The rate-distortion dimension of sets and measures
The rate-distortion dimension of sets and measures
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集合和测度的率失真维度
DOI：
10.1109/18.333868
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
A. Dembo
中科院分区：
文献类型：
--
作者：
T. Kawabata;A. Dembo
从分形集的独立样本的数据压缩被认为是。速率与幅度对数失真的渐近比表征了底层分布所占据的有效维数。这个量被证明与Renyi（1959）的信息维度相同。对于自相似分形集，这个维数是分布相关的，与绝对连续测度的行为形成鲜明对比。一个集合的率失真维数被定义为该集合上支持的分布的最大率失真维数。Kolmogorov度量维数是率失真维数的上界，而Hausdorff维数是下界。提供了率失真维度不同于这些界限的集合的示例。>
Data compression of independent samples drawn from a fractal set is considered. The asymptotic ratio of rate to magnitude log distortion characterizes the effective dimension occupied by the underlying distribution. This quantity is shown to be identical to Renyi's (1959) information dimension. For self-similar fractal sets this dimension is distribution dependent-in sharp contrast with the behavior of absolutely continuous measures. The rate-distortion dimension of a set is defined as the maximal rate-distortion dimension for distributions supported on this set. Kolmogorov's metric dimension is an upper bound on the rate-distortion dimension, while the Hausdorff dimension is a lower bound. Examples of sets for which the rate-distortion dimension differs from these bounds are provided. >