We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.
翻译:我们用历史数据分析的持久性同系法和多层面分析技术来研究世界语言合成结构的数据; 我们分析多元性、等级组合结构和非三重循环等综合参数之间的关系; 我们展示了跨语言家庭的关系,以及家庭特有的其他关系; 然后我们分析了描述不同语言家庭语言中持久性关联组成部分的合并结构的树木, 我们显示它们部分地与历史植物树相关,但差异很大。 我们还显示了不同语言家庭存在有趣的非三重持久性第一同系物组。 我们举例说明了可识别持久性第一同系物的明显产生者,其中一些似乎与同系物现象相对应,而另一些则可能具有历史语言学的解释,与已知的不同语言次家庭在同源性借贷方面的情况相对应。