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    Area of Science:

    • Graph Machine Learning
    • Network Science
    • Information Theory

    Background:

    • Real-world networks (social, biological, communication) offer rich data for unsupervised learning.
    • Extracting information from graph-structured data into embeddings without supervision is a key challenge.

    Purpose of the Study:

    • To develop a method for preserving and extracting information from graph data into an embedding space without supervision.
    • To introduce Graphical Mutual Information (GMI) and its extension GMI++ for measuring graph-representation correlation.

    Main Methods:

    • Generalized mutual information computation from vector space to graph domain, introducing Graphical Mutual Information (GMI).
    • GMI++ captures global topological properties by analyzing node co-occurrence, complementing GMI's local perspective.
    • Developed an unsupervised embedding model utilizing GMI for downstream tasks.

    Main Results:

    • GMI and GMI++ are invariant to isomorphic transformations of input graphs.
    • These methods are efficiently estimated and maximized using current mutual information techniques.
    • Theoretical analysis confirms the correctness and rationality of GMI and GMI++.

    Conclusions:

    • GMI-based methods provide a robust framework for unsupervised graph representation learning.
    • The developed model achieves promising performance in node classification, link prediction, and anomaly detection.
    • GMI offers a novel approach to harnessing the information within complex network structures.