Multidimensional Scaling with Application to Twitter Network Data

Abstract

Multidimensional scaling is applied in varied fields such as marketing, genetics, ecology, molecular biology, psychology and social networks. In majority, multidimensional scaling has its main purpose to verify the relationship between individuals by embedding high-dimensional observations on a sphere to points on a lower-dimensional sphere. Simply put, multidimensional scaling makes it possible to look through the large data by illustrating them with a simple plot. In the process of applying multidimensional scaling to the data, we need to define a dissimilarity matrix, which reflects the distance between the each pair of the entities. Under the certain restrictions, there can be a variety of distance measures to construct the dissimilarity matrix. In this paper, we introduce several different distance measures possibly used for multidimensional scaling and categorize those measures so that they can be used in an appropriate circumstance. An application to the actual data has been done with the network data from Twitter. By implementing different types of measures to the specific data, we would like to show the importance of selecting an appropriate distance measure for the data.