## 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.

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.

Original language | English |
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Title of host publication | Interface '01 - Frontiers in Data Mining and Bioinformatics |

Publication status | Published - 2001 |