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    This study introduces a new framework using locality-sensitive hashing (LSH) for efficient comparison of merge trees in topological data analysis. This approach scales better for large scientific datasets and complex analyses.

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    Area of Science:

    • Scientific Visualization
    • Topological Data Analysis
    • Computer Science

    Background:

    • Scalar field comparison is crucial in scientific visualization.
    • Topological descriptors like merge trees offer robust data representations.
    • Existing similarity measures for merge trees do not scale well for large-scale, time-varying data.

    Purpose of the Study:

    • To develop a scalable framework for comparative analysis of merge trees.
    • To introduce novel similarity measures for merge trees using locality-sensitive hashing (LSH).
    • To enable efficient analysis of large-scale scientific datasets and ensembles.

    Main Methods:

    • Developed a new framework inspired by locality-sensitive hashing (LSH).
    • Proposed two novel LSH-based similarity measures for merge trees: extensions of Recursive MinHash and subpath signature.
    • Implemented and evaluated the efficiency and accuracy of the proposed measures.

    Main Results:

    • The proposed LSH framework significantly improves the scalability of merge tree comparison.
    • New similarity measures are computationally efficient and closely approximate existing methods like edit distance.
    • Demonstrated utility in shape matching, clustering, key event detection, and ensemble summarization.

    Conclusions:

    • The LSH-based framework offers a highly efficient and scalable solution for merge tree comparison.
    • This approach facilitates advanced comparative analysis on large scientific datasets.
    • The proposed methods are valuable for various applications in data analysis and visualization.