A Survey on Multidimensional Scaling

Abstract

This survey presents multidimensional scaling (MDS) methods and their applications in real world. MDS is an exploratory and multivariate data analysis technique becoming more and more popular. MDS is one of the multivariate data analysis techniques, which tries to represent the higher dimensional data into lower space. The input data for MDS analysis is measured by the dissimilarity or similarity of the objects under observation. Once the MDS technique is applied to the measured dissimilarity or similarity, MDS results in a spatial map. In the spatial map, the dissimilar objects are far apart while objects which are similar are placed close to each other. In this survey article, MDS is described in comprehensive fashion by explaining the basic notions of classicalMDS and how MDS can be helpful to analyze the multidimensional data. Later on, various special models based on MDS are described in a more mathematical way followed by comparisons of various MDS techniques.