Vasilii A. Gromov, Nikita S. Borodin, Asel S. Yerbolova
{"title":"A Language and Its Dimensions: Intrinsic Dimensions of Language Fractal Structures","authors":"Vasilii A. Gromov, Nikita S. Borodin, Asel S. Yerbolova","doi":"10.1155/2024/8863360","DOIUrl":null,"url":null,"abstract":"<div>\n <p>The present paper introduces a novel object of study, a language fractal structure; we hypothesize that a set of embeddings of all <i>n</i>-grams of a natural language constitutes a representative sample of this fractal set. (We use the term <i>Hailonakea</i> to refer to the sum total of all language fractal structures, over all <i>n</i>). The paper estimates intrinsic (genuine) dimensions of language fractal structures for the Russian and English languages. To this end, we employ methods based on (1) topological data analysis and (2) a minimum spanning tree of a data graph for a cloud of points considered (Steele theorem). For both languages, for all <i>n</i>, the intrinsic dimensions appear to be noninteger values (typical for fractal sets), close to 9 for both of the Russian and English language.</p>\n </div>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2024/8863360","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complexity","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2024/8863360","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper introduces a novel object of study, a language fractal structure; we hypothesize that a set of embeddings of all n-grams of a natural language constitutes a representative sample of this fractal set. (We use the term Hailonakea to refer to the sum total of all language fractal structures, over all n). The paper estimates intrinsic (genuine) dimensions of language fractal structures for the Russian and English languages. To this end, we employ methods based on (1) topological data analysis and (2) a minimum spanning tree of a data graph for a cloud of points considered (Steele theorem). For both languages, for all n, the intrinsic dimensions appear to be noninteger values (typical for fractal sets), close to 9 for both of the Russian and English language.
本文提出了一个新的研究对象--语言分形结构；我们假设，自然语言所有 n 个词组的嵌入集构成了这个分形集的代表性样本。(我们使用 Hailonakea 一词来指所有 n 中所有语言分形结构的总和）。本文估算了俄语和英语语言分形结构的内在（真实）维度。为此，我们采用了基于（1）拓扑数据分析和（2）考虑点云的数据图最小生成树（斯蒂尔定理）的方法。对于这两种语言，在所有 n 的情况下，内在维数似乎都是非整数值（分形集的典型值），俄语和英语的内在维数都接近 9。
期刊介绍：
Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
