The Manifold Nature of Vowel Sounds

Recently there has been great interest in geometricallymotivated approaches to data analysis and pattern recognition. Low-dimensional structure in higher-dimensional data can be exploited by manifold-based data reduction and learning algorithms to improve performance. The existence of such a structure in speech has not been formally documented. Toward this end, I present a derivation of the approximate discrete spectra of sustained vowel phonemes using standard tube models of the vocal tract. Adopting a geometrical approach, each N -point discrete frequency spectrum produced using these models represents a point in R . Given a continuous range of vocal tract model parameters, I either formally or graphically demonstrate that the subsets of Euclidean space traced out by the resulting spectra positions form low-dimensional, extrinsically curvedmanifolds that span the ambient space. Tubemodel parameters that approximate the vocal tract configurations for various vowel phonemes determine the approximate manifold structure for several sustained vowel sounds. Using the manifolds for the phonemes /a/ and /æ/ as input, the manifold-based Laplacian eigenmap dimensionality reduction algorithm of Belkin and Niyogi [1] outperforms traditional principal component analysis, both with and without the introduction of noise.