Using Optimal Classification for multidimensional scaling analysis of linguistic data

Multidimensional scaling (MDS) is a technique for visualizing the relationships among data that are similar to each other on very many dimensions. For example, meanings of words such as indefinite pronouns are similar to each other by virtue of being expressed by the same indefinite pronoun in one language or another (Haspelmath 1997). If one compares indefinite pronouns of a large number of languages, the meanings they express are similar to each other on a very large number of “dimensions”, namely all the different indefinite pronouns of all the languages. MDS reduces the large number of dimensions of similarity to a small number—typically one or two dimensions—which can then be visually displayed and interpreted by the analyst. The example of indefinite pronouns illustrates one use of MDS in linguistic analysis: the analysis of complex patterns of crosslinguistic comparison. MDS is a mathematical technique which has been computationally implemented, and so can handle large and complex datasets that are difficult to analyze by hand in the semantic map model which is currently used for typological analysis (Haspelmath 1997, 2003; but see Regier et al. 2013). A description of the use of MDS for this type of crosslinguistic analysis can be found in Croft and Poole (2008) and Croft (2010). A more general and mathematical discussion of MDS and the Optimal Classification algorithm (see below) can be found in Poole (2000, 2005).