We investigate the use of the new Cross Entropy method as a tool for exploratory data analysis. We show how this method can be used to perform linear projections such as principal component analysis, exploratory projection pursuit and canonical correlation analysis. We further go on to show how topology preserving mappings can be created usin the cross entropy method. We also show how the cross...

In this thesis we will introduce topological automata and the topological entropy of a topological automaton, which is the topological entropy of the dynamical system contained in the automaton. We will use these notions to define a measure of complexity for formal languages. We assign to every language the topological entropy of the unique minimal topological automaton accepting it. We contrib...

Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P. Saparin et al., Chaos, Solitons and Fractals 4, 1907 (1994)] and applied to several physiological time sequences, including electroencephalograms (EEGs) of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (KL) relative entropy, and it gives similar numerical results...

Different approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for different data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, ...

Introduction and Aims: Alzheimer’s disease is the most prevalent neurodegenerative disorder and a type of dementia. 80% of dementia in older adults is because of Alzheimer’s disease. According to multiple research articles, Alzheimer's has several changes in EEG signals such as slowing of rhythms, reduction in complexity and reduction in functional associations, and disordered functional commun...