Classification and Clustering of Stop Consonants via Nonlinear Transformations for Prediction in Stochastic Processes

CCNY Data Science, Networks, and Biology Seminar

Time and place

3:30 PM on Thursday, May 18th, 2017; NAC 4/156

Basilis Gidas (Division of Applied Mathematics, Brown University)

Abstract

An effort to develop a framework in speech recognition alternative to that of HMM (Hidden Markov Models), lead us to the study of classification and clustering of the six stop consonants /p, t, b, d, k, g/ -- an outstanding problem in phonetic theories. The stop consonants differ from one another in two phonetic features: Place of articulation (closure of the vocal track) and voicing (the onset of phonation or VOT). The former divides them into labials /p, b/, alveolars /t, d/, and velars /k, g/. Voicing divides them into voiced /b, d, g/ and voiceless /p, t, k/. We developed a procedure for the classification and clustering with three powerful components: (i) a wavelet transform of the acoustic signal, (ii) a nonlinear transformation of the wavelet transform, and (iii) a nonlinear discrimination rule based on the nonlinear transformation of step (ii). Part (ii) lead to some interesting mathematical problems: (a) the existence of the nonlinear transformations is reduced to the study of the spectrum of certain singular integral operators on Hardy type spaces and certain spaces of entire functions of exponential type; (b) the estimation of the nonlinear transformations on the basis of data is an interesting nonparametric statistical learning problem; it involved some mathematical tools not very common in statistics. The main goal of the talk will be to present the overall algorithmic classification procedure as well as some the above mathematical and statistical estimation problems.