Work

Quantization for uniform distributions on equilateral triangles

Year: 2015

Type: preprint

Abstract: We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical optimization results for $n\leq 21$, and a bound on the quantization error for $n\to\infty$. The equilateral triangle has particularly efficient quantizations due to its connection with the triangular lattice. Our methods can be applied to the uniform distributions on general sets with piecewise smooth boundaries.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1508.00498

Authors: Dettmann, Carl P., Roychowdhury, Mrinal Kanti

Institutions: University of Bristol, The University of Texas Rio Grande Valley

Language: English

Topic: Advanced Clustering Algorithms Research

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Security Agency, Engineering and Physical Sciences Research Council

Awards: Spatially Embedded Networks, G7243506635, G7845798442, G8433258759, G859290583

OpenAlex ID: W2171990664

Cites: 5

Cited by:

Related to: 20