Clustering by compression
Rudi Cilibrasi and Paul M.B. Vitanyi
IEEE Transactions Information Theory
Volume To Appear,
We present a new method for clustering based on compression.
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 in the sense that it minorizes
every computable normalized metric that satisfies a certain density requirement.
However, the optimality comes at the price
of using 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 optimality.
To extract a hierarchy of clustersfrom 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,
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.