AN INFORMATION THEORY MODEL FOR CHARACTER ANALYSIS

Abstract

Describing is an essential function of science. Developing more efficient and accurate means of describing has been a primary concern of many investigators, and many diverse means of describing have been used, from mathematical formulae to Latin species descriptions. The problem of describing is of especial interest to workers in areas of research, such as taxonomy and ecology, where large collections of objects (specimens, plant communities, etc.)are to be organized into information preserving structures (such as classifications). Here the problems consist in part of: 1. discovering which properties should be described, and 2. deciding how the descriptions of the properties should be made. Rogers (1963) indicates that this problem is of classical origin and has played a major role in traditional taxonomic studies, but since the techniques for its solution have been largely informal, they have not been subjected to mathematical analysis. Part one of the problem still lies, for the most part, within the professional providence of the worker. The second part has been addressed in many ways. In some cases different descriptive schemes have been empirically tried in an attempt to discover a more pleasing result (Beers et al., 1962). In particular, Rohlf (1965), has described a statistical test to compare two different schemes of describing, when the descriptors are numerical. Analytical techniques from linear algebra (Rohlf and Sokal, 1962) have been used with some success to discover more efficient descriptors. Techniques using statistical methods of correlation are common. In other cases the force of precedent and convention is strong and some traditional scheme is adopted without question. Although much productive work toward measuring the efficiency and accuracy of descriptors has been done, the problem is still real, especially in cases where the descriptors are non-numerical. The following discussion is concerned with a general class of descriptors which are not necessarily numerical. A method is presented for: 1. measuring the interdependence of: a. two descriptors b. two sets of descriptors 2. measuring how successfully a given classification preserves the information in: a. a descriptor b. a set of descriptors. An example of the procedure using a group of orchids is provided.