Implicit Multidimensional Projection of Local Subspaces

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2020
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Bian, Rongzheng
Zhou, Liang
Zhang, Jian
Chen, Baoquan
Weiskopf, Daniel
Wang, Yunhai
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National Natural Science Foundation of China: 61772315
National Natural Science Foundation of China: 61861136012
Deutsche Forschungsgemeinschaft (DFG): 251654672 - TRR161
Deutsche Forschungsgemeinschaft (DFG): 251654672
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IEEE Transactions on Visualization and Computer Graphics. IEEE. 2020, 27(2), pp. 1558-1568. ISSN 1077-2626. eISSN 1941-0506. Available under: doi: 10.1109/tvcg.2020.3030368
Zusammenfassung

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.

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ISO 690BIAN, Rongzheng, Yumeng XUE, Liang ZHOU, Jian ZHANG, Baoquan CHEN, Daniel WEISKOPF, Yunhai WANG, 2020. Implicit Multidimensional Projection of Local Subspaces. In: IEEE Transactions on Visualization and Computer Graphics. IEEE. 2020, 27(2), pp. 1558-1568. ISSN 1077-2626. eISSN 1941-0506. Available under: doi: 10.1109/tvcg.2020.3030368
BibTex
@article{Bian2020-10-13Impli-68742,
  year={2020},
  doi={10.1109/tvcg.2020.3030368},
  title={Implicit Multidimensional Projection of Local Subspaces},
  number={2},
  volume={27},
  issn={1077-2626},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  pages={1558--1568},
  author={Bian, Rongzheng and Xue, Yumeng and Zhou, Liang and Zhang, Jian and Chen, Baoquan and Weiskopf, Daniel and Wang, Yunhai}
}
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