INFORMATION RADIUS
INFORMATION RADIUS
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DOI：
10.1007/bf00537520
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发表时间：
1969-01-01
期刊：
影响因子：
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通讯作者：
SIBSON, R
中科院分区：
文献类型：
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作者：
SIBSON, R
本文描述了一种构建概率测度之间差异测度的新方法；如此构建的新散度度量称为信息半径度量。它们本质上是信息论的，并且基于 Rényi [8] 和 Csiszár [2, 3] 的工作。散度测度 K1 可用于数值分类学中相异性的测量，Jardine 和 Sibson [5] 讨论了其在该领域的应用；正是这个应用最初激发了信息半径的研究。其他形式的信息半径与变化距离有关，第3节中讨论的正常信息半径与Mahalanobis’D2统计有关。本文的部分目的是为[5]奠定数学基础，但由于信息半径似乎具有一定的普遍意义，因此对其属性的研究在此比[5]中讨论的应用所需进行得更深入。
This paper is an account of a new method of constructing measures of divergence between probability measures; the new divergence measures so constructed are calledinformation radiusmeasures. They are information-theoretic in character, and are based on the work of Rényi [8] and Csiszár [2, 3]. The divergence measureK1can be used for the measurement of dissimilarity in numerical taxonomy, and its application to this field is discussed in Jardine and Sibson [5]; it was this application which originally motivated the study of information radius. Other forms of information radius are related to the variation distance, and thenormal information radiusdiscussed in § 3 is related to Mahalanobis’D2Statistic. This paper is in part intended to lay the mathematical foundations for [5], but because information radius appears to be of some general interest, the investigation of its properties is here carried further than is needed for the applications discussed in [5].