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    Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections

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    v37i3pp241-251.pdf (19.29Mb)
    Date
    2018
    Author
    Thiagarajan, Jayaraman J.
    Liu, Shusen
    Ramamurthy, Karthikeyan Natesan
    Bremer, Peer-Timo
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    Abstract
    Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to bivariate relationships. Linear project can be considered as a compromise between complexity and interpretability, as they allow explicit axes labels, yet provide significantly more degrees of freedom compared to axis-aligned projections. Nevertheless, interpreting the axes directions, which are often linear combinations of many non-trivial components, remains difficult. To address this problem we introduce a structure aware decomposition of (multiple) linear projections into sparse sets of axis-aligned projections, which jointly capture all information of the original linear ones. In particular, we use tools from Dempster-Shafer theory to formally define how relevant a given axis-aligned project is to explain the neighborhood relations displayed in some linear projection. Furthermore, we introduce a new approach to discover a diverse set of high quality linear projections and show that in practice the information of k linear projections is often jointly encoded in ~ k axis-aligned plots. We have integrated these ideas into an interactive visualization system that allows users to jointly browse both linear projections and their axis-aligned representatives. Using a number of case studies we show how the resulting plots lead to more intuitive visualizations and new insights.
    BibTeX
    @article {10.1111:cgf.13416,
    journal = {Computer Graphics Forum},
    title = {{Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections}},
    author = {Thiagarajan, Jayaraman J. and Liu, Shusen and Ramamurthy, Karthikeyan Natesan and Bremer, Peer-Timo},
    year = {2018},
    publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/cgf.13416}
    }
    URI
    http://dx.doi.org/10.1111/cgf.13416
    https://diglib.eg.org:443/handle/10.1111/cgf13416
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    Eurographics Association copyright © 2013 - 2022 
    Send Feedback | Contact - Imprint | Data Privacy Policy | Disable Google Analytics
    Theme by @mire NV
    System hosted at  Graz University of Technology.
    TUGFhA