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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">umovest</journal-id><journal-title-group><journal-title xml:lang="ru">Статистика и Экономика</journal-title><trans-title-group xml:lang="en"><trans-title>Statistics and Economics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2500-3925</issn><publisher><publisher-name>Plekhanov Russian University of Economics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21686/2500-3925-2018-2-30-37</article-id><article-id custom-type="elpub" pub-id-type="custom">umovest-1252</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>СОЦИАЛЬНАЯ СТАТИСТИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SOCIAL STATISTICS</subject></subj-group></article-categories><title-group><article-title>Кластерный анализ кардиологических данных</article-title><trans-title-group xml:lang="en"><trans-title>Cluster analysis of cardiac data</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Зимина</surname><given-names>Е. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Zimina</surname><given-names>E. Y.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Аспирант НИУ ВШЭ, Москва, Россия Тел.: 8 906 082 99 04</p></bio><bio xml:lang="en"><p>Postgraduate student Higher School of Economics, Moscow,  Russia Tel.: 8 906 082 99 04</p></bio><email xlink:type="simple">ezimina@hse.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>НИУ ВШЭ</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Higher School of Economics</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>09</day><month>06</month><year>2018</year></pub-date><volume>15</volume><issue>2</issue><fpage>30</fpage><lpage>37</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Зимина Е.Ю., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Зимина Е.Ю.</copyright-holder><copyright-holder xml:lang="en">Zimina E.Y.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://statecon.rea.ru/jour/article/view/1252">https://statecon.rea.ru/jour/article/view/1252</self-uri><abstract><p>В статье рассматривается применение статистического метода, а именно кластерного  анализа на примере исследования кардиологических данных. Использованы методы  классификации Data Mining для обработки кардиологических данных, анализа состояния  пациента. Целью данного исследования было поставлено проверка гипотезы о возможности  диагностики состояния здоровья сердца пациента, а также выявления у него патологий, при помощи анализа серий ЭКГ и выделения схожих кластеров по результатам данного проводимого анализа. Тематика применимости известных методов кластеризации применительно к обработке и анализу электрокардиограммам по признакам  подобия из форм ранее широко не исследовалась. В модели сердца, которая применяется в  данном исследовании, в основе явления возврата ФПУ является понятия состояния сердца, в качестве фиксируемого колебательного процесса. Но, с другой стороны, так как сердце  является автоколебательной системой и ему не требуется для начала колебаний получения энергии «возмущения», то при исследовании сердца вводится понятие  автовозврата ФПУ. Сердце можно рассматривать как распределенную автоколебательную  систему, которая имеет бесконечное число автовозвратов Ферми-Паста-Улама (ФПУ), при  которых вводится понятие кластера, получаемого в процессе серии сравнений ЭКГ спектров  Фурье друг с другом и выявления повторяющихся. Сравнение Фурье спектров ЭКГ  производится на основе явления возврата ФПУ, на основе визуального восприятия спектра.  Для этого было введено понятие формы спектра. Форма спектра – сглаженная кривая. В  ходе работы было произведено математическое моделирование работы сердца путем  использования разложения ФПУ и представлено формальное описание математической  модели сердца как система связанных клеток миоцитов, представляющих отдельные  автоколебательные степени свободы, описываемые системой связанных нелинейных  дифференциальных уравнений второго порядка как уравнения Ван дер Поля. Кластерный  анализ проводится на основе поиска схожих форм спектров Фурье, полученных путем  моделирования работы сердца ФПУ. Таким образом, разрабатывается система обработки  кардиологической информации, обеспечивающая персонифицированный мониторинг,  анализ и прогнозирование развития состояния пациента в реальном времени. Система  представляет собой устройство для съема ЭКГ и пульсовой волны, с помощью которого  сразу после окончания сбора данных пациента информация отправляется посредством  Интернет в облако для дальнейшей обработки, анализа и хранения. На данный момент были уже получены результаты: гипотеза подтвердилась. При математическом моделировании работы сердца ФПУ, на основе которых были выделены формы спектров Фурье, были  выделены кластеры, среди которых образовались различные подмножества как форм  спектров Фурье с патологиями, так и форм спектра Фурье здоровых людей. Из данного  проведенного исследования следует, что по результатам кластерного анализа  электрокардиограммы возможно отнести данную ЭКГ к какому-либо кластеру и тем самым  продиагностировать состояние кардиологического здоровья данного пациента.</p></abstract><trans-abstract xml:lang="en"><p>The article includes the observation of the cluster analysis of medicaldata on the example of the cardiac data. One of the main effective and commonly used Data Mining methods that applied to  the large amounts of information (for example, mathematical  economics) are clustering methods: the search for signs of similarity  between objects in the study of the subject area and the subsequent merger of objects into subsets (clusters) according to the established affinity. The main purpose of the investigation is to examine the  hypothesis of the possibility of diagnosing the patient health status,  as well as identifying his pathologies, using the analysis of  electrocardiogram (ECG) series and the allocation of similar clusters  based on the results of this analysis. However, the subject of  clustering techniques implementation to the ECG on the grounds of  similarity of forms have not previously been extensively investigated. In the model of the heart, which is used in this study,  the state of the heart is taken as a fixed oscillatory process of the  phenomenon of the FPU auto-return. But, on the other hand, since  the heart is an self-oscillating system and it has no need to start the  oscillations by obtaining the energy of “perturbation”, the concept of  FPU autoreturn is introduced in the study of the heart. The  mathematical modeling of the heart work by using a decomposition of the Fermi-Pasta-Ulam (FPU) was investigated. The formal description of the mathematical model of the heart as a system of connected cells myocytes is presented. This represents a  single oscillatory degree of freedom described by a  system of coupled nonlinear differential equations of the second  order equation of Van der Pol. Cluster analysis bases on the search  of similar clusters of Fourier spectrum which are received by FPU  recurrence. The current results that are obtained show that the  hypothesis is confirmed. In mathematical modeling of the FPU heart  modeling, which is based on the forms of Fourier spectra, were  identified. Subsets were identified, among which various subsets of  both forms of Fourier spectra with pathologies and forms of the  Fourier spectrum of healthy people were formed. From this study it  follows that the cluster analysis of the electrocardiogram may refer this ECG to any cluster and thereby diagnose the state of  cardiac health of the patient.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>кластеризация</kwd><kwd>цифровая экономика</kwd><kwd>кардиология</kwd><kwd>большие данные</kwd><kwd>математическое моделирование</kwd></kwd-group><kwd-group xml:lang="en"><kwd>clustering</kwd><kwd>digital economy</kwd><kwd>cardiology</kwd><kwd>big data</kwd><kwd>mathematical modeling</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Дюк В., Самойленко А. 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