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Quantifying the Alignment of Graph and Features in Deep Learning.

Yifan Qian, Paul Expert, Tom Rieu

    IEEE Transactions on Neural Networks and Learning Systems
    |January 11, 2021
    PubMed
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    Graph convolutional networks (GCNs) classification performance depends on feature, graph, and ground truth alignment. A new subspace alignment measure (SAM) quantifies this relationship, revealing feature and graph importance.

    Area of Science:

    • Machine Learning
    • Network Science
    • Data Mining

    Background:

    • Graph convolutional networks (GCNs) are powerful tools for data analysis on graph structures.
    • Understanding factors influencing GCN classification performance is crucial for effective application.
    • Existing methods lack a unified measure to assess the alignment critical for GCNs.

    Purpose of the Study:

    • To introduce a novel Subspace Alignment Measure (SAM) for quantifying the alignment between features, graph structure, and ground truth in GCNs.
    • To establish a theoretical and empirical link between SAM and GCN classification performance.
    • To determine the relative importance of graph structure versus features for classification tasks.

    Main Methods:

    • Developed SAM based on principal angles between three subspaces: features, graph, and ground truth.

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  • Quantified SAM using the Frobenius norm of pairwise chordal distances.
  • Investigated SAM's relationship with GCN performance using limiting cases, randomizations, and real-world citation network datasets.

    • Main Results:

    • Demonstrated a clear correlation between SAM values and GCN classification performance across various datasets.
    • Showcased that higher alignment, as measured by SAM, leads to improved classification accuracy.
    • Empirically validated the spectral and geometrical interpretations of the proposed measure.
    • Identified the relative contributions of graph structure and features to classification outcomes.

    Conclusions:

    • The proposed Subspace Alignment Measure (SAM) effectively predicts and explains GCN classification performance.
    • Alignment between data features, graph topology, and labels is a critical determinant of GCN success.
    • The findings provide insights into optimizing GCN models by understanding feature and graph importance.