel density estimation with adaptive varying window size
Pattern Recognition Letters
Grid generation and optimization based on centroidal Voronoi tessellations
Applied Mathematics and Computation
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
Least squares quantization in PCM
IEEE Transactions on Information Theory
Barley seeds classification with a genetically optimized kernel density estimator
CIMMACS'07 Proceedings of the 6th WSEAS international conference on Computational intelligence, man-machine systems and cybernetics
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A novel non-parametric density estimator is developed based on geometric principles. A penalised centroidal Voronoi tessellation forms the basis of the estimator, which allows the data to self-organise in order to minimise estimate bias and variance. This approach is a marked departure from usual methods based on local averaging, and has the advantage of being naturally adaptive to local sample density (scale-invariance). The estimator does not require the introduction of a plug-in kernel, thus avoiding assumptions of symmetricity and morphology. A numerical experiment is conducted to illustrate the behaviour of the estimator, and it's characteristics are discussed.