On dimensionality of embedding space in multidimensional scaling. (English) Zbl 1211.90174

Žilinskas, Julius

Informatica, Vilnius 19, No. 3, 447-460 (2008).

Summary: Multidimensional scaling is a technique for exploratory analysis of multidimensional data widely usable in different applications. By means of this technique the image points in a low-dimensional embedding space can be found whose inter-point distances fit the given dissimilarities between the considered objects. In this paper dependence of relative visualization error on the dimensionality of embedding space is investigated. Both artificial and practical data sets are used. The images in three-dimensional embedding space normally show the structural properties of sets of considered objects with acceptable accuracy, and widening of applications of stereo screens makes three-dimensional visualization very attractive.

MSC:

90C26	Nonconvex programming, global optimization
62P30	Applications of statistics in engineering and industry; control charts

Keywords:

multidimensional scaling; global optimization; city-block distances