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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Development and Implementation of the Algorithm for Automatic Analysis of Metrorhythmic Characteristics of Russian Poetic Texts</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vladimir Barakhnin</string-name>
          <email>bar@ict.nsc.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olga Kozhemyakina</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Irina Kuznetsova</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute of Computational Technologies SB RAS</institution>
          ,
          <addr-line>Novosibirsk</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Novosibirsk State University</institution>
          ,
          <addr-line>Novosibirsk</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <fpage>290</fpage>
      <lpage>298</lpage>
      <abstract>
        <p>This paper presents the implementation of the program module responsible for the analysis of the structural level - the definition of the poem's metrorhythmics (meter, number of feet, and rhyme) in Russian poetic texts. The algorithm for determination of meter and number of feet takes into account the problem of the ambiguity of the placement of emphasis in homographs, possible omissions of schematic emphasis (pyrrhic), overlay of over schematic emphasis (spondee), which are solved by method “by analogy”. The algorithm to identify the cases of shifting the emphasis from one part of speech to another (proclitic) is described. The algorithm of rhymes search is presented, the result of which is the definition of the stanzas of the poem.</p>
      </abstract>
      <kwd-group>
        <kwd>analysis of poetic texts</kwd>
        <kwd>meter definition</kwd>
        <kwd>metrorhythmic analysis</kwd>
        <kwd>rhyme identification</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>The compilation of metric reference books to the corpus of poems is an important task
of Russian literary researches. At the moment, the development of information
technologies allows to automate the analysis of poetic texts, which in turn will reduce the
amount of routine work of philologists. To solve this problem, it is necessary to develop
algorithms for automating the analysis of the structural level of the poetic text,
including the following metrorhythmic characteristics: meter, number of feet (foot – the basic
unit of measurement of accentual-syllabic meter), rhyme.</p>
      <p>
        Among similar works for other languages the system “SPARSAR” [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] can be
identified, which provides automatic analysis of poetic texts in English and Italian. This
system performs analysis at the quantitative, syntactic and semantic levels using NLP
(Natural language processing). The obtained data are visualized in the form of
developed schemes that allow comparing the works of one poet with each other and the
works of different poets. The works of William Shakespeare, Thomas S. Eliot and
Sylvia Plaza were used as a test sample. The program determined the size of their works
with an accuracy of 90%. The system analyzed 500 poems, then the expert checked the
accuracy of the analysis of 50 randomly selected poems. 5% of errors were detected.
      </p>
      <p>
        In work [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] the static methods for the analysis, generation and translation of rhythmic
poetry were used. The authors used machine learning without a teacher (unsupervised
learning) to identify the patterns of stress placement in the number of poems to
supplement in doubtful cases the proposed rhyme model. The authors also conducted
experiments on the generation of English-language love lyrics and translations of Italian
poetry into English with the preservation of the desired rhythmic scheme. The authors
used 5 Shakespeare sonnets (70 lines) as a test sample; 81.4% of lines (57 lines) were
correctly classified by metrorhythmics.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], the authors have classified the texts according to the meter. They used an open
source “the Scandroid” [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] to extract features (the program contains an algorithm for
determining the stress in words and its own dictionary with accentuation of words –
exceptions) and machine learning to classify poems by meter. Also in this work was
implemented a module that defines the rhyme using the dictionary “The Carnegie
Melon University Pronouncing Dictionary” [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] as a source of information about the
pronunciation. To determine the accuracy of the work the sample of 205 poems was
used, 88% of the words were correctly divided into syllables, the number of feet was
determined with an accuracy of 99%.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] the corpus of poems was analyzed using the “connectionist model” of poetic
meter. It was shown that the prosodic picture of the poetic text is individual, and it is
possible to determine the author by it, as well as that it reflects the aesthetics of the
period of the author's creative work. As a test sample, a number of 1000 lines (100 lines
by ten different authors) was used. The software package for statistical data processing
SPSS Statistics was applied for the analysis [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>
        In the work [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] it is described how to create software to determine the quantitative
characteristics of the style of American poets and the visualization of a collection of
poems in relation to each other. To visualize the obtained metrics, the authors used the
principal component analysis and Classical Multidimensional Scaling.
      </p>
      <p>It should be noted that it is impossible to design a universal system of automatic
analysis of meter and rhythm, suitable at least for a group of more or less similar
languages, because each language requires the development of its approaches, taking into
account its structure. Such an experiment was conducted for similar in structure (Latin
and Greek) languages, but even in this case, the study revealed features of languages,
because of which their joint analysis is impossible [9, p. 52–54].</p>
      <p>
        Finally, although in the analysis of the lower levels of the structure of the Russian
verse the simplest mathematical approaches have been used for a long time – for
example, numerous studies of the statistics of the types of Russian rhyme (including those
applied to the temporal dynamics), generalized in [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], but often the collection of
statistical information is still carried out almost manually (except for content analysis).
      </p>
      <p>
        Some studies describing an integrated approach to automating the characteristics of
Russian poetic texts (for example, [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]), affect, as a rule, very specific genres of poetry
– for example, folk poetry, structural characteristics of which, such as metric, themes,
etc., are significantly different from the corresponding structures in “literary” verse, or
are of a rather private nature: the quantitative analysis of semantic associations of
pentameter on the material of a number of Russian poets studied by M. L. Gasparov [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ],
the effect of metrorhythmic on semantics in the work of I. A. Brodsky – by M. Yu.
Lotman [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], the metric halo’s of “Black shawl” by A. S. Pushkin – by M. Wachtel [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ],
etc. The similar studies in relation to Czech poetry were conducted by M. Chervenka
(see, for example, [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]).
      </p>
      <p>
        For the analysis of the structural level of Russian poetic texts there are no practically
implemented systems (at least in the open access), except for the pilot project of the
system [
        <xref ref-type="bibr" rid="ref15 ref16">15, 16</xref>
        ], developed at the Institute of Computing Technologies of SB RAS.
      </p>
      <p>
        The algorithm from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] is at the core of this system, but it has several disadvantages,
for example, does not take into account unequal meter of the poem, while in
syllabictonic versification, there are meters, like the free amphibrach, choree, pentameter,
characterized by a different number of feet in lines. In addition, the usage of the algorithm
in its “pure” form, without taking into account the possible ambiguities of automatic
accentuation, gives a relatively high percentage of errors in determining of the number
of feet.
      </p>
      <p>
        For these reasons, it was decided to implement the algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ], which
includes a more strict classification of poems by meter. However, it does not affect such
problems as ambiguous accentuation of homographs and clitics, so it also needs some
modification. This study describes the development and implementation of the
algorithm for analyzing the structural level: meter, number of feet, and rhyme; the
modifications of the algorithm [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ], features of its implementation and results are presented.
The results of the work of two systems are compared: the one, which is developed on
the basis of a modified algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ], and the one which is already existing on
the basis of the algorithm from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ].
2
      </p>
    </sec>
    <sec id="sec-2">
      <title>The Algorithm for Determining the Meter and Number of Feet</title>
      <p>
        Let’s describe the steps of the algorithm for determining the meter and number of feet,
presented in [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ]. The essence of this algorithm is to compare the rhythmic variants of
the verse of the studied poetic text with a set of rhythmic patterns from a certain
repertoire of metrorhythmic variants of the verse. This algorithm consists of five steps:
1. The pre-processing of a text. The lines of poetic text are numbered (St(n)), and
PT={St(n)}, n=1, 2, …, N, where N is the total number of lines. All
punctuation marks are deleted.
2. The accentuation is carried out on the basis of the dictionary A.A. Zaliznyak
[
        <xref ref-type="bibr" rid="ref19">19</xref>
        ], which contains the accented word forms.
3. Each word of poetic text is divided into syllables and translated into a
sequence of characters “c” and “C”, denoting unstressed and stressed syllables
respectively. The spaces between words are removed to display the syllabic
scheme Sl:
      </p>
      <p>Sl =
=  1 …   (0)  1 …   (1) …    1 …   ( ) …  −1  1 …   (−1 )   1 …   ( ), (1)
where с ( ) is the unstressed syllable of the i-th word, i∈[0,k], Ci is the
stressed syllable of the i-th word at i∈[0, k], k is the number of stressed
syllables;
Scheme (1) is converted into syllabic rhythmic scheme Rs:
Rs =   (0) 1  (1) …     ( ) +1 …  −1   (−1 )    ( ),
(2)
where k is the number of stressed syllables in the string, R is the number of all
syllables in a line, r(i) is the interaccent interval, where i∈[1,k–1], r(0) and
r(k) is the anacrusis and the clause. After that, the parameters k, r(i), R-r(k) are
extracted, what further determine the type of rhythmic scheme of a poem.
The selection of the terms of classification of poetic text by metrorhythmic
based on existing principles of versification. Depending on whether the
parameters k, r(i), R-r(k) take constant or non-constant values for different foot
lines, the authors formulate 5 classification conditions that can be
implemented in Russian versification (Table 1).</p>
      <p>The first condition describes the often encountered type – syllabic-tonic versification
with violation of the number of feet in the line – free syllabic-tonic versification. The
second and third conditions of classification describe verses with specific
metrorhythmics, and in this work will not be considered. The fourth condition classifies the verses
with ideal meter without breaking the rhythm caused by omissions of schematic
emphasis or overlay of over schematic emphasis. This kind of metrorhythmics are rare,
because most poems contain alternating male and female rhymes, which automatically
violate the condition of the constancy of the parameter R - r(k) (see Table 1). Most
poetic texts contain disturbances in the rhythm; and are described in the algorithm of
the fifth condition for classification as isosyllabic poems.</p>
      <p>In the framework of this research the implementation and testing of the first and fifth
conditions according to the classification of poetic text in metrorhythmic schemas was
carried out.</p>
    </sec>
    <sec id="sec-3">
      <title>Modification of the Meter and Number of Feet Detection</title>
    </sec>
    <sec id="sec-4">
      <title>Algorithm</title>
      <p>This paper proposes a number of modifications to optimize the algorithm to improve
the accuracy in the analysis of poetic texts.</p>
      <p>
        Modification 1. The algorithm [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] assumes an “ideal” accentuation of words and
completely ignores the existence of problems related to the omissions of schematic
emphasis (pyrrhic). An example of pyrrhic can be shown in the quatrain of “Eugene
Onegin”:
Мой дядя самых честных правил,
Когда не в шутку занемог,
Он уважать себя заставил
И лучше выдумать не мог.
      </p>
      <p>That quatrain will translate into:
сС сС сС сС с
сС сС сс сС
сс сС сС сС с</p>
      <p>Only the first line of the scheme is strictly maintained (iambic tetrameter), and in
others there are three accents, the one is missing. In the case of missing of the metric
stress there is a special auxiliary foot of two unstressed syllables – pyrrhic (сс), which
can replace the foot of iamb and of choree (e.g «Нет, не черкешенка она» from the
“Answer to F.T.” by A.S. Pushkin).</p>
      <p>
        The algorithm [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] does not consider the overlay of over schematic emphasis
(spondee), an example of which is illustrated by line «Швед, русский, колет, рубит, режет»
from the “Poltava” by A.S. Pushkin with the scheme: сс сС сС сСс, the transfer of the
emphasis from one part of speech to another (proclitic: «уронили мишку нА пол»)
and homographs («чЕстных», «честнЫх»).
      </p>
      <p>
        These problems are solved by the method “by analogy”, the idea of which in relation
to this problem was expressed in [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. The essence of the method is the following: lines
and stanzas with ambiguous accent arrangement are compared with lines and stanzas,
in the words of which the stress is placed unambiguously, and the choice of accent is
made, providing the unity of metric characteristics for the whole poem.
      </p>
      <p>To implement this method, when the poetic text is translated into a sequence of
characters “c” and “C” (denoting unstressed and stressed syllables, respectively) in words
with an ambiguous arrangement of accent, the positions of all possible variants of the
accent are denoted by the symbol “x”. Thus, the text is represented as a table of
characters “C”, “c”, “x” of dimension n (the number of lines of poetic text) on m (the line
with the maximum length).</p>
      <p>Further, to eliminate the ambiguity of the accent arrangement in each line of the
table, the element “x” is searched and the column of the table is taken by the index of
this element. In this column, the most common single element is looked for and its
value is assigned to the element “x”.</p>
      <p>
        The algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] does not consider the proclitics (the pulling the accent on
the preposition, for example, in the poem “Teddy Bear” by A. Barto – «уронили
мишку нА пол»), so the database of proclitics on the basis of the dictionary of
A. Zaliznyak [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] has compiled, To resolve the ambiguities associated with proclitics.
It contains the information on the variants of accentuation of combinations of some
words and prepositions. The text is analyzed for the presence of prepositions. If there
is a preposition in the text, then the search for a combination of this preposition in
conjunction with the word standing to the right of it is carried out. Upon detection of
this combination in the database of proclitics, the information about the variants of
accentuations in this combination is retrieved. In the case of ambiguous variants of the
arrangement of accents, we again resort to the method “by analogy”.
      </p>
      <p>
        Modification 2. The algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] is sensitive to the parameters which it
receives (R–r(k), k, r(i)), what leads to an incorrect definition of the meter and number of
feet. Therefore, for the parameters the inaccuracies have been introduced: the
parameters considered to be constant (=const), if they are constant for at least 90% of the lines
of the poem.
      </p>
      <p>
        Modification 3. The step of the algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] is worked out in detail,
specifically the fifth condition, the classification of poems according to metrorhythmic, which
takes into account pyrrhic and spondee (R–r(k)=const, k≠const, r(i)≠const). If the text
satisfies this condition, then further clarification to determine the meter and number of
feet of the poetic text is made as follows. After each word is divided into syllables and
translated into a sequence of characters “c” and “C”, the syllabic pattern is compared
to the pre-compiled patterns, which are the foot of the intended meter. Using statistical
evaluation the most suitable pattern from which the most suitable meter follows is
revealed, that is the pattern with minimal difference from the syllabic scheme corresponds
to a certain meter.
4
      </p>
    </sec>
    <sec id="sec-5">
      <title>Approach to the Implementation of the Module Definition of the Rhyming Lines</title>
      <p>
        In the article [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ], in the algorithm for determining rhyme of poetic text it is suggested
to seek rhyming lines in a poem, using the web app “Big rhyming dictionary” [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]. This
app takes a word and returns a set of words rhyming with it.
      </p>
      <p>Because the sending of requests to the web application for each word is a long
process and the extraction of all the words and sets, and rhyming words to them with their
following conservation in the database, is the process requiring big resources, in this
paper we used an alternative way to search rhymed lines.</p>
      <p>The rhyme search algorithm is implemented for reasons of the possibility of rhyme
formation: the lines are rhymed if the last words in the line have the same position of
the stressed syllable and the endings are phonetically coincided.</p>
      <p>
        To identify the phonetically matched endings, we used data about the endings from
the article [
        <xref ref-type="bibr" rid="ref22">22</xref>
        ]. It contains a pair of letter combinations, reflecting the sounds of
rhyming verse endings from the literature of the 18–19 century:
[('и', 'ы'), ('и', 'ый'), ('ы', 'ый'), ('и', 'е'), ('и', 'ий'), ('у', 'уй'), ('ой', 'о'), ('кий', 'ки'),
('ей', 'е'), ('ай', 'о'), ('ой', 'а'), ('ей', 'и'), ('ий', 'е'), ('и', 'ьи'), ('и', 'ья'), ('ьи', 'ья'), ('и', 'ье'),
('е', 'ье'), ('к', 'г'), ('х', 'к',), ('г', 'х'), ('а', 'о'), ('е', 'и'), ('ья', 'ье'), ('ьи', 'ье'), ('ом', 'ым'),
('ит', 'ет'), ('ин', 'ен'), ('ий', 'а'), ('ой', 'а'), ('ый', 'а'), ('о', 'у'), ('уг', 'ок'), ('ах', 'ых'), ('е',
'ы'), ('ив', 'ов'), ('и', 'ой'), ('и', 'а'), ('я', 'и',), ('а', 'ы'), ('ы', 'у'), ('я', 'е'), ('ы', 'о'), ('ый', 'о'),
('ы', 'ой'), ('у', 'ой'), ('у', 'ый'), ('ы', 'ей'), ('ешь', 'ишь'), ('он', 'ен'), ('ел', 'ол'), ('ей', 'ой'),
('ом', 'ем'), ('ть', 'дь'), ('д', 'т'), ('ор', 'ер'), ('ом', 'им')]
      </p>
      <p>With their usage, the algorithm for determining rhyme was developed, which
consists of the following sequential steps:
1. The splitting of the text into stanzas.
2. The line numbering and extracting the last word from each line of the stanza.
3. The definition of accentuation for each word. The search for sets of words with
the same accentuation.</p>
      <p>4. The search for sets of words whose endings are rhymed (phonetically matched)
5. The search for the intersection of sets from p. 4 and 5 – the obtained rhyming
lines.</p>
      <p>6. The representation of rhymes in letter form: each set of rhymed lines is assigned
a letter of the Latin alphabet, and the male – a lowercase letter, the female – a capital
letter. On the basis of the received designations the letter sequence of lines in a stanza
is made.
5</p>
    </sec>
    <sec id="sec-6">
      <title>Obtained Results</title>
      <p>
        As a test sample we have used a corpus of lyrical works of Alexander Pushkin (156
poems from the period of 1818–1825), pre-marked by meter, foot, rhyme with the help
of reference book [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ]. The algorithms for the definition of the meter and number of
feet were tested (we modified the algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] and implemented the algorithm
from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]).
      </p>
      <p>
        The accuracy of the determination of meter and number of feet in the modified
algorithm [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] increased in comparison with the algorithm from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] (Table 2). The
difference in the work of the algorithms is due mainly to the fact that the first of the
presented algorithms recognizes the metric versification with unequal feet, while the
second incorrectly classifies it. Also, the sensitive parameters of the first algorithm made
it possible to increase the accuracy in determining the number of feet in comparison
with the already existing algorithm.
      </p>
      <p>Among the disadvantages of this algorithm for determining the meter and stop we
can underline: the limited database compiled on the basis of the dictionary A. Zaliznyak
(a lack of some words), the replacing the letter “ё” by “e” in the test sample, what is
allowed by the rules of the Russian language, but is critical for this algorithm, these
problems are partially offset by the usage of the method “by analogy”. Further
researches will address these shortcomings.</p>
      <p>The main percentage of errors is due to the fact that there are unfinished poems in
the corpus, in which one or more words are missing, they are replaced by supplemented
ones, hereupon the standard algorithm that provides a full line does not work correctly.
The further purpose of the study will be the identification of such lines to be excluded
from the General analysis.</p>
      <p>Also, this algorithm does not distinguish a meter with unequal feet and complex
meter. This will also be done in a further study.</p>
      <p>
        The module of the rhyme definition in modified algorithm of [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] has identified
correctly 95% of the strophic patterns.
6
      </p>
    </sec>
    <sec id="sec-7">
      <title>Conclusions</title>
      <p>
        The article compares the work of two algorithms for the analysis of the structural level
of Russian poetic texts: a relatively simple one from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ], which was used by us in the
implementation of the pilot project of the system [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ], and a more advanced algorithm
from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ], modified by us, first of all, in order to eliminate possible ambiguities of
automatic accentuation. It is shown that the modified algorithm from [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] gives a higher
accuracy in determining the meter and number of feet, and also determines the strophic
pattern with an accuracy of 95 %.
      </p>
      <p>Further researches will be aimed at identifying typical problem situations that
generate the errors in the work of the algorithm, and their subsequent elimination.</p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgements</title>
      <p>The study was carried with the support of the Russian Science Foundation (project No.
19-1800466).</p>
    </sec>
  </body>
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