Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves

Authors

Gabriela Pena, The University of Texas Rio Grande Valley
Hansapani Rodrigo, The University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley
Josef A. Sifuentes, The University of Texas Rio Grande Valley
Erwin Suazo, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

1-2021

Abstract

In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form n = 6k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on the boundary of a semicircular disc, and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n-means and the nth quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n.

Comments

Original published version available at https://doi.org/10.1007/s10957-020-01771-1

https://rdcu.be/dX8uI

Recommended Citation

Pena, Gabriela, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef Sifuentes, and Erwin Suazo. "Quantization for uniform distributions on hexagonal, semicircular, and elliptical curves." Journal of Optimization Theory and Applications 188 (2021): 113-142. https://doi.org/10.1007/s10957-020-01771-1

Publication Title

Journal of Optimization Theory and Application

DOI

10.1007/s10957-020-01771-1