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Disputed Authorship Resolution Using
Relative Empirical Entropy For Markov Chain
of Letters in a Text
D.V. Khmelev
25 August 2000
AFFILIATION: Heriot-Watt University, Edinburgh, U.K. and Isaac Newton
Institute for Mathematical Sciences, Cambridge, U.K.
POSTAL ADDRESS: 20 Clarkson Road, Cambridge, CB3 0EH, U.K.
FAX NUMBER: (01223) 330508
E-MAIL ADDRESS: D.Khmelev@newton.cam.ac.uk
A new statistical method in the analysis of literary style for disputed
authorship resolution is considered here. It was tested in the following ex-
periment.
We take a training set of 304 text samples (novels, stories and short
stories) of 82 dierent authors in Russian. The total size of training text
samples for each author exceeds 100,000 symbols. We also take one control
text sample per each author. The size of the control sample exceeds 100,000.
The total volume of text samples is about 120Mb.
Each control text is considered to be anonymous. Our method determines
the true author for 69 control texts. In 3 (resp. 2, 1) cases the true author
is second (resp. third, fourth) in the list of pretenders to its own text. Note
that the analysis of frequencies of isolated letters guesses the true author for
just 2 control texts.
Let us describe the method in detail. Consider a sequence of letter of text
as a Markov chain. The matrices of transition frequencies of letters pairs are
calculated over all texts for each author. Therefore we know (approximately)
the probability of transition from one letter to another for each author. The
author of the control text is guessed by the principle of maximal likelihood,
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i.e., for each matrix we calculate the probability of anonymous text and we
choose the author with the maximal corresponding probability. The chosen
author is supposed to be the true author.
Suppose we take the logarithm of each probability, change a sign, and
divide it by the length of control text; then each of the numbers obtained is
called the relative empirical entropy. Relative empirical entropy is more con-
venient for computing than actual probabilities. Besides, the chosen author
(who often happens to be a true author) has the minimal relative entropy.
Now we shall give a list of 82 authors included to the experiment. There
are a lot of well-known Russian writers of the XIX and XX centuries among
them: K. Bulychev, O. Avramenko, A. Bol'nykh, A. Volkov, G. Glazov,
M. i S. Djachenko, A. Etoev, A. Kabakov, V. Kaplan, S. Kazmenko, V. Klimov,
I. Krashevskij, I. Kublickaja, L. Kudrjavcev, A. Kurkov, Ju. Latynina, A. Lazare-
vich, A. Lazarchuk, S. Lem, N. Leonov, S. Loginov, E. Lukin, V. Chern-
jak, A.P. Chekhov, I. Khmelevskaja, L. and E. Lukiny, S. Luk'janenko,
N.Ju. Markina, M. Naumova, S. Pavlov, B. Rajjnov, N. Rerikh, N. Roma-
neckijj, A. Romashov, V. Rybakov, K. Seramov, I. Sergievskaja, S. Scheglov,
A. Schegolev, V. Shinkarev, K. Sitnikov, S. Snegov, A. Stepanov, A. Stol-
jarov, R. Svetlov, A. Sviridov, E. Til'man, D. Truskinovskaja, A. Tjurin,
V. Jugov, A. Molchanov, F.M. Dostoevskij, N.V. Gogol', D. Kharms, A. Zhitin-
skij, E. Khaeckaja, V. Khlumov, V. Kunin, A. Melikhov, V. Nabokov, JU. Nikitin,
V. Segal', V. Jan, A. Tolstoj, I. Efremov, E. Fedorov, O. Grinevskij, N. Gu-
milev, L.N. Tolstoj, V. Mikhajlov, Ju. Nesterenko, A.S. Pushkin, L. Reznik,
M.E. Saltykov-HHedrin, V. Shukshin, S.M. Solov'ev, A. Kac, E. Kozlovskij,
S. Esenin, A. Strugackij, A. and B. Strugackie and B. Strugackij.
Note that transition frequencies of letter pairs are frequent, easily quan-
tiable and relatively immune from conscious control. The author of this
study performed the same computations on English, French, and German
texts and received similar results. Its description needs a separate paper
and is beyond the scope of this short thesis. Clearly, further studies in this
direction may be the best approach to \stylometry's `holy grail', the fully
automated identier" (Holmes, 1998).
Holmes, D.I. (1998) The Evolution of Stylometry in Humanities Scholarship.
Literary and Linguistic Computing, 13: 111{17.
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