准熵的性质及其应用

Properties of quasi-entropy and their application

准熵将信息论中熵的特定凸函数推广到任意凸函数,研究了这种推广能否提高熵的性能.提出并证明了准熵与熵的一些共同性质.以独立性度量问题为例,研究了凸函数对准熵最小值形状的影响,提出了凸函数品质因数的概念,用来刻画准熵最小值的显著性.发现了品质因数比熵中凸函数更好的无穷多凸函数.给出了凸函数品质因数在混沌信号分析中的应用实例.结果表明,根据特定应用,恰当选取凸函数,可令准熵获得比熵更好的性能.

Quasi-entropy （QE） generalizes the specific convex function in the entropy in information theory to an arbitrary convex function. Whether this generalization can improve the performance of entropy was studied. Some common properties of QE and entropy were proposed and proved. Using the independence-measuring problem as an example, the influence of the convex function on the shape of the minima of QE was studied. The concept of the quality factor of convex function was proposed, which was used to characterize the prominence of the minimum of QE. Infinitely many convex functions with quality factors better than that of the convex function in entropy were discov- ered. An application of the quality factor of convex function to chaotic signal analysis was given. The results show that, by properly choosing convex function according to specific application, the performance of QE can be made better than that of entropy.