Some convex functions based measures of independence and their application to strange attractor reconstruction
type: Item
instance of: scholarly article
title: Some convex functions based measures of independence and their application to strange attractor reconstruction
zbMATH Open document ID: 1229.94029
author: Yang Chen
author: Kazuyuki Aihara
published in: Entropy
publication date: 2012-01-09T00:00:00Z
review text: Summary: The classical information-theoretic measures such as the entropy and the mutual information (MI) are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO) and the quasientropy (QE) as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar's generalized mutual information (GMI). A quality factor (QF) is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney's algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5995947
zbMATH Keywords: entropy
zbMATH Keywords: mutual information
zbMATH Keywords: convex function
zbMATH Keywords: quality factor
zbMATH Keywords: strange attractor
zbMATH Keywords: delay-coordinate
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e13040820
OpenAlex ID: W1981071650
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DOI: 10.3390/E13040820
description: scientific article; zbMATH DE number 5995947