Non-normal models for classification of speech sounds

Abstract

The speech analysis problem under consideration is to classify, by an optimum procedure, a speech sound (phoneme) on the basis of certain electronically measured variables. For the vowel phonemes (designated by pi_l, . . ., pi_m) of specific interest, the appropriate variables are fractions x_1, . . ., x_p of the total power contained in p mutually exclusive portions of the frequency spectrum such that pΣi=1 x_i=1. Some related variables designated by y_l, . . .,y_p are approximately proportional to sqrt(x_1), . . ., sqrt(x_p) so that pΣi=1 (y^2)_i=1. In order to apply the statistical criterion of maxime likelihood (assuming equal costs of misclassification and equal a priori probabilities), it is necessary to make reasonable assumptions as to the mathematical form of the probability distributions 0_g(x) or 0_g(y) in the population pi_g, g=1, . . ., m, where x and y represent the sets of p variables, Certain conditions of formal symmetry are set up for 0_g(x) or 0_g(y), along with requirements derived from observed data that variances should be smallest for means close to zero or 1, and that provision should be made for positive probability that x_i=zero. These conditions combine to rule out the usual normal model, with the same covariance matric in all populations, which leads to the linear discriminant function. [TRUNCATED]