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Using functional data analysis for investigating multidimensional dynamic phonetic contrasts

Gubian, M., Torreira, F., & Boves, L. (2015). Using functional data analysis for investigating multidimensional dynamic phonetic contrasts. Journal of Phonetics, 49, 16-40. doi:10.1016/j.wocn.2014.10.001.
The study of phonetic contrasts and related phenomena, e.g. inter- and intra-speaker variability, often requires to analyse data in the form of measured time series, like f0 contours and formant trajectories. As a consequence, the investigator has to find suitable ways to reduce the raw and abundant numerical information contained in a bundle of time series into a small but sufficient set of numerical descriptors of their shape. This approach requires one to decide in advance which dynamic traits to include in the analysis and which not. For example, a rising pitch gesture may be represented by its duration and slope, hence reducing it to a straight segment, or by a richer coding specifying also whether (and how much) the rising contour is concave or convex, the latter being irrelevant in some context but crucial in others. Decisions become even more complex when a phenomenon is described by a multidimensional time series, e.g. by the first two formants. In this paper we introduce a methodology based on Functional Data Analysis (FDA) that allows the investigator to delegate most of the decisions involved in the quantitative description of multidimensional time series to the data themselves. FDA produces a data-driven parametrisation of the main shape traits present in the data that is visually interpretable, in the same way as slopes or peak heights are. These output parameters are numbers that are amenable to ordinary statistical analysis, e.g. linear (mixed effects) models. FDA is also able to capture correlations among different dimensions of a time series, e.g. between formants F1 and F2. We present FDA by means of an extended case study on diphthong – hiatus distinction in Spanish, a contrast that involves duration, formant trajectories and pitch contours.
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