Clustering by Compression

R. Cilibrasi, P.M.B. Vitanyi
2005 IEEE Transactions on Information Theory  
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 parameter-free, 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 not restricted to a specific application area, and works across
more » ... area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the non-computable notion of Kolmogorov complexity. We propose axioms to capture the realworld setting, and show that the NCD approximates optimality. 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. We give axioms determining a large family of compressors that both include most (if not all) real-world compressors and ensure the desired properties of the NCD to be defined later. Definition 3.1 A compressor C is normal if it satisfies, up to an additive O(log n) term, with n the maximal binary length of an element of Ω involved in the (in)equality concerned, the following:
doi:10.1109/tit.2005.844059 fatcat:imrem6kkszbfjhh6aom6udfhga