Abstract—We present a new method for clustering based on compression. The method does not 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 application 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 noncomputable notion of Kolmogorovcomplexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary 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. Index Terms—Heterogenous data analysis, hierarchical unsupervised clustering, Kolmogorovcomplexity, normalized compression distance, parameter-free data mining, quartet tree method, universal dissimilarity distance. I.

All musical pieces are similar, but some are more similar than others. Apart from serving as an infinite source of discussion (‘‘Haydn is just like Mozart—No, he’s not!’’), such similarities are also crucial for the design of efficient music information retrieval systems. The amount of digitized music available on the Internet has grown dramatically in recent years, both in the public domain and on commercial sites; Napster and its clones are prime examples. Web sites offering musical content in some form like MP3, MIDI, or other, need a way to organize their wealth of material; they need to somehow classify their files according to musical genres and subgenres, putting similar pieces together. The purpose of such organization is to enable users to navigate to pieces of music they already know and like, but also to give them advice and recommendations (‘‘If you like this, you might also like...’’). Currently, such organization is mostly done manually by humans, or based on patterns in the purchasing behaviors of customers. However, some recent research has been examining the possibilities of automating music classification. A human expert, comparing different pieces of music with the goal of clustering similar works together, will generally look for certain specific similarities. Previous attempts to automate this process do the same. Generally speaking, they take a file containing a piece of music and extract from it various specific numerical features, related to pitch, rhythm, harmony, etc. One can extract such features using, for instance, Fourier transforms (Tzanetakis and Cook 2002) or wavelet transforms