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

Peter Tino, Ian T. Nabney, Yi Sun, Bruce S. Williams

Research output: Contribution to conferencePaper

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 languageEnglish
Publication statusIn preparation - 2002
EventInterface '01 - Frontiers in Data Mining and Bioinformatics -
Duration: 1 Jan 20021 Jan 2002

Other

OtherInterface '01 - Frontiers in Data Mining and Bioinformatics
Period1/01/021/01/02

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Visualization
Drug products
Industry
Statistical Models

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

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, .
Tino, Peter ; Nabney, Ian T. ; Sun, Yi ; Williams, Bruce S. / A principled approach to interactive hierarchical non-linear visualization of high-dimensional data. Paper presented at Interface '01 - Frontiers in Data Mining and Bioinformatics, .
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title = "A principled approach to interactive hierarchical non-linear visualization of high-dimensional data",
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.",
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",
author = "Peter Tino and Nabney, {Ian T.} and Yi Sun and Williams, {Bruce S.}",
year = "2002",
language = "English",
note = "Interface '01 - Frontiers in Data Mining and Bioinformatics ; Conference date: 01-01-2002 Through 01-01-2002",

}

Tino, P, Nabney, IT, Sun, Y & Williams, BS 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, 1/01/02 - 1/01/02, .

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data. / Tino, Peter; Nabney, Ian T.; Sun, Yi; Williams, Bruce S.

2002. Paper presented at Interface '01 - Frontiers in Data Mining and Bioinformatics, .

Research output: Contribution to conferencePaper

TY - CONF

T1 - A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

AU - Tino, Peter

AU - Nabney, Ian T.

AU - Sun, Yi

AU - Williams, Bruce S.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Hierarchical visualization

KW - linear hierarchical visualization system

KW - Generative Topographic Mapping

KW - hierarchical probabilistic models

KW - hierarchical tree

KW - folding patterns

KW - low-dimensional projection

KW - magnification factors

KW - directional curvatures

KW - pharmaceutical industry

M3 - Paper

ER -

Tino P, Nabney IT, Sun Y, Williams BS. A principled approach to interactive hierarchical non-linear visualization of high-dimensional data. 2002. Paper presented at Interface '01 - Frontiers in Data Mining and Bioinformatics, .