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    Area of Science:

    • Data Science
    • Computer Vision
    • Machine Learning

    Background:

    • Analyzing high-dimensional data often requires assumptions about underlying structures like clusters or manifolds.
    • Model and parameter selection for such data can be a time-consuming trial-and-error process.

    Purpose of the Study:

    • To develop an exploratory interface for visually identifying low-dimensional structures within high-dimensional datasets.
    • To facilitate the optimized selection of data models and configurations based on identified structures.

    Main Methods:

    • Abstracting global and local feature descriptors from neighborhood graph representations.
    • Utilizing pairwise geodesic distance (GD) and local tangent space divergence (LTSD) among points.
    • Proposing a novel LTSD-GD view by mapping LTSD and GD to axes via 1D multidimensional scaling.

    Main Results:

    • The LTSD-GD view visualizes the distribution of local tangent spaces (LTS) and their variations within data structures.
    • Unlike traditional methods, this view focuses on the properties of local geometry rather than just pairwise distances.
    • A suite of visual tools was designed and implemented for navigating and understanding intrinsic data structures.

    Conclusions:

    • The proposed exploratory interface and LTSD-GD view effectively support the visual identification of low-dimensional structures.
    • This approach aids in optimizing the selection of appropriate data models and parameters for high-dimensional datasets.
    • Case studies demonstrate the practical utility and effectiveness of the developed visual tools.