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iHELP: interactive hierarchical linear projections for interpreting non-linear projections

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Abstract

We propose an interactive analytical system for exploring and interpreting non-linear projections. Although non-linear projections are widely used in disclosing complex structures in high-dimensional analysis, there is a strong need to interpret them due to their inherent complexity and weak interpretability. In the machine learning and visualization communities, it is inspiring to use local linear models to fit and interpret non-linear models. Regarding non-linear projections, there are research gaps in both generation and exploration of linear fitting segments. To fill this gap, we propose an optimization algorithm to partition a non-linear projection into linear segments according to the feature of local affine transformations. We then construct a hierarchy of linear segments and conjunct hierarchical visualizations to support a coarse-to-fine exploration. After that, we design and implement a visual interface that integrates the proposed algorithms and a suite of visual tools. Three case studies demonstrate that the proposed approach facilitates the interpretation of non-linear projections.

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Acknowledgements

We would like to thank the helpful comments from the anonymous reviewers. This work is supported by the National Natural Science Foundation of China (61872389, 62077039).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Central South University, Changsha, China

    Xingchen Zeng, Haowen Zhou, Zhicong Li, Chenqi Zhang & Xiaoyan Kui

  2. School of Computer Science and Engineering, Central South University and Academy of Plateau Science and Sustainability, Qinghai Normal University, Xining, China

    Jiazhi Xia

  3. Health Management Center of the Second Xiangya Hospital, Central South University, Changsha, China

    Yanyi Yang

  4. Software School of Xiamen University, Xiamen University, Xiamen, China

    Juncong Lin

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  1. Xingchen Zeng
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  2. Haowen Zhou
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  3. Zhicong Li
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  5. Juncong Lin
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  6. Jiazhi Xia
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Correspondence to Jiazhi Xia or Yanyi Yang.

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Zeng, X., Zhou, H., Li, Z. et al. iHELP: interactive hierarchical linear projections for interpreting non-linear projections. J Vis 26, 631–648 (2023). https://doi.org/10.1007/s12650-022-00900-4

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