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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">sergeogr</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Российской академии наук. Серия географическая</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestiya Rossiiskoi Akademii Nauk. Seriya Geograficheskaya</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2587-5566</issn><issn pub-type="epub">2658-6975</issn><publisher><publisher-name></publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.7868/S2658697526030014</article-id><article-id custom-type="elpub" pub-id-type="custom">sergeogr-3174</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>ТЕОРИЯ И МЕТОДОЛОГИЯ ГЕОГРАФИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Theory and Methodology of Geography</subject></subj-group></article-categories><title-group><article-title>Феноменология пространственного анализа: модели географической редукции и методы пространственной статистики</article-title><trans-title-group xml:lang="en"><trans-title>The Phenomenology of Spatial Analysis: Models of Geographical Reduction and Methods of Spatial Statistics</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>Шелудков</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Sheludkov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Москва</p></bio><bio xml:lang="en"><p>Moscow</p></bio><email xlink:type="simple">a.v.sheludkov@igras.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт географии РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Institute of Geography, Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>18</day><month>08</month><year>2026</year></pub-date><volume>90</volume><issue>3</issue><fpage>453</fpage><lpage>469</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шелудков А.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Шелудков А.В.</copyright-holder><copyright-holder xml:lang="en">Sheludkov A.V.</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://izvestia.igras.ru/jour/article/view/3174">https://izvestia.igras.ru/jour/article/view/3174</self-uri><abstract><p>Автор анализирует, как существующие в географии репрезентации пространственных феноменов соотносятся с допущениями методов статистики и геоинформатики. В широком смысле география проблематизирует разномасштабные проявления пространственной гомогенности и гетерогенности, связывая их с положением наблюдений в пространстве. Модели географической редукции — это разные способы репрезентации пространства, его элементов, пространственных отношений между ними и проистекающих пространственных эффектов. Модели определяют способы описания положения наблюдений в пространстве и механизмов формирования пространственных феноменов. Автор рассматривает три базовых типа таких репрезентаций (моделей) — поля, дискретные объекты и сети — с описанием их ключевых свойств, примерами из разных дисциплин географии и различиями применения методов пространственного анализа и статистики, таких как кригинг, операции со скользящими окнами, пространственная регрессия и др. Более подробно модели редукции рассматриваются на примере географии населения и мобильности. В отличие от сетевой гравитационной модели мобильности, не учитывающей пространственного контекста перемещений, альтернативные модели вмешивающихся возможностей основаны на топологическом описании потенциальных точек движения агентов, а результаты моделирования можно представить в виде поля вероятности перемещений. Модели географической редукции задают рамки постановки исследовательских задач и применения статистических и геоинформационных методов. Одни и те же географические явления могут быть одновременно представлены через разные модели, что открывает новые способы решения исследовательских задач, а методы, которые работают с этими моделями, могут таким образом переноситься в разные предметные области географии.</p></abstract><trans-abstract xml:lang="en"><p>The author analyzes how existing representations of spatial phenomena in geography relate to the assumptions underlying statistical and geoinformatic methods. In a broad sense, geography problematizes multi scale manifestations of spatial homogeneity and heterogeneity, linking them to the spatial positions of observations. Models of geographic reduction are different ways of representing space, its elements, the spatial relationships among them, and the resulting spatial effects. These models determine how the positions of observations in space and the mechanisms of formation of spatial phenomena are described. The author considers three basic types of such representations (models)—fields, discrete objects, and networks—describing their key properties, providing examples from different subdisciplines of geography, and outlining differences in the application of spatial analysis and statistical methods such as kriging, movingwindow operations, spatial regression, and others. Models of reduction are discussed in greater detail using population geography and mobility as examples. In contrast to networkbased gravity models of mobility, which do not take the spatial context of movements into account, alternative interveningopportunities models are based on a topological description of potential movement destinations for agents, and the modeling results can be represented as a probability field of movements. Models of geographic reduction define the framework for formulating research questions and for applying statistical and geoinformatic methods. The same geographic phenomena can be represented simultaneously through different models, which opens up new ways of addressing research problems, while the methods that operate on these models can thus be transferred across different domains of geography.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>географический анализ</kwd><kwd>теория и методология географии</kwd><kwd>пространственные данные</kwd><kwd>статистические методы</kwd><kwd>расселение</kwd><kwd>мобильность населения</kwd></kwd-group><kwd-group xml:lang="en"><kwd>geographical analysis</kwd><kwd>theory and methodology of geography</kwd><kwd>spatial data</kwd><kwd>statistical methods</kwd><kwd>settlement pattern</kwd><kwd>population mobility</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Раздел “Географическая редукция в изучении расселения и мобильности” подготовлен в Институте географии РАН по проекту РНФ  № 25 27 00316 “Суточная пространственновременная динамика плотности населения в городах и городских агломерациях: теория и моделирование”.Автор благодарит коллег из Института географии РАН и факультета географии и геоинформационных технологий НИУ ВШЭ Виктора Михайловича Матасова за идею написания работы и Ольгу Борисовну Глезер за ценные замечания к ранней рукописи статьи, двух рецензентов за конструктивную и крайне полезную критику работы, а также студентов группы БГЕО211/212 факультета географии и геоинформационных технологий НИУ ВШЭ за плодотворные обсуждения предмета исследования в рамках семинарских занятий по курсу “Статистические методы пространственного анализа”</funding-statement><funding-statement xml:lang="en">The Section “Geographical Reduction in Studying Settlement Pattern and Population Mobility” was funded by the Russian Science Foundation grant no. 252700316 “Daily Spatial and Temporal Dynamics of Population Density in Cities and Urban Agglomerations: Theory and Modeling,” carried out at the Institute of Geography of the Russian Academy of Sciences. The author expresses gratitude to colleagues from the Institute of Geography of the Russian Academy of Sciences and the Faculty of Geography and Geoinformation Technology at HSE University Viktor Mikhailovich Matasov for the idea of writing this paper, and Olga Borisovna Glezer for her valuable comments on an early version of the manuscript; to the two reviewers for their constructive and extremely helpful criticism; and to the students of groups BGEO211/212 of the Faculty of Geography and Geoinformation Technology at HSE University for fruitful discussions of the research subject during seminar sessions of the course “Statistical Methods of Spatial Analysis.”</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Аксенов К.Э. Системообразующие свойства пространствавремени при трансформации общественногеографического пространства // Изв. РГО. 2014. 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