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    Area of Science:

    • Data Visualization
    • Computational Geometry
    • Statistical Graphics

    Background:

    • Scatterplot matrices (SPLOMs) are crucial for multidimensional data exploration.
    • Existing scatterplot diagnostics (scagnostics) capture either shape or orientation, but not both.
    • A unified approach is needed to enhance SPLOM analysis scalability and effectiveness.

    Purpose of the Study:

    • To develop a novel scagnostics approach combining shape and orientation for scatterplot analysis.
    • To introduce skeleton-based similarity metrics for improved visual exploration of SPLOMs.
    • To evaluate the performance of the proposed method against existing techniques and human perception.

    Main Methods:

    • Utilized skeletonization (medial axes) from shape analysis to represent scatterplots.
    • Developed new similarity metrics based on these skeleton representations.
    • Conducted a user study to compare perceptual similarity with computational metrics.

    Main Results:

    • Skeleton-based scagnostics effectively capture both scatterplot shape and orientation.
    • The proposed metrics demonstrate robustness to noise and handle complex spatial distributions.
    • User study results indicate superior performance of skeleton-based metrics compared to graph-based scagnostics and other visual quality metrics in terms of perceptual similarity and computational efficiency.

    Conclusions:

    • Skeleton-based scagnostics offer a powerful, unified approach for scatterplot analysis.
    • This method enhances the scalability and effectiveness of exploring high-dimensional data with SPLOMs.
    • The findings suggest a new standard for scatterplot characterization and similarity measurement.