The Past, Present, and Future of Multidimensional Scaling

Multidimensional scaling (MDS) has established itself as a standard tool for statisticians and applied researchers. Its success is due to its simple and easily interpretable representation of potentially complex structural data. These data are typically embedded into a 2-dimensional map, where the objects of interest (items, attributes, stimuli, respondents, etc.) correspond to points such that those that are near to each other are empirically similar, and those that are far apart are different. In this paper, we pay tribute to several important developers of MDS and give a subjective overview of milestones in MDS developments. We also discuss the present situation of MDS and give a brief outlook on its future. Multidimensional scaling (MDS) has become one of the core multivariate analysis techniques discussed in any standard data analysis, multivariate analysis, or computer science text book. A search in the Thomson Reuters Web of Science on the topic “multidimensional scaling” yielded 5,186 papers that were cited in 68,429 other papers (per January 2013). This clearly shows that MDS is an established multivariate analysis technique. Several important milestones in the development of MDS can be distinguished and the present paper is a subjective interpretation of that. As the present authors have been working in the area since the 1970s, they have developed their own subjective view of what they consider to be milestones in the development of MDS. The emphasis here lies on algorithmic milestones as they have cleared the way for practical use. We do not intend to provide an exhaustive overview of the history of MDS as that could easily require a book by itself (for further details, see Borg and Groenen (2005)). The remainder of this paper is organized both chronologically and per topic. We roughly distinguish three periods: past (until 1980), present (1980-2000), future (from 2000). Even though the future necessarily lies ahead, it always takes time for developments to be used by a wider audience, which explains the lag of about 15 years. Table 1 gives an overview of these subjective milestones of the authors, which are discussed in more detail in the subsequent sections. 1 The basic ideas of Multidimensional Scaling The core idea of MDS is explained by the first sentence in Borg and Groenen (2005): “Multidimensional scaling (MDS) is a method that represents measurements of similarity