Mutational and Nonmutational Similarity Measures: A Preliminary Examination

Abstract

An examination of many of the indices proposed as numerical measures of pairwise similarity shows that they have strong relationships to string-to-string measures variously known as ‘Levenshtein distance’, ‘longest common subsequence’ or ‘minimal mutation distance’. The variations among coefficients are created in several ways, including changing the set of operations, using a richer structural pattern, modifying weights, limiting the extent of operations and varying the basis for normalisation. In total these measures provide a very flexible means of assessing similarity and can be extended to similarities based on collections of strings. While not denying the interest to the user of other properties, such as metricity or embedding in a euclidean space, examining the coefficients as variations on the Levenshtein theme provides a common basis for their comparison and provides the user with a means of choosing between coefficients in a rational manner. But however interesting this array of coefficients might be, it remains true that only some features of similarity will be captured in a minimal mutational measure. These features may be more or less than are actually required by the user. In this paper I have made a preliminary examination of various measures, some of which are related to the Levenshtein metric, and some of which appear to capture other aspects of similarity (i.e. topological, functional, analogic and/or conceptual). These latter are all measures which I have been unable to relate to the Levenshtein distance, although I have not pursued this very far as yet. All measures were applied to vegetation data, classifying both plots and attributes into a two-way table. The SAHN algorithm has been used for most of the clusterings, so that differences between measures of similarity are the primary cause of differences in results. In a few cases other clustering algorithms have been used and the data has been converted to presence/absence when this was necessary with the particular coefficient.