Visual exploration of data through their graph representations

Abstract

This chapter considers the problem of visually exploring structured and unstructured data sets. The representation of the data as the adjacency matrix of an appropriately defined graph transforms the problem into one of graph drawing. The basic idea of visual data exploration is to present the data in some visual form, allowing the human eye to gain insight from the representation, so that the user can draw conclusions and interact with the data in order to enhance her understanding. Visual data mining techniques have proven to be of high value in exploratory data analysis, as the increased research interest on the topic and the number of new data visualization products attest. A popular multivariate analysis technique that can be used for graph drawing purposes is multidimensional scaling. Its objective is to embed the vertices in a Euclidean space of appropriate dimensionality so that the Euclidean distances between the points that represent the nodes approximate well the path-length distances defined between the vertices in the original graph. The improvements that may be obtained by introducing negative weights in the underlying graph structure are also investigated.