Clustering by compression

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.Comment: LaTeX, 27 pages, 20 figure

Reducing the loss of information through annealing text distortion

Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Granados, A. ;Cebrian, M. ; Camacho, D. ; de Borja Rodriguez, F. "Reducing the Loss of Information through Annealing Text Distortion". IEEE Transactions on Knowledge and Data Engineering, vol. 23, no. 7 pp. 1090 - 1102, July 2011Compression distances have been widely used in knowledge discovery and data mining. They are parameter-free, widely applicable, and very effective in several domains. However, little has been done to interpret their results or to explain their behavior. In this paper, we take a step toward understanding compression distances by performing an experimental evaluation of the impact of several kinds of information distortion on compression-based text clustering. We show how progressively removing words in such a way that the complexity of a document is slowly reduced helps the compression-based text clustering and improves its accuracy. In fact, we show how the nondistorted text clustering can be improved by means of annealing text distortion. The experimental results shown in this paper are consistent using different data sets, and different compression algorithms belonging to the most important compression families: Lempel-Ziv, Statistical and Block-Sorting.This work was supported by the Spanish Ministry of Education and Science under TIN2010-19872 and TIN2010-19607 projects