Gaussian Tree Constraints Applied to Acoustic Linguistic Functional Data

TL;DR

This paper introduces a novel method combining canonical function analysis with Gaussian tree constraints to evaluate if acoustic linguistic data from Romance languages fit an evolutionary tree model, revealing partial compatibility.

Contribution

It presents a new approach integrating CFA and Gaussian tree constraints for assessing linguistic data against tree models, specifically applied to acoustic speech features.

Findings

Certain language features fit a tree model

The method identifies features incompatible with a tree structure

Separable CFA basis emphasizes language differences

Abstract

Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.