A Unifying View of Second-Order Measures of Quality for Signal Classification

The major purpose of this paper is to promote interchange between the fields of pattern recognition and communications, in the realm of statistical classification. The general class of second-order measures of quality for statistical classification is defined. The variety of members in this class that have been used by practitioners or proposed by theorists for numerical pattern-classification and signal waveform-classification are compared and contrasted. The several measures that are the most generally applicable are shown to be either equivalent to each other or characterizable in terms of each other, thereby revealing an inherent unity. For example, the ratio of between-class-scatter to within-class-scatter used in pattern recognition and the ratio of signal-energy to noise-energy used in communications are unified through an identification of signal with between-class-scatter and noise with within-class-scatter. Results on equivalences are stated and proved for waveform classification rather than numerical classification in order to complement the extensive literature on the latter, and to emphasize applicability to communications. This entails introduction of a scatter ratio for waveforms. In a companion paper, second-order measures of quality are used as a basis for a general nearestprototype signal-classification methodology; canonical signal features for this methodology are identified, and a general approach for determining appropriate class prototypes is given. These two papers provide an integrated approach to the design of a complete signal classifier, i.e., feature extraction and discriminant-functional design tailored to fit a minimumdistance discrimination rule.