Pattern Recognition, Functionals, and Entropy

Pattern recognition (including sound recognition) is described mathematically as the problem to compute for any element of a given class its image in a classification set. The difficulty lies in the fact that the map may be implicitly defined by a property or must be extrapolated from prototypes. An entropy measure and an equivocation measure are defined that permit an assessment of the improvement gained (and the price in confusion paid) by a set of Linear ``features´´ are identified as measures and L2 functions, respectively. It is shown that certain important normalizations (position, size, pitch, etc.) are nonlinear operations. Finally, the method of spectral analysis which is widely used for speech analysis is examined critically. It is shown that contrary to common belief Fourier analysis is not very suitable for detecting certain speech particles (consonants, stops, etc.).