Dimension of the speech space

Defines a statistic for estimating the intrinsic dimension of a finite set of points on the assumption that they lie on a smoothly embedded manifold, when of course, the dimension is an integer, The authors test the method on finite sets drawn from known manifolds and show that it is robust. They also apply it to the Lorenz attractor. Finally they apply it to speech data of the type used by Tattersal et al (1983). It is concluded that the speech space is not discernibly a low-dimensional manifold at all, and that a more plausible hypothesis is that the space is an open subset of the enclosing space. A measure is constructed of the extent to which the surface that the Kohonen algorithm fits to the speech space is buckled or crinkled related to the mean absolute curvature. The speech space can be approximated with a low-dimensional manifold, but it has dimension greater than two.<>