Voromap: A Voronoi-based tool for visual exploration of multi-dimensional data

Abstract

A map of multi-dimensional data is a graphical representation -defined in 2D or 3D space -of a set of data points that reflects similarity relationships amongst them. Triangulations of those points can be produced to generate surface meshes on which additional information can be mapped to visual attributes such as color or height. Such surfaces may then be used to explore the data set and the similarities between the different data points. In this paper we introduce Voromap, an exploration tool that is based on Voronoi diagrams of the projected data, and compare that representation with a standard representation that uses triangulations. Voronoi diagrams represent each element in the data set by the area of a polygon in which every point within the polygon is closer to its generating point than to any other point from the data set. A user experiment was conducted to compare Voronoi maps with equivalent maps represented by surface triangulations explored with a similar triangulation-based tool.

CheckViz: Sanity Check and Topological Clues for Linear and Non‐Linear Mappings

“…Colouring data points to display local information on the mapping is not new. See, for example [PFM*06]. This is easy to set up when dealing with a one‐dimensional index using for example a grey‐scale.…”

Hierarchical cluster visualization in web mapping systems

“…Techniques have been proposed that render clusters using icons [2], cells [16] and container shapes such as bounding boxes and hulls [8]. Space partitioning techniques, such as Voronoi tessellations that produce Voronoi polygons, have also been used to represent clusters [20]. Given a set of points, Voronoi polygons are polygons whose boundaries define the area that is closest to each point relative to all other points.…”

Vizualizing Large Spatial Datasets in Interactive Maps

“…Techniques have been proposed that render clusters using icons [9], cells [6] and container shapes such as boxes or hulls [10]. Space partitioning techniques, such as Voronoi tessellations that produce Voronoi polygons, have also been used to visualize clusters of objects [11].…”