Benedetto, Caglioti, and Loreto Reply:

Abstract

Benedetto, Caglioti, and Loreto Reply: In [1] Khmelev et al. claim that [2] contains many misleading statements and that Markov chain approaches represent a more attractive technique than Lempel-Ziv (LZ)-based compression schemes.The authors recall the results of the experiments reported in [3] where it is shown that Markov chain based methods outperform gzip based methods. First of all, it is important to remember that in [3] an LZ-based scheme (rarw) outperformed the Markov chain approach. The generic claim made in [1] that the Markov chain approach outperforms LZ-based schemes is then not so general. On the other hand, in our opinion, even the claim that Markov chain approaches outperform gzip-based schemes is not well supported by the experiments presented in [3].In [3] the authors used a method which is slightly but crucially different from ours [2]. The authorship attribution of a text X is performed by comparing this file with one very long file per author to be used as the reference file (created by simply appending all the files of each single reference author in one single file) whose length is between 140 Kb and 6.9 Mb (average length 1.2 Mb). This procedure seems to us to be definitively wrong in the perspective of using the gzip compression scheme. Gzip has a sliding window of 32 Kb over which it looks for the longest matchings. Now, using as reference file a file longer than 32 Kb and appending to it the file X, only the last 32 Kb (which depend on the way the reference file has been created) are compared with the unknown file. Therefore most of the available information is lost. In our method [2] we use all the available files as reference files and we compare the unknown file X with all the other files. The indication of the authorship is given by the reference text closest to the unknown text.In order to show how this slight difference in the procedure could bring drastically different results we have performed two sets of experiments. The first experiment concerns the classification of a corpus of newsgroup messages widely used for the comparison of different approaches [4]. The rate of success is 60% with the method of [3] and 85% with our method. The second experiment concerned the data presented in [2]. In this case our prescription allows for 93% (84=90) of success, while with the prescription adopted in [3] we get a success rate of 77% (69=90).As for the usefulness of compression techniques for DNA analysis, in our opinion this is a very challenging field where it is almost impossible at present to say which method will be asymptotically successful. Just to give some examples, in [5] a method has been proposed to compress DNA sequences based on the backward search of approximate repeats. This allows one to define a distance between sequences useful to compare different genomes and build Phylogenetic trees.As for our definition of remoteness [Eq. (1) in [2] ] it is important to stress that relative entropy is a positive defined object. Since data compression schemes provide an estimate of...

Language Trees and Zipping

“…if most of the matches occur in the English part, the expression (1) will give a measure of the relative entropy. We have checked this method on sequences for which the relative entropy is known, obtaining an excellent agreement between the theoretical value of the relative entropy and the computed value [15]. The results of our experiments on linguistic corpora turned out to be very robust with respect to large variations on the size of the file b (typically 1 − 15 Kilobytes (Kb) for a typical size of file A of the order of 32 − 64 Kb).…”

“…it tends progressively to find most of the matches in the Italian part with respect to the English one, and changes its rules. Therefore if the length of the Italian file is "small enough" [15], i.e. if most of the matches occur in the English part, the expression (1) will give a measure of the relative entropy.…”

Measuring complexity with zippers

“…It is important to remark that the relative and cross entropies are not distances (metric) in the mathematical sense, since they are not symmetric and do not satisfy in general the triangular inequality. Defining a true distance between strings is an important issue both for theoretical and practical reasons (see for some recent approaches [11,12,13] and for a short review [21]). …”

“…Recently, a method has been proposed for the estimate of the cross entropy between two strings based on LZ77 [11]. Recalling that the cross entropy C(A|B) between two strings A and B, is given by the entropy per character of B in the optimal coding for A, the idea is that of appending the two sequences and zipping the resulting file A + B.…”

Testing time symmetry in time series using data compression dictionaries

“…This statement is technically only true asymptotically but in practice exceptions grow exponentially unlikely for mixing sources. This property concerning the relative entropy was recently used to distinguish and categorize natural languages from only representative samples of their texts [15], although there the slightly different algorithm was used and adaptation to the second sequence continued during its parsing, lowering the discrimination power somewhat.…”