A new proposal for metric in perceptual multidimensional scaling

We analyze a simplified probability model that assumes normality and homoscedasticity of vowel parameters’ distributions. We arrive at explicit formulae that describe functional relationship between a natural Euclidean distance function in the model and the confusability of vowel categories. We propose a solution to address a common case when confusability of a pair of vowel categories is very low, which leads to uncertainty of distance value. The solution is applicable when the class boundary is provided by a real-valued discriminating function. Examples of perceptual vowel diagrams obtained with new metric are presented based on vowel samples spoken by male speakers from TIMIT corpus.