Multidimensional scaling and linguistic theory

This paper reports on the state-of-the-art in the application of multidimensional scaling (MDS) techniques to create semantic maps in linguistic research. MDS refers to a statistical technique that represents objects (lexical items, linguistic contexts, languages, etc.) as points in a space so that close similarity between the objects corresponds to close distances between the corresponding points in the representation. We focus on the recent trend to apply MDS to parallel corpus data in order to investigate a certain linguistic phenomenon from a cross-linguistic perspective.
We first introduce the mathematical foundations of MDS, intended for non-experts, so that readers understand notions such as 'eigenvalues', 'dimensionality reduction', 'stress values', etc. as they appear in linguistic MDS writing.
We then give an exhaustive overview of past research that employs MDS techniques in combination with parallel corpus data, and propose a set of terminology to succinctly describe the key parameters of a particular MDS application. We go over various research questions that have been answered with the aid of MDS maps, showing that the methodology covers topics in a spectrum ranging from classic typology (e.g. language classification) to formal linguistics (e.g. study of a phenomenon in a single language).
We finally identify two lines of future research that build on the insights of earlier MDS research described in the paper. First, we envisage the use of MDS in the investigation of cross-linguistic variation of compositional structures, an important area in variation research that has not been approached by parallel corpus work yet. Second, we discuss how MDS can be complemented and compared with other dimensionality reduction techniques that have seen little use in the linguistic domain so far.