Conditions for Optimal Efficiency of Relative MDS

Article type: Research Article

Authors: Bernatavičienė, Jolita | Dzemyda, Gintautas | Marcinkevičius, Virginijus

Affiliations: Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania, e-mail: {jolitab, dzemyda, virgism}@ktl.mii.lt

Abstract: In this paper, the relative multidimensional scaling method is investigated. This method is designated to visualize large multidimensional data. The method encompasses application of multidimensional scaling (MDS) to the so-called basic vector set and further mapping of the remaining vectors from the analyzed data set. In the original algorithm of relative MDS, the visualization process is divided into three steps: the set of basis vectors is constructed using the k-means clustering method; this set is projected onto the plane using the MDS algorithm; the set of remaining data is visualized using the relative mapping algorithm. We propose a modification, which differs from the original algorithm in the strategy of selecting the basis vectors. The experimental investigation has shown that the modification exceeds the original algorithm in the visualization quality and computational expenses. The conditions, where the relative MDS efficiency exceeds that of standard MDS, are estimated.

Keywords: multidimensional scaling, visualization, clustering, relative MDS, large data sets, data mining

Journal: Informatica, vol. 18, no. 2, pp. 187-202, 2007