19 papers
Linear stability analysis of the Lloyd algorithm on a circle
Silpi Saha, Sangita Jha, Mrinal Kanti Roychowdhury
Lloyd algorithm is the standard iterative method for computing quantizers and codebooks in source coding and vector quantization. In this article, we study the dynamical and stabil…
Discrete Quantization on Spherical Geometries: Explicit Models, Computations, and Didactic Exposition
Mrinal Kanti Roychowdhury
We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on…
Optimal Quantization for Nonuniform Densities on Spherical Curves
Silpi Saha, Sangita Jha, Mrinal Kanti Roychowdhury
We present an analysis of optimal quantization of probability measures with nonuniform densities on spherical curves. We begin by deriving the centroid condition, followed by a hig…
Constrained quantization for probability distributions
Megha Pandey, Mrinal Kanti Roychowdhury
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces by introducing and analyzing the notions of t…
Optimal Quantization of Finite Uniform Data on the Sphere
Mrinal Kanti Roychowdhury
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere , focusing on finite uniform probability distributions supported on th…
Optimal Quantization on Spherical Surfaces: Continuous and Discrete Models -- A Beginner-Friendly Expository Study
Mrinal Kanti Roychowdhury
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sph…