Kernel density estimation of Tsalli’s entropy with applications in adaptive system training

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 Tsallis-estimator 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.