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¹High Performance Computing Laboratory Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo, São Carlos, São Paulo, Brazil

Correspondence to: Rosane Minghim, Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo, Av. do Trabalhador São-Carlense, 400 - PO Box 668 São Carlos, São Paulo, CEP 13560-970, Brazil. Tel: +55(16)273 9730; fax: +55(16)273 9751; E-mail: rminghim@icmc.usp.br

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.

Information Visualization (2003) 2, 218-231. doi:10.1057/palgrave.ivs.9500054

dimensionality reduction; projection-based visualization techniques; Fastmap; NNP; force scheme; projection error estimation