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arXiv cs/0312044cs.CVcond-mat.stat-mechcs.AIphysics.data-anq-bio.GNq-bio.QM
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压缩聚类

Clustering by compression

Rudi Cilibrasi, Paul Vitanyi

摘要:

提出了一种基于压缩的聚类方法。该方法不使用特定于主题的特征或背景知识,其工作原理如下:首先,我们确定通用相似性距离,即标准化压缩距离或NCD,根据压缩数据文件的长度(单个和成对连接)计算。第二,我们采用层次聚类方法。非传染性疾病是普遍的,因为它不限于特定的应用领域,并跨越应用领域的界限。一个理论上的先驱,归一化信息距离,由作者之一共同开发,是可证明的最优,但使用了不可计算的概念柯尔莫哥洛夫复杂性。我们提出了精确的概念相似性度量,正常的压缩机,并表明,NCD基于正常的压缩机是一个相似性度量,近似的普遍性。为了从距离矩阵中提取聚类的层次结构,我们通过一种新的四元组方法和一种快速启发式算法来确定树状图(二叉树),该方法已作为公共软件实现,并且在不同压缩器的选择下具有鲁棒性。为了证实我们的普遍性和鲁棒性的索赔,我们报告的证据成功应用于不同领域的基因组学,病毒学,语言,文学,音乐,手写数字,天文学,和组合的对象从完全不同的领域,使用统计,字典,和块排序压缩器。在基因组学方面,我们基于全线粒体基因组分析为哺乳动物进化中的主要问题提供了新的证据:真兽目和有袋目假说反对兽目假说。

英文摘要:

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is universal in that it is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal but uses the non-computable notion of Kolmogorov complexity. We propose precise notions of similarity metric, normal compressor, and show that the NCD based on a normal compressor is a similarity metric that approximates universality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (binary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis.

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。

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