A Geometric Perspective on Speech Sounds
In order to effectively approach high dimensional pattern recognition problems, one seeks to understand and exploit any inherent low dimensional structure. Recently, a number of manifold learning algorithms have been motivated by a geometric point of view that models high dimensional data as lying near a low dimensional submanifold of the original space. Our paper has two main goals: (i) to investigate this manifold assumption for natural speech data. It seems intuitive that a human speech producing apparatus with few degrees of freedom would not produce sounds that fill up the acoustic space. We formalize this intuition by considering a concatenated acoustic tube model of the vocal tract and showing that the sounds generated by such a system lie on a low dimensional curved submanifold of the ambient acoustic space. To the extent that this model captures the essence of human speech production, the manifold assumption is true of natural speech data. (ii) to explore the implications of this geometric point of view towards human speech. We show that the manifold structure of speech sounds may be exploited for dimensionality reduction, semi-supervised learning, and speech representation with sometimes striking perfomance improvements in simulated and real speech data. The non-linear geometry of speech sounds suggests new interpretations of phenomena such as the perceptual magnet effect or quantal theory.