A Principled Approach to InteractiveHierarchical Non-Linear Visualization ofHigh-Dimensional Data

摘要

Hierarchical visualization systems are desirable because a single twodimensionalrnvisualization plot may not be sufficient to capture all of therninteresting aspects of complex high-dimensional data sets. We extendrnan existing locally linear hierarchical visualization system PhiVis [1] inrnseveral directions: (1) we allow for non-linear projection manifolds (thernbasic building block is the Generative Topographic Mapping – GTM), (2)rnwe introduce a general formulation of hierarchical probabilistic modelsrnconsisting of local probabilistic models organized in a hierarchical tree,rn(3) we describe folding patterns of low-dimensional projection manifoldrnin high-dimensional data space by computing and visualizing the manifold’srnlocal directional curvatures. Quantities such as magnification factorsrn[3] and directional curvatures are helpful for understanding the layoutrnof the nonlinear projection manifold in the data space and for furtherrnrefinement of the hierarchical visualization plot. Like PhiVis, our systemrnis statistically principled and is built interactively in a top-down fashionrnusing the EM algorithm. We demonstrate the visualization system principlernof the approach on a complex 12-dimensional data set and mentionrnpossible applications in the pharmaceutical industry.