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.
翻译:本文报告了应用多维缩放(MDS)技术在语言研究中创建语义地图的数学基础。 MDS将代表物体(语言项目、语言背景、语言等)的统计技术作为空间中的点,以使对象之间的近似性与代表中相应点之间的距离相近。我们侧重于最近的趋势,即将MDS应用于平行物质数据,以便从跨语言角度调查某种语言现象。我们首先为非专家介绍MDS的数学基础,以便读者理解“egenvalue”、“demoity reduction”、“respress value”等在语言MDS的写作中出现的概念。然后我们详尽地概述过去使用MDS技术与平行物质数据之间的近距离。我们提出了一套术语,简明地描述特定MDS应用的关键参数。我们用MDS地图解答了各种研究问题,显示该方法覆盖了从典型类型结构的频谱范围(例如:MDS的跨语言结构,我们最终用一种语言流化研究领域来解释,而另一种语言流化研究领域,我们用另一种语言流化的流化研究领域,最后用一种预论,我们先行,用一种语言流学的流略法的流略研究领域,然后用另一种方法可以理解。