Geometrical approach to similarity representation in pattern recognition for speech-spectral deformation

We study the relation between a spectral deformation in speech processing and a geometrical deformation theory. We show that topological field theory yields the systematic treatment of these two methods. Some of the examples and the application to speech-spectra of classical mathematical ideas - for example, Morse theory in higher dimensions - for topological field theory are discussed. These discussions are deeply concerned with many of the issues in computer graphics tools recently developed by M. Ferri and P. Frosini.