# Topological Analysis of Syntactic Structures

## TL;DR

This paper applies topological data analysis to syntactic data of world languages, revealing universal and family-specific relations, and uncovering complex hierarchical and homological structures that relate to linguistic history and borrowing.

## Contribution

It introduces a novel application of persistent homology to syntactic structures, identifying both universal patterns and language-family-specific features.

## Key findings

- Relations across language families and family-specific syntactic relations
- Persistent homology reveals non-trivial loops and homology groups in language data
- Partial correlation of topological structures with historical linguistic trees

## Abstract

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.