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        A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

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        Final Accepted Version (PDF, 201Kb)
        Author
        Tino, P.
        Nabney, I.
        Sun, Yi.
        Williams, B.S.
        Attention
        2299/16757
        Abstract
        Hierarchical visualization systems are desirable because a single twodimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: (1) we allow for non-linear projection manifolds (the basic building block is the Generative Topographic Mapping – GTM), (2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, (3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold’s local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.
        Publication date
        2001
        Published in
        Interface '01 - Frontiers in Data Mining and Bioinformatics
        Other links
        http://hdl.handle.net/2299/16757
        Relations
        School of Physics, Engineering & Computer Science
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