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Linguistics from a topological viewpoint

Rui Dong

Abstract

Typological databases in linguistics are usually categorical-valued. As a result, it is difficult to have a clear visualization of the data. In this paper, we describe a workflow to analyze the topological shapes of South American languages by applying multiple correspondence analysis technique and topological data analysis methods.

Linguistics from a topological viewpoint

Abstract

Typological databases in linguistics are usually categorical-valued. As a result, it is difficult to have a clear visualization of the data. In this paper, we describe a workflow to analyze the topological shapes of South American languages by applying multiple correspondence analysis technique and topological data analysis methods.
Paper Structure (20 sections, 3 theorems, 18 equations, 17 figures)

This paper contains 20 sections, 3 theorems, 18 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Related work
  3. Multiple correspondence analysis
  4. Topological data analysis
  5. A toy example of pretzel
  6. The TDA workflow
  7. Data analysis procedure
  8. Data preprocessing
  9. MCA processing
  10. The shapes of languages
  11. Applications of TDA
  12. Nuclear-Macro-Jê
  13. Quechuan
  14. Discussion
  15. Multiple correspondence analysis
  16. ...and 5 more sections

Key Result

Theorem B.1

For any $p$-chain $\gamma$, $\partial_{p-1}\cdot \partial_{p}(\gamma)=0$.

Figures (17)

  • Figure 1: A pretzel-shaped point cloud
  • Figure 2: From (a) to (d): the radius ranges from $0$, the circular structures were born, remained, and dead.
  • Figure 3: A $2$-simplex $\langle p_0, p_1, p_2\rangle$
  • Figure 4: The boundary of the $2$-simplex $\langle p_0, p_1, p_2\rangle$.
  • Figure 5: The dim-$1$ persistence diagram of the pretzel-shaped point cloud
  • ...and 12 more figures

Theorems & Definitions (26)

  • Remark
  • Example 1
  • Remark
  • Remark
  • Remark
  • Remark
  • Definition B.1
  • Definition B.2: Simplex
  • Remark
  • Definition B.3: Simplicial complex
  • ...and 16 more