### Abstract

Hierarchical visualization systems are desirable because a single two-dimensional 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: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(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.

Original language | English |
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Publication status | In preparation - 2002 |

Event | Interface '01 - Frontiers in Data Mining and Bioinformatics - Duration: 1 Jan 2002 → 1 Jan 2002 |

### Other

Other | Interface '01 - Frontiers in Data Mining and Bioinformatics |
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Period | 1/01/02 → 1/01/02 |

### Keywords

- Hierarchical visualization
- linear hierarchical visualization system
- Generative Topographic Mapping
- hierarchical probabilistic models
- hierarchical tree
- folding patterns
- low-dimensional projection
- magnification factors
- directional curvatures
- pharmaceutical industry

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## Cite this

Tino, P., Nabney, I. T., Sun, Y., & Williams, B. S. (2002).

*A principled approach to interactive hierarchical non-linear visualization of high-dimensional data*. Paper presented at Interface '01 - Frontiers in Data Mining and Bioinformatics, .