归一化信息距离的非逼近性
Nonapproximablity of the Normalized Information Distance
摘要：
标准化信息距离（NID）使用柯尔莫哥洛夫复杂度的理论概念，实际上是使用真实世界的压缩程序，通过所涉及文件的压缩版本的长度来近似计算。这种实际应用被称为“归一化压缩距离”，并且它是可平凡计算的。它是一种基于压缩的无参数相似性度量，用于模式识别、数据采掘、遗传学、聚类和分类。它的理论先驱NID的复杂性属性已经公开。我们表明，NID既不是上半可计算的，也不是下半可计算的任何合理的精度。
英文摘要：
Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program. This practical application is called `normalized compression distance' and it is trivially computable. It is a parameter-free similarity measure based on compression, and is used in pattern recognition, data mining, phylogeny, clustering, and classification. The complexity properties of its theoretical precursor, the NID, have been open. We show that the NID is neither upper semicomputable nor lower semicomputable up to any reasonable precision.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
