Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Term-weighting approaches in automatic text retrieval
Information Processing and Management: an International Journal
Laying out and visualizing large trees using a hyperbolic space
UIST '94 Proceedings of the 7th annual ACM symposium on User interface software and technology
A focus+context technique based on hyperbolic geometry for visualizing large hierarchies
CHI '95 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
An initial examination of ease of use for 2D and 3D information visualizations of Web content
International Journal of Human-Computer Studies - Empirical evaluation of information visualizations
Visual information foraging in a focus + context visualization
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Multidimensional Scaling by Deterministic Annealing
EMMCVPR '97 Proceedings of the First International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Drawing Large Graphs with H3Viewer and Site Manager
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
On interactive visualization of high-dimensional data using the hyperbolic plane
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
H3: laying out large directed graphs in 3D hyperbolic space
INFOVIS '97 Proceedings of the 1997 IEEE Symposium on Information Visualization (InfoVis '97)
Interactive Visualization and Navigation in Large Data Collections using the Hyperbolic Space
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Image fusion based on topographic mappings using the hyperbolic space
Information Visualization
Large-scale data exploration with the hierarchically growing hyperbolic SOM
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Journal of Multivariate Analysis
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We introduce a novel projection-based visualization method for high-dimensional data sets by combining concepts from MDS and the geometry of the hyperbolic spaces. This approach hyperbolic multi-dimensional scaling (H-MDS) is a synthesis of two important concepts for explorative data analysis and visualization: (i) multi-dimensional scaling uses proximity or pair distance data to generate a low-dimensional, spatial presentation of the data; (ii) previous work on the "hyperbolic tree browser" demonstrated the extraordinary advantages for an interactive display of graph-like data in the two-dimensional hyperbolic space (H2).In the new approach, H-MDS maps proximity data directly into the H2. This removes the restriction to "quasihierarchical", graph-based data--a major limitation of (ii). Since a suitable distance function can convert all kinds of data to proximity (or distance-based) data, this type of data can be considered the most general.We review important properties of the hyperbolic space and, in particular, the circular Poincaré model of the H2. It enables effective human-computer interaction: by mouse dragging the "focus", the user can navigate in the data without loosing the context. In H2 the "fish-eye" behavior originates not simply by a non-linear view transformation but rather by extraordinary, non-Euclidean properties of the H2. Especially, the exponential growth of length and area of the underlying space makes the H2 a prime target for mapping hierarchical and (now also) high-dimensional data.Several high-dimensional mapping examples including synthetic and real-world data are presented. Since high-dimensional data produce "ring"-shaped displays, we present methods to enhance the display by modulating the dissimilarity contrast. This is demonstrated for an application for unstructured text: i.e., by using multiple film critiques from news:rec.art.movies.reviews and www.imdb.com, each movie is placed within the H2--creating a "space of movies" for interactive exploration.