Optimal transformations for prediction in continuous time weakly stationary processes and applications to phoneme recognition
Basilis Gidas, Alejandro Murua · 1994
A nonparametric framework is proposed for developing a new acoustic model for speech recognition, that provides a relation between acoustic data and phonetic models alternative to that offered by hidden Markov models. This proposal leads to the study of three topics treated in this Thesis. The first one is a mathematical study of Optimal Transformations for Prediction--a problem that may be viewed as a fundamental variation of the classical Wiener-Kolmogorov prediction theory. These transformations are designed to capture the nonlinearities present in the acoustic signal (e.g. in transitions from a consonant to a vowel), that are known to contain important features for recognition. They lead to interesting mathematical issues whose resolution involves sophisticated tools from Sobolev, Hardy and other function spaces. The second topic is an application of nonlinear optimal transformations to the design of a classification rule and clustering procedure for the classification and clustering of stop consonants on the basis of consonant-vowel syllables. In experiments realized with this procedure, this classification rule achieves rates of correct classification over 95%, and higher than those reported in similar studies with other methods. The third topic concerns the relation between the sampled and analogue signals, as the sampling rate varies. In particular, a rigorous study of various aspects related to the aliasing effect is provided, together with some convergence results as the sampling rate goes to zero, that are useful in proving the consistency of nonparametric estimators for linear predictors and optimal transformations, from a finite data set.