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MSU-LGCLL:: O.V. Kukushkina, A.A. Polikarpov, D.V. Khmelev - Authorship Attribution through Using Information on Letters and Grammatical Constructions
O.V. Kukushkina, A.A. Polikarpov, D.V. Khmelev
USING LETTERS AND GRAMMATICAL STATISTICS
FOR AUTHORSHIP
ATTRIBUTION
Translation from Russian (being published
in the Journal "Problems of Transmitting of Information", Vol. 37,
№2, - Moscow, 2001)
In this paper the problem of identification of text's author is presented
as follows. Some large fragments of prose works by a number of authors
are given. These texts are in Russian or in different written
phonological (non-hieroglyph, non-character) language1.
An anonymous text known to be from one of these authors is disputed
between all of them. One have to predict the correct author.
D.V. Khmelev in [] has offered and
tested statistically a technique giving correct predictions
with quite a high probability. The technique chosen is based on
the data about usage of subsequent elements in the text (letters,
morphemes etc).
To the best of our knowledge, first attempts in the search of technique
for author authorship attribution was given in [].
Markov [] have almost immediately replied to [].
This shows that the founder of theory of Markov chains was
quite interested in this field. Notice also that the first
application of "events which are linked to a chain'' Markov described
in [], where he studied the distribution of vowels
and consonants among initial 20000 letters of "Evgenij Onegin''.
Modern methods of authorship attribution are reviewed for our country
in [,Chapter. 1] and good review of foreign papers is given
in []. Despite the huge variety of methods described, none
of them have been applied to a large number of texts. Often,
these methods are not automatic and require some human intervention
which makes the computing of a large number of large texts almost impossible.
Hence a question of generalization raises: can they
be used outside the situation they were developed for?
Until recent times the only exception was paper [],
where the chosen technique has been tested on a number of texts. They
examine the proportion of function words used by the author and find
that this proportion is stable for each author among a large number of Russian
writers of XVIII-XX century.
This technique has been applied in []
to the problem of determining plagiarism.
New method of authorship attribution for natural language texts
(actually, independent on a language), have been offered for the first time
by Khmelev in [].
New technique is based on the Markov model for the sequence
of letters (and any other elements) of texts, i.e., the sequence
of letters is considered as a Markov chain, where each letter (element)
depends on only on the preceding letter (element).
The matrices of transition frequencies of element (letter, grammatical code,
etc) pairs are calculated over all texts of each author.
Therefore we know (approximately) the probability of
transition from one letter to another for each author.
The true author of an anonymous text is calculated with the
principle of maximal likelihood, i.e., for each matrix we calculate
the probability of the anonymous text and we choose the author with
the maximal corresponding probability and the chosen author is
supposed to be the true author.
This method is amazingly precise as was shown in [],
where this method was applied to a large number of various texts.
The result becomes even more amusing if we recall that only
frequencies of letter pairs are taken into account.
Markov models of first and higher orders have been used in a large number of
works of 50-60 years of XX century in order to estimate
an entropy of various kinds of texts. A lot of those works
are described in [,Ch. 4.3].
But, none of works mentioned have raised a question of application
Markov chains for the problem of authorship attribution. Moreover,
a generally accepted viewpoint was that characteristics
of any fiction text measured through of letters and
letter pairs frequencies are close to average characteristics
of the language. Hence these characteristics are indistinguishable
from practical viewpoint (see [,footnote on the p.181]
and [,,]).
A principle of maximal likelihood also have never been applied in
authorship attribution because of the following reasons.
Firstly, computing of a large data was awkward until appearance of
computers and a large number of electronic texts. Secondly,
a kind of psychological barrier was in absence of underlying
theory, since Markov chain of first order is just a first and a very
bad approximation for a natural language text. This fact
is pointed out in many papers concerning estimating the texts entropy
via Markov chains of high order [,p.187]
Finally, in authorship attribution it was believed that there
exists stable quantitative characteristics for grammatical information,
and these characteristics are useful in distinguishing of writers. To
the best of our knowledge, until recent time the only significant
result for Russian language in this direction was obtained in [].
In this work we develop further a validation procedure
of method [] and apply the method of []
for different units of analysis:
(a) letter pairs in their natural sequences in a text, i.e.,
in words (as they appeared in the text) and spaces between them;
(b) letter pairs in sequences of letters in vocabulary form of words;
for example, the previous sentence
is reduced as follows "letter pair in sequence of
letter in vocabulary form of word''; for Russian texts this reduction is
much more significant, since Russian words have a lot of various forms.
(c) pairs of most generalized ("incomplete'') grammatical classes
of words and parts of speech in their sequences in sentences of the text.
In Russian, 14 parts of speech are traditionally assigned: nouns,
verbs, adjectives etc. We introduce the other 4 categories: "end of sentence'', "shortening'',
"unclear class'', "dash sign''.
A category "unclear class'' was introduced, since grammatical
classes were assigned automatically for more than 99%
of words, but some words (for example, misprinted) was not assigned
automatically, and hence, their grammatical class have not been clear.
(d) pairs of less generalized ("complete'') grammatical classes of
words, for example, animated noun, unanimated noun, qualitative adjective,
relative adjective, possessive adjective etc.
A full cross-validation was carried out over 385 texts of 82 writers.
Results are presented in Tables and .
The details of authors and texts are given in
Table ; the size of texts and the number
of texts per author are included.
To gauge the precision of the method one can calculate a percent
of correctly classified texts. The best
results were obtained in cases (a) and (b) (73% and 62% of
correct classification, resp.). 61%
of texts were correctly classified in case (c). For case (d)
results are much worse (4%).
In Section 2 principles and results of preprocessing are describes.
In Section 3 the procedure of cross-validation is described.
A detailed description of results is given in Section 4 with
presenting conclusions in Section 5. In Appendix written
by D.V. Khmelev, another approach to authorship attribution is
presented. This approach uses data compression algorithms.
After pre-processing the source corpora of texts was presented in
all forms (a)-(d).
In case (a) all words with unclear grammatical class were
omitted, i.e., words, not recognized automatically, were ignored
(and this is the main difference of present research
from []). These words are ignored, since
we are now able to compare results of case (a) with
results of case (b). Also, text
is converted into a sequence of words and delimiting spaces
without any formatting. All punctuation is removed. Finally,
words beginning with a capital letter are also omitted (in
particular, all first words of sentences are removed). It was shown
in [] that the last trick significantly
increases the precision of authorship attribution. There is a
conjecture that this improvement is implied by ignoring of
names of characters, that are usually not related to the style
of the author of the fiction text.
A letter "ë'' in Russian alphabet was glued with letter "e'',
and hence we had 33 characters including the space. Each letter was
encoded with its number: letter "a'' corresponding to 1, letter "ya'' corresponding to 32. The space is corresponding to 0.
The total number of letters in all texts is 96209964.
The total number of different pairs of letters found in the
corpora of text is 1011 (out of possible 33×33=1089).
Clearly, 1011 is larger than an actual number of different
letter pairs to be found in Russian texts. This is a result of
a number of misprints in electronic versions of books and this fact
can lead to errors in computations.
In order to obtain an estimate of this noise, there were selected
121 letter pairs such that their appearance in Russian text
is unlikely. In total, they were used 38495 times or 0,04%
of total size of the corpora, and hence they could be disregard.
Pre-processing of source corpora in cases (b), (c) and (d) is
carried out with help of automatic classifier developed
by O.V. Kukushkina at the Laboratory for General and
Computational Lexicology and Lexicography
of the Philological faculty at Lomonosov Moscow State University.
The classifier is based on the grammar
vocabulary of Zaliznyak []
and Academic grammar [,].
Case (c) is based on the information obtained from the most
general grammatical class of word form,
i.e., we use only information about part of the speech
(particles, prepositions, interjections, copulatives and
adversative conjunctions, other conjunctions, verbs, pronouns,
adverbs, adjectives, nouns, numerals, predicate nouns,
comparatives, modal adverbs).
Case (d) is based on the information obtained from
lexical and grammatical category of the given part of speech
(animated noun, unanimated noun etc)
Let us present some data about cases (b)-(d).
In case (b) the total number of letter is 110704464. There is
1029 different pairs of letters out of 33×33=1089. As one
can see, figures are increased w.r.t. case (a). This effect
is related to conversion of oblique forms to vocabulary ones.
In cases (c) and (d) the number of elements is 20262449.
In case (c) the total number of different pairs of elements is
302 out of possible 18×18=324. In case (d)
the number of different pairs of elements is 8124
out of possible 112×112=12544.
An analysis of texts in each case was carried out basing
on software developed by Khmelev.
For each case we present results of cross-validation
of the method of [].
Cross-validation is carried out as follows.
Let us recall that elements of texts are encoded with numbers
from 0 to 32 (in cases (a) or (b)), 17 or 111 (in cases (c)
and (d), respectively). Code 0 always corresponds to a delimiter
between large blocks, i.e., in cases (a) and (b)
code 0 corresponds to the space between words
and in cases (c) and (d) code 0 corresponds to delimiter
between sentences ("end of sentence'').
Given W writers each of which has Nw texts,
where w=0, ..., W-1, we count
Qijwn which is the number of transitions from letter
i to letter j for text n (n=0, ..., Nw-1) from
writer w (w=0, ..., W-1).
In order to find the predicted author for text [^n]
(of known author [^w]) using information about authorship
of the other texts for all authors including [^w],
we have
Qijk=
Nw-1 е
n=0
Qijkn, Qik=
е
j
Qijk
for authors k № [^w],
and for author [^w] we exclude text [^n]
from a training set
Qij[^w]=
е
n № [^n]
Qij[^w]n, Qi[^w]=
е
j
Qij[^w].
We then have
Lk (
^
w
,
^
n
) = -
е
i: Qik > 0
е
j: Qijk > 0
Qij[^w] [^n] ln
Qijk
Qik
and
L[^w] (
^
w
,
^
n
) = -
е
i: Qi[^w] > 0
е
j: Qij[^w] > 0
Qij[^w] [^n] ln
Qij[^w]
Qi[^w]
.
Ignoring degenerate cases
Qkij=0 and Qki=0, one can see that
each Lk([^w],[^n]) is the minus logarithm
of the probability of the text [^n] from writer [^w],
when the text [^n] from writer [^w] is
generated by the Markov chain with transition probabilities
Pkij=Qkij/Qki. The hint to ignore the
degenerate summands is given by results about
optimal maximal likelihood estimate, given
in [,p.224].
We also define rank Rk([^w],[^n]) to be the
rank of
Lk([^w],[^n]) in {Lk([^w],[^n]), k=0,ј, W-1}, where the smallest rank is 0, i.e.,
Rk([^w],[^n]) О {0, ј,W-1}, and
the smallest number has the smallest rank. If the text is assigned
to the correct author, then R[^w]([^w],[^n])=0.
If the text is assigned to the other author, and the
correct author is second among other pretenders, then
R[^w]([^w],[^n])=1 etc.
A result of cross-validation is a set of ranks
{R[^w](
^
w
,
^
n
)}[^w] О {0,ј,W-1},[^n] О {0,ј,N[^w]-1}.
The precision of the technique for authorship attribution
is measured by this set of numbers. The proportion of
correct predictions is the proportion of zero ranks.
When the true author was close to be correctly predicted,
we have small ranks. Another measure of the precision
of the technique for authorship attribution is given by
average rank
M=
1
W-1 е
[^w]=0
N[^w]
W-1 е
[^w]=0
N[^w]-1 е
[^n]=0
R[^w](
^
w
,
^
n
).
(1)
We shall also present results of cross-validation
in case of analysis of individual letters (in cases (a) and (b))
and individual grammatical classes (in cases (c) and (d)).
All the calculation are the same, but we additionally
calculate
Qk=
е
i
Qkiand Q[^w]=
е
i
Q[^w]i
and the following quantaties Gk([^w], [^n]) are used
instead of Lk([^w], [^n]):
Table 1: Full cross-validation of the authorship attribution
based on the sequence of letters
Case (a)
Case (b)
Words as
appeared in the text
Words in
vocabulary form
R
Letters pairs
Individual
R
Letter pairs
Individual
0
282/385
27/385
0
240/385
12/385
1
21/385
55/385
1
29/385
40/385
2
9/385
25/385
2
17/385
19/385
3
5/385
24/385
3
9/385
16/385
4
5/385
17/385
4
6/385
16/385
і 5
63/385
237/385
і 5
84/385
282/385
M
3,38
12,69
M
4,77
17,88
Table 2: Full cross-validation of the authorship attribution
based on the sequence of grammatical classes
Case (c)
Case (d)
Generalized
grammatical classes
"Complete''
grammatical classes
R
Pairs
Individual
R
Pairs
Individual
0
235/385
128/385
0
15/385
6/385
1
31/385
43/385
1
21/385
12/385
2
16/385
29/385
2
9/385
6/385
3
8/385
15/385
3
12/385
6/385
4
11/385
17/385
4
19/385
8/385
і 5
84/385
153/385
і 5,
309/385
347/385
M
5,43
10,13
M
17,76
31,93
The results of the research are presented in
Tables 1, 2. The column R corresponds to ranks
0, ..., 4 and ranks, exceeding 4.
The row with rank 0 contains the proportion of correctly
assigned texts. The row with rank 1 contains the proportion
of texts such that the correct author was the second among
the other pretenders etc. Finally, the row і 5 contains
the proportion of texts such that the correct author was on the
place not better than 6.
The row M contains the average rank, determined by (1).
Straight away notice that the frequencies of individual letters
and individual grammatical classes gives low but significantly
non-random level of correct authorship attribution (except
the case of individual "complete'' grammatical classes, the reasons
of bad results are to be studied).
All calculation with pairs of elements (letters or grammatical classes)
gives a better result w.r.t. calculations with individual letters or
grammatical classes.
Let us now study the difference in results of analysis
using information about usage of letter pairs in words as they
appeared in the text and letter pairs in vocabulary forms of words.
Comparison shows that the success rate of
the authorship attribution is better in the case
of natural sequences of letters in the text (there are 73% against 62%
of correct authorship predictions and average rank is 3,38
against 4,77). Perhaps, an "equalization'' of different forms
for a word reduced to vocabulary form eliminates
some information useful for authorship attribution and leads
to fall in success rate in case (b) w.r.t. case (a).
Comparison of results of authorship attribution using
information of pairs of letters and pairs of generalized ("incomplete'')
grammatical classes (cases (a) and (c)) shows that the success rate
in both cases is quite high, i.e., we have 73% and 61%
correctly classified texts, respectively. An average rank of correct
authorship attribution falls in 2 ranks from letter pairs to
generalized grammatical classes. Perhaps, a relatively
lower efficiency of pairs
of grammatical classes (in comparison with letter pairs for
words as they appeared in the text) on the same data set is concerned
with smaller magnitude of sample size on the grammatical classes
(let us recall that on the same corpora of texts there
are 96 millions of letter usages in case (a) and there are
20 millions of grammatical classes usages in case (c)).
Also, it pays attention that the usage of individual
grammatical classes in case (c) (see Table 2)
is significantly more effective than usage of individual letters:
there are 33% of correct authorship attributions
in case (c) against 7% in case (a).
The average rank in case (c) is two and a half times less than
the average rank in case (a). Perhaps, this result is concerned with
more specific information (more precisely characterising
stable structure characteristics of texts for each author) given
by individual grammatical codes in contrast to individual
letters.
"Complete'' grammatical classes were the most ineffective
in authorship attribution either in case of pairs frequencies
or in case of individual frequencies. The reasons for this results
are to be studied.
The details about authors of the corpora of texts, the
number texts per author, the dispersion of text sizes
with minimal, average (in brackets) and maximal size, results
of authorship attribution in all four cases ((a)-(d))
with minimal, average (in brackets) and maximal rank of the text
examined on its author are given in Table .
The corpora also containes some translated texts (S. Lem,
I. Khmelevskaja, B. Rajnov). It is interesting that
the quality of attribution of these texts is not worse than
texts, written by authors whose mothers language is Russian
(although corpora contains Lem's translation by different
interpreters)
Table 3: The number of and size of texts in corpora by author
The main result of carried-out research is that
the usage of grammatical information in authorship attribution
is not only useful, but is efficient and even is comparable
with usage of information about letter pairs frequencies
(the effectiveness of the last method was shown before in []).
At the same time it is still amazing that the usage of such a
seemingly simple unit as a pair of subsequent letters in the text
gives more precise results than the usage of such a language categories
as individual grammatical codes and their pairs. Perhaps,
letter pairs contain a kind of converted and incomplete
information about structure of morphemes of words as they appeared
in the text (prefixes, roots, suffixes and inflexions).
Therefore, a lot of information about words changing and formation
is contained in statistics of usage of letter pairs and this leads
to quite a high efficiency of letter pairs statistics for authorship
attribution.
In other words, the letter pairs frequencies take into account
the vocabulary used by the author and by implication it takes
into account information about preferred grammatical structures.
Although the differences in usage of particular pairs of letters
are likely to be non-significant (since they are converging
to average frequencies for the language, as it was noticed
by Markov [] long ago), the maximal "likelihood''
takes into account the "total'' effect in changing of usage
of pair of letters and nevertheless it provides a high precision in
assignment of the text to the correct author, as it was
shown before in [] and as it
was approved in this research by full cross-validation.
However, the further experiments with grammatical classes of
words with more precise grammatical analysis would probably lead
to a higher success rate in assigning of correct author than
it was achieved in this research. Perhaps, the usefulness of usage
of grammatical information is shown in the observation that
the usage of information on individual generalized grammatical classes
is significantly more effective than the usage of information
in individual grammatical classes.
Since results with usage of different units (letters and generalized
grammatical classes) are compatible with each other, one can assume
that future well-developed methods for authorship attribution will
use different representation of the text, obtained with this units,
for mutual cross-validation of results.
Appendix. Application of Data Compression Algorithms
in Authorship Attribution.
In this Appendix it is shown how one could use data compression
algorithms for authorship attribution. Also results of
cross-validation for this new method are given. Here
we use the corpora of texts used in [] and
in the main body of the article.
The corpora of texts in [] is obtained from 82
authors. One randomly-chosen text from
each author is held out to make up a test set. The other texts
are used as the learning sample. Afterwards all the control
texts were classified and the correct author was assigned in
69 cases. To estimate how good is this result in terms of
probability of correct authorship attribution let
us consider the following hypothesise situation.
Suppose that we have a black box such that given two texts
it produces 1 if these texts are of the same author and
0 if these texts are definitely of different authors.
Suppose that the level of alpha and beta
errors for each trial is 0 < p < 1. One can apply
the black box assigning an anonymous text to correct author as follows.
Given 82
alternatives and one anonymous text, this black box should
produce 81 zeros corresponding to comparison
of the control text to learning samples of wrong authors and only one 1
corresponding to comparison of the control text to the correct author.
Of course, all other outcomes are considered as misclassification.
Assume that results for each of these pairwise comparisons are
independent of each other. Then, the probability of correct
classification is (1-p)82. For alpha-beta error p=0,05 we have
(1-0.05)82 » 0.015, p=0,01 corresponds to
(1-0,01)82 » 0,439 and for p=0,005
we obtain (1-0,005)82 » 0,663. Notice that
69/82 » 0,84 and if we want to surpass the method of
Khmelev (2000) in quality of recognition, we should require that, for example,
p=0,001 and it turns out that (1-0,001)82 » 0,921.
Therefore 69 correct classifications with choice among 82 writers
should be considered as an extremely good result. With certain
reservations this argumentation is applicable to the results of the
main text of the article.
Here by text we understand a sequence of letters from some alphabet
A. Denote by |B| the length of text B. Let us call a
concatenation of texts A and B the sequence S of length
|B|+|A| such that first |B| letters of S coincide
with B and the last |A| letters of S coincide with A. We
shall write S=B.A.
Now let us give an "ideal'' definition of relative complexity
following definition of Kolmogorov complexity
(see [,]):
the relative complexity K(A | B) of text A
w.r.t. text B is the length of shortest program in
binary alphabet which translates text B to the text A.
Unfortunately, K(A | B) is
not computable and it is not clear, how can one use it.
A first approximation to K(A | B) (however, it is
enough for authorship attribution as we shall see later)
could be obtained from data compression algorithms.
Let us define the relative complexity C(A | B)
of text A w.r.t. text B as follows.
Compress
text B to a text Bў and text S=B.A to a text Sў. Now put
C(A | B)=|Sў|-|Bў|.
This definition is ambiguous since we have not not fix the data
compression algorithm. All algorithms
used in this research are described later.
We shall apply C(A | B) for authorship attribution.
Given texts from n authors, form a test set by
holding out one control text from each author U1, ..., Un.
The other texts of each author are concatenated in texts
T1, ..., Tn.
The predicted author for text Ui is determined as follows.
Firstly, find the rank Ri of a number C(Ui | Ti) in
set {C(Ui | T1), ј, C(Ui | Tn)},
where ranks take values from 0 to n-1. If rank Ri equals 0,
then the control text Ui is correctly assigned.
Like [] one can introduce different
measures of precision for the method
of disputed authorship resolution.
For example,
1. The simplest measure - a number of zero ranks Ri;
2. More generalized measure is given by an average rank
M=
1
n
n е
i=1
Ri.
Cross-validation of different data compression algorithms is
carried out on the corpora of texts used in []
and in the main body of this paper.
Let us recall, that the corpora consists of
385 texts from 82 writers. The total size of texts is about 128
million letters. Some pre-processing of texts was carried out.
Firstly, all words carried over to the next line
were restored. Further, words beginning with capital letter
were omitted. The other words were kept in the order as they appeared
in the text. They were delimited by new-line character.
A control text Ui was selected from texts of each of n=82
authors. The other texts of each author was concatenated into texts
Ti, i=1, ..., 82.
The size of each Ui was not less that 50-100 thousand letters.
Let us consider lossless data compression algorithms.
The following algorithm have been most popular recently:
Huffman coding, arithmetic coding, Burrows-Wheeler technique []
and lot of variations of Lempel-Zip coding [].
Some algorithms are specially aimed on text coding: these are PPM []
(this algorithm uses Markov model of small order)
and DMC [] (this algorithm uses dynamical Markov Coding).
Each algorithm has huge number of
variations and parameters (for example, there exists so-called dynamic
Huffman coding, also the size of vocabulary varies etc).
Moreover, there exists a lot of "mixed''
algorithms, when the text obtained with PPM compression is
additionally compressed by Huffman coding.
All these algorithm are found in huge variety of compression programs,
whose number exceeds 150. Each of those programs implements
different data compression algorithm. More variety appears because
of multiple versions of data compression programs with
different data compression algorithms. All programs selected
in this research are shown in Table .
Most of these programs with their descriptions can be obtained
from Archiver
index2
supported by Jeff Gilchrist3.
Program compress was taken from SunOS 5.6 operating system.
Program dmc is available by ftp4.
Notice that the program dmc has an
option of maximal memory to use. In this research this optoin was set to
100000000 bytes.
LDS 1.1 is a lossless data compression sources kit and it is also available
by ftp5.
Program ppm is available from
personal page of
its author6.
The results of application of these programs are given in
Table . The last line of Table
contains results of application of Markov chains []
on the same corpora of texts. Computations for data shown in
Table were performed under different operation
systems on different types of computers and took about
three weeks of non-stop computing.
Table 5: The precision of authorship attribution through using
data compression algorithms
Program
Rank
0
1
2
3
4
і 5
M
7zip
39
9
3
2
3
26
6,43
arj
46
5
2
7
2
20
5,16
bsa
44
9
3
1
1
24
5,30
bzip2
38
5
5
1
33
13,68
compress
12
1
1
3
2
63
24,37
dmc
36
4
3
4
4
31
9,81
gzip
50
4
1
2
1
24
4,55
ha
47
8
1
3
3
20
5,60
huff1
10
11
4
4
2
51
15,37
lzari
17
5
4
2
6
48
14,99
lzss
14
3
1
1
3
60
20,05
ppm
22
14
2
1
3
40
10,39
ppmd5
46
6
6
2
22
5,96
rar
58
1
1
1
21
7,22
rarw
71
3
2
1
5
1,44
rk
52
9
3
1
17
4,20
Markov Chains (see [])
69
3
2
1
7
2,35
It follows from the data of Table 5
that data compression algorithms assign correct author
to control text quite often. Therefore they are undoubtfully
useful.
Notice that application of the program rarw
yields even better results than results obtained with
help of Markov chains in [].
Although such a superiority could be related to
some statistical mistake, it is the best result
achieved recently.
Perhaps an explanation of such a splendid results is as follows.
Data compression algorithms actually adapts well to the control text
after pre-processing of texts of correct author and adaptation
is not so good if the texts of different author
have been pre-processed.
The disadvantage of this method with respect to method of Markov
chains [] is that data
compression algorithms are not so clear
and they are even not available for study in commercial software.
Nevertheless, a lot of programs among presented in Table 4
has an open source code and well-described open algorithms.
The further study of those programs could open the reasons for
the efficiency of complexity approach to authorship attribution.
Notice that the authorship attribution technique described here
does not require any special programs
when one chooses the correct author among small number of pretenders.
A great advantage of the method presented
is its availability on almost every computer,
since most of compression programs mentioned here are widely spread
and some of them (like gzip or rar) are implemented
for all types of computers and for all operation systems.
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Footnotes:
1Written
non-character (non-hieroglyph) texts are mentioned, since character
written language reduces opportunities in analysis of subsequent
elements because of very implicit phonological data (telling apart
morphemes)