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John Aston, Warwick Print
Thursday, 17 October 2013, 12:15 - 13:15

John Aston, Warwick

Functions, Covariances and Learning Foreign Languages


Distances and Inference for Covariance Operators

Supplementary Material for "Distance and Inference for Covariance Operators"

Abstract: Functional Data Analysis (FDA) is an area of statistics concerned with analysing statistical objects which are curves or surfaces. This makes FDA particularly applicable in phonetics, the branch of linguistics concerned with speech, in that each sound or phoneme which makes up a syllable can be characterised as a time-frequency spectrogram surface.

One question of particular significance in phonetics is how languages are related, and concepts as simple as how close are two languages have proved difficult to quantify. Recent work on FDA and phonetics in Mandarin and Qiang (Chinese dialects) has suggested that the use of covariance functions might facilitate the finding of new measures of closeness of languages. However, working with covariance functions immediately raises the issue that the functions lie on a manifold (of positive definite operators) rather than in a standard Euclidean space. Here, a new metric for covariance functions is introduced which allows valid inference for covariance functions, but also which possess good properties when examining extrapolations, something that can be used to determine phonetic relationships.

The theory and methodology of the new distance metrics for covariance functions will be illustrated using the some of the Romance languages (the languages which are have Latin as a root).

Location: R42.2.113
Contact: Claude Adan, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it