Distance Measures : Physical and Perceptual Aspects

Distance measures are used to specify the (amount of) (dis)similarity between (two) events, on the basis of specific properties. This definition of distance measures makes it possible to emphasis various characteristics which I consider to be important. In the speech domain one can replace the general term 'event' in this definition by '(multidimensional) speech signal'. Uni-dimensional physical characteristics, such as time, amplitude, or fundamental frequency, as well as their perceptual counter parts (duration, loudness, and pitch), are generally represented on a physical or perceptual scale. And although also with scale definitions there are already considerable difficulties, I will not discuss these any further. I will rather concentrate on spectro­ temporal (multi-dimensional) aspects of speech signals, such as one individual vowel spectrum, or a sequence of spectra describing a word, or one measure such as fundamental frequency as a function of time ('pitch contour'). A measure of similarity or distortion on the basis of such signal characteristics is an ever returning problem in all the areas of speech research indicated below. In speech analysis and coding an error signal is frequently used to optimize a parametric representation, such as linear predictive coefficients, or pitch extraction. In rule synthesis one has again to optimize parametric fits, such as pitch and formant contours. The area of speech recognition and understanding is most strongly related to distance measures. They are needed, among other things, for segmentation, clustering, vector quantization, and for testing the input parameters against reference data. However, also in speech perception there is a strong emphasis on (dis)similarity between signals. Confusion matrices as a result of identification experiments, similarity matrices as a result of triadic comparison or other similarity judgments, or scores on semantic scales, are all indications of perceptual distances. Furthermore it is important to study the relation between perceptual similarity and physical distance measures, or in other words, the perceptual relevance of distance measures . Especially in speech perception, one also should be aware of the distinction between physical identity and perceptual and phonetic identity: Two physically different signals might be identified as the same vowel /a/, for instance in various phonetic contexts, or from different speakers, or in different noise backgrounds. Depending upon its purpose, a distance measure should include all relevant information and neglect information irrelevant for that condition. In the following sections I will first give some general properties of distances and then describe perceptual and physiCal approaches for studying and optimizing distance measures.