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All Journal International Journal of Electrical and Computer Engineering IAES International Journal of Artificial Intelligence (IJ-AI)
Chawla, Leena
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Computer Science & IT Electrical & Electronics Engineering Engineering

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Estimation of kernel density function using Kapur entropy Chawla, Leena; Kumar, Vijay; Saxena, Arti
International Journal of Electrical and Computer Engineering (IJECE) Vol 14, No 5: October 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijece.v14i5.pp6016-6022

Abstract

Information-theoretic measures play a vital role in training learning systems. Many researchers proposed non-parametric entropy estimators that have applications in adaptive systems. In this work, a kernel density estimator using Kapur entropy of order α and type β has been proposed and discussed with the help of theorems and properties. From the results, it has been observed that the proposed density measure is consistent, minimum, and smooth for the probability density function (PDF) underlying given conditions and validated with the help of theorems and properties. The objective of the paper is to understand the theoretical viewpoint behind the underlying concept.
Kernel density estimation of Tsalli’s entropy with applications in adaptive system training Chawla, Leena; Kumar, Vijay; Saxena, Arti
IAES International Journal of Artificial Intelligence (IJ-AI) Vol 13, No 2: June 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijai.v13.i2.pp2247-2253

Abstract

Information theoretic learning plays a very important role in adaption learning systems. Many non-parametric entropy estimators have been proposed by the researchers. This work explores kernel density estimation based on Tsallis entropy. Firstly, it has been proved that for linearly independent samples and for equal samples, Tsallis-estimator is consistent for the PDF and minimum respectively. Also, it is investigated that Tsallisestimator is smooth for differentiable, symmetric, and unimodal kernel function. Further, important properties of Tsallis-estimator such as scaling and invariance for both single and joint entropy estimation have been proved. The objective of the work is to understand the mathematics behind the underlying concept.
Co-Authors Saxena, Arti Vijay Kumar