Heat Kernel analysis of Syntactic Structures
This work provides an incremental analysis of syntactic structures using existing methods, potentially aiding linguists in understanding parameter relationships.
The authors applied the Belkin-Niyogi heat kernel method to analyze syntactic parameter datasets, detecting relations and clustering structures, and identified regions of maximal variance to determine independent variable choices.
We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin-Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood information. We analyze the different connectivity and clustering structures that arise in the two datasets, and the regions of maximal variance in the two-parameter space of the Belkin-Niyogi construction, which identify preferable choices of independent variables. We compute clustering coefficients and their variance.