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Full-Text Articles in Physical Sciences and Mathematics
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n -means and the n th quantization errors for different …
Quantization For Infinite Affine Transformations, Dogan Comez, Mrinal Kanti Roychowdhury
Quantization For Infinite Affine Transformations, Dogan Comez, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of affine transformations {S-ij} on R-2 with associated probabilities {p(ij)} such that p(ij) > 0 for all i, j is an element of N and Sigma(infinity)(i,j=1) p(ij) = 1. For such a probability measure P, the optimal sets of n-means and the nth quantization error are calculated for every natural number n. It is shown that the distribution of such a probability measure is the …
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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 …
Optimal Quantization Via Dynamics, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Optimal Quantization Via Dynamics, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using stationary processes arising in dynamical systems, followed by a discussion of the special cases of stationary processes: random processes and Diophantine processes. We are interested in how close stationary process can be to giving optimal n-means and nth optimal mean distortion errors. We also consider different ways of measuring the degree of approximation by quantization, and their advantages and disadvantages in these different contexts.
Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury
Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of n-means and the nth quantization errors are calculated for some positive integers n.