We discuss methodology for multidimensional scaling (MDS) and its implementation in two software systems, GGvis and XGvis. MDS is a visualization technique for proximity data, that is, data in the form of N × N dissimilarity matrices. MDS constructs maps (“configurations, ” “embeddings”) in IR k by interpreting the dissimilarities as distances. Two frequent sources of dissimilarities are high-dimensional data and graphs. When the dissimilarities are distances between high-dimensional objects, MDS acts as a (often nonlinear) dimension-reduction technique. When the dissimilarities are shortest-path distances in a graph, MDS acts as a graph layout technique. MDS has found recent attention in machine learning motivated by image databases (“Isomap”). MDS is also of interest in view of the popularity of “kernelizing ” approaches inspired by Support Vector Machines (SVMs; “kernel PCA”). This article discusses the following general topics: (1) the stability and multiplicity of MDS solutions; (2) the analysis of structure within and between subsets of objects with missing value schemes in dissimilarity matrices; (3) gradient descent for optimizing general MDS loss functions (“Strain ” and “Stress”); (4) a unification of classical

. In this paper the problem of visualizing categorical multivariate data sets is considered. By representing the data as the adjacency matrix of an appropriately defined bipartite graph, the problem is transformed to one of graph drawing. A general graph drawing framework is introduced, the corresponding mathematical problem defined and an algorithmic approach for solving the necessary optimization problem discussed. The new approach is illustrated through several examples. 1.

It is often useful to get high-level views of datasets in order to identify areas of interest worthy of further exploration. In relational databases, the high-level view can be described using Entity-Relationship diagrams, which identify relationships between entities in the data model. Such high-level views are useful for database design activities, and can be used to generate user interfaces for constructing queries. This research introduces techniques for visualizing structural similarity of database queries. We demonstrate that individual queries can be visualized using graph visualization techniques. A distance measure based on query structure is proposed that provides database designers and administrators with a high-level perspective of relationships in the underlying data.