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.
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