Clustering by compression

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...

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Veröffentlicht in:IEEE transactions on information theory Jg. 51; H. 4; S. 1523 - 1545
Hauptverfasser: Cilibrasi, R., Vitanyi, P.M.B.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.04.2005
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Application software
Astronomy
Axioms
Bioinformatics
Cluster analysis
Clustering
Clustering methods
Compressing
Compressors
Computer programs
Data compression
Data mining
Dictionaries
Exact sciences and technology
Genomics
Heterogenous data analysis
hierarchical unsupervised clustering
Information theory
Kolmogorov complexity
Mathematics
normalized compression distance
Numerical analysis
Numerical analysis. Scientific computation
Optimization
Optimization techniques
parameter-free data mining
quartet tree method
Robustness
Sciences and techniques of general use
Similarity
Sorting
universal dissimilarity distance
Cluster analysis
Data analysis
Tree structured method
Similarity
Data compression
Unsupervised classification
Data mining
normalized compression distance
hierarchical unsupervised clustering
parameter-free data mining
Kolmogorov law
Kolmogorov complexity
universal dissimilarity distance
quartet tree method
Heterogenous data analysis
ISSN:0018-9448, 1557-9654
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Beschreibung
Zusammenfassung: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 Kolmogorov complexity. 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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.844059