A regression approach to vowel normalization for missing and unbalanced data

Abstract

Researchers investigating the vocalic systems of languages or dialects frequently employ normalization methods to minimize between-speaker variability in formant patterns while largely preserving dialectal, between-phoneme variability. One popular method, log-mean normalization, relies on estimating the logarithm of the geometric mean formant-frequency (Gs) produced by a speaker across their vocalic inventory, and then expressing the formant patterns produced by a speaker as deviations from this mean. However, in the face of missing or unbalanced data, the traditional approach to calculating Gs for a speaker will usually lead to biased estimates, which will produce artificial asymmetries in the normalized vowel spaces of different speakers. An alternative method is proposed for the estimation of Gs based on a linear-regression framework, which avoids the biases associated with traditional estimation of Gs when data is unbalanced. The regression method to normalization is described, and simulations are carried out to compare the accuracy of Gs estimates via regression to other estimation methods. Results indicate that the proposed method is substantially more accurate than the traditional approach to estimating Gs in the face of missing or unbalanced data.