Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
H-BLOB: a hierarchical visual clustering method using implicit surfaces
Proceedings of the conference on Visualization '00
HD-Eye: Visual Mining of High-Dimensional Data
IEEE Computer Graphics and Applications
3D Grand Tour for Multidimensional Data and Clusters
IDA '99 Proceedings of the Third International Symposium on Advances in Intelligent Data Analysis
Automatic Linguistic Indexing of Pictures by a Statistical Modeling Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parallel coordinates: a tool for visualizing multi-dimensional geometry
VIS '90 Proceedings of the 1st conference on Visualization '90
On improved projection techniques to support visual exploration of multidimensional data sets
Information Visualization - Special issue on coordinated and multiple views in exploratory visualization
Viz3D: Effective Exploratory Visualization of Large Multidimensional Data Sets
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Visualization Task Performance with 2D, 3D, and Combination Displays
IEEE Transactions on Visualization and Computer Graphics
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Visual analysis of image collections
The Visual Computer: International Journal of Computer Graphics - Special Issue SIBGRAPI 2008
Enclosing surfaces for point clusters using 3d discrete voronoi diagrams
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework's applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.