On Improved Projection Techniques to Support Visual Exploration of Multi-Dimensional Data Sets

Projection (or dimensionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose, projections should be fast to allow multiple views of the same data set. In this work we present a novel fast technique for projecting multi-dimensional data sets into bidimensional (2D) spaces that preserves neighborhood relationships. Additionally, a new technique for improving 2D projections from multi-dimensional data is presented, that helps reduce the inherent loss of information yielded by dimensionality reduction. The results are stimulating and are presented in the form of comparative visualizations against known and new 2D projection techniques. Based on the projection improvement approach presented here, a new metric for quality of projection is also given, that matches well the visual perception of quality. We discuss the implication of using improved projections in visual exploration of large data sets and the role of interaction in visualization of projected subspaces.

[1]  William Schroeder,et al.  The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics , 1997 .

[2]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[3]  Herbert Edelsbrunner,et al.  Geometry and Topology for Mesh Generation , 2001, Cambridge monographs on applied and computational mathematics.

[4]  Christos Faloutsos,et al.  Deflating the dimensionality curse using multiple fractal dimensions , 2000, Proceedings of 16th International Conference on Data Engineering (Cat. No.00CB37073).

[5]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[6]  Urska Cvek,et al.  High-Dimensional Visualizations , 2002 .

[7]  Herbert Edelsbrunner,et al.  Geometry and Topology for Mesh Generation , 2001, Cambridge monographs on applied and computational mathematics.

[8]  Charu C. Aggarwal,et al.  A human-computer cooperative system for effective high dimensional clustering , 2001, KDD '01.

[9]  Christos Faloutsos,et al.  FastMap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets , 1995, SIGMOD '95.

[10]  Rosane Minghim,et al.  An interaction model for scientific visualization using sound , 2003, 16th Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI 2003).