some convex functions based measures of independence and their application to strange attractor reconstruction一些凸函数基础措施的独立和奇怪吸引子重构他们的应用程序.pdf

Entropy 2011, 13, 820-840; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Some Convex Functions Based Measures of Independence and Their Application to Strange Attractor Reconstruction Yang Chen 1,* and Kazuyuki Aihara 2,3 1 School of Information Science and Engineering, Southeast University, Nanjing 210096, China 2 Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; E-Mail: aihara@sat.t.u-tokyo.ac.jp 3 Aihara Complexity Modelling Project, ERATO, JST, Saitama 332-0012, Japan * Author to whom correspondence should be addressed; E-Mail: cheny@. Received: 8 February 2011; in revised form: 28 March 2011 / Accepted: 28 March 2011 / Published: 8 April 2011 Abstract: 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