  This paper reports on the state-of-the-art in 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 use of MDS in
combination with parallel corpus data as used in research on cross-linguistic
variation.
  We first introduce the mathematical foundations of MDS and then give an
exhaustive overview of past research that employs MDS techniques in combination
with parallel corpus data. We propose a set of terminology to succinctly
describe the key parameters of a particular MDS application. We then show that
this computational methodology is theory-neutral, i.e. it can be employed to
answer research questions in a variety of linguistic theoretical frameworks.
Finally, we show how this leads to two lines of future developments for MDS
research in linguistics.
