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    We present Generative Topographic Mapping for Structured Data (GTM-SD), a novel compositional model for mapping tree-structured data. GTM-SD enhances data discrimination by recursively mapping hierarchical information and shared substructures.

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    Area of Science:

    • Machine Learning
    • Data Science
    • Computational Linguistics

    Background:

    • Topographic mapping is crucial for visualizing complex data structures.
    • Existing methods often struggle with hierarchical and tree-structured data.
    • Compositional generative models offer a promising avenue for improved data representation.

    Purpose of the Study:

    • Introduce GTM-SD, the first compositional generative model for topographic mapping of tree-structured data.
    • Develop a scalable, recursive approach for hierarchical information mapping.
    • Improve the discrimination of sample structures compared to existing methods.

    Main Methods:

    • Utilize a scalable bottom-up hidden-tree Markov model for recursive mapping.
    • Implement recursive upward propagation for efficient exploitation of contextual information.
    • Project data onto a lattice of distinct subtrees for comprehensive mapping.

    Main Results:

    • GTM-SD enables topographic mapping of the full sample tree, including all distinct subtrees.
    • The model efficiently distributes substructure information across the topographic map.
    • Experimental results demonstrate finer-grained discrimination of sample structures.

    Conclusions:

    • GTM-SD offers a significant advancement in topographic mapping for tree-structured data.
    • The compositional and recursive nature of GTM-SD leads to superior data representation.
    • This approach outperforms state-of-the-art recursive neural networks in structure discrimination.