A dimensionality reduction algorithm and its application for interactive visualization

Authors:
Jiyuan An;Jeffrey Xu Yu;Chotirat Ann Ratanamahatana;Yi-Ping Phoebe Chen
Affiliations:
School of Information Technology, Faculty of Science & Technology, Deakin University, Melbourne, Australia;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, China;Department of Computer Science & Engineering, University of California, Riverside, CA 92521, USA;Faculty of Science & Technology, Deakin University, Melbourne, Australia and Australia Research Council Centre in Bioinformatics, Australia
Venue:
Journal of Visual Languages and Computing
Year:
2007

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Abstract

Visualization is one of the most effective methods for analyzing how high-dimensional data are distributed. Dimensionality reduction techniques, such as PCA, can be used to map high dimensional data to a two- or three-dimensional space. In this paper, we propose an algorithm called HyperMap that can be effectively applied to visualization. Our algorithm can be seen as a generalization of FastMap. It preserves its linear computation complexity, and overcomes several main shortcomings, especially in visualization. Since there are more than two pivot objects in each axis of a target space, more distance information needs to be preserved in each dimension. Then in visualization, the number of pivot objects can go beyond the limitation of six (2-pivot objects x 3-dimensions). Our HyperMap algorithm also gives more flexibility to the target space, such that the data distribution can be observed from various viewpoints. Its effectiveness is confirmed by empirical evaluations on both real and synthetic datasets.