5 citations · 11 across the 45 of their papers we have counts for
56 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…
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…
Optimal Sets and Quantization Errors under Geometric Constraints for Discrete Distributions
Prabhat Tamrakar, Bismark Bimpong, S. K. Katiyar +2
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specif…
Quantization for a condensation system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , represents the rate at which the th quantization error of order …
Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , of a Borel probability measure on represents the sp…
Constrained quantization for the Cantor distribution with a family of constraints
Megha Pandey, Mrinal Kanti Roychowdhury
In this paper, for a given family of constraints and the classical Cantor distribution we determine the constrained optimal sets of -points, th constrained quantization error…
Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions
Evans Nyanney, Megha Pandey, Mrinal Kanti Roychowdhury
Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimen…
Conditional quantization for uniform distributions on line segments and regular polygons
Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez +1
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If…
Conditional constrained and unconstrained quantization for uniform distributions on regular polygons
Christina Hamilton, Evans Nyanney, Megha Pandey +1
In this paper, we have considered a uniform distribution on a regular polygon with -sides for some and the set of all its vertices as a conditional set. For the un…
Constrained quantization for a uniform distribution
Pigar Biteng, Mathieu Caguiat, Dipok Deb +2
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points ly…
Conditional constrained and unconstrained quantization for probability distributions
Megha Pandey, Mrinal Kanti Roychowdhury
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on considering both constrained and unconstrained fra…
Constrained Quantization for Uniform Distributions with Two Constraint Families
Pavjeet Singh, S. K. Katiyar, Megha Pandey +1
In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of -points an…
Constrained quantization for the Cantor distribution
Megha Pandey, Mrinal K. Roychowdhury
The theory of constrained quantization has been recently introduced by Pandey and Roychowdhury. In this paper, they have further generalized their previous definition of constraine…
Quantization for a set of discrete distributions on the set of natural numbers
Juan Gomez, Haily Martinez, Mrinal K. Roychowdhury +2
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitel…
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…
Quantization dimensions for inhomogeneous bi-Lipschitz Iterated Function Systems
Amit Priyadarshi, Mrinal K. Roychowdhury, Manuj Verma
Let be a Borel probability measure on a -dimensional Euclidean space , , with a compact support, and let be a probabili…
Quantization dimensions for the bi-Lipschitz recurrent Iterated function systems
Amit Priyadarshi, Mrinal K. Roychowdhury, Manuj Verma
In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong op…
Quantization dimension for self-similar measures of overlapping construction
Mrinal Kanti Roychowdhury, Karoly Simon
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open…
Quantization for the mixtures of overlap probability distributions
Asha Barua, Angelina Chavera, Ivan Djordjevic +4
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions…
Quantization for the mixtures of uniform distributions on connected and disconnected line segments
Asha Barua, Gustavo Fernandez, Ashley Gomez +2
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the…
Quantization dimension and stability for infinite self-similar measures with respect to geometric mean error
Mrinal K. Roychowdhury, Saurabh Verma
Let be a Borel probability measure associated with an iterated function system consisting of a countably infinite number of contracting similarities and an infinite probability…