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    New metrics, Steadiness and Cohesiveness, accurately measure inter-cluster reliability in multidimensional projection (MDP). These metrics ensure accurate cluster relationship identification, unlike previous methods.

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    Area of Science:

    • Data Visualization
    • Machine Learning
    • High-Dimensional Data Analysis

    Background:

    • Multidimensional projection (MDP) techniques reduce data dimensionality for visualization.
    • Assessing inter-cluster reliability is vital for tasks like identifying cluster relationships.
    • Existing metrics (e.g., Trustworthiness, Continuity) inadequately measure inter-cluster reliability.

    Purpose of the Study:

    • Introduce Steadiness and Cohesiveness, novel metrics for multidimensional projection (MDP) inter-cluster reliability.
    • Evaluate how well inter-cluster structures are preserved between high-dimensional and low-dimensional spaces.
    • Address the limitations of current metrics in capturing inter-cluster reliability distortions.

    Main Methods:

    • Developed Steadiness and Cohesiveness metrics to quantify inter-cluster reliability.
    • Steadiness assesses cluster preservation from projected to original space; Cohesiveness assesses the reverse.
    • Metrics extract random clusters and measure their distortion across spaces, enabling pointwise reliability assessment.

    Main Results:

    • Quantitative experiments confirm Steadiness and Cohesiveness accurately capture distortions affecting inter-cluster reliability.
    • Previous metrics demonstrated difficulty in detecting these specific distortions.
    • A reliability map visualization was introduced, highlighting pointwise inter-cluster reliability.

    Conclusions:

    • Steadiness and Cohesiveness provide a reliable measure of inter-cluster structure preservation in multidimensional projections (MDP).
    • The reliability map aids in selecting appropriate projection techniques and hyperparameters.
    • These metrics prevent misinterpretation in inter-cluster tasks, ensuring accurate identification of cluster structures.