Adaptive Graph Convolutional Neural Networks (1801.03226v1)

Abstract: Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for each graph data while training. To efficiently learn the graph, a distance metric learning is proposed. Extensive experiments on nine graph-structured datasets have demonstrated the superior performance improvement on both convergence speed and predictive accuracy.

• The paper presents an adaptive approach that generates unique graph Laplacians per input, overcoming the rigidity of fixed graph structures.
• The paper introduces residual graph learning to capture overlooked sub-structures and enhance feature representation during training.
• The paper leverages distance metric learning for computational efficiency, achieving improved RMSE and ROC-AUC scores across nine datasets.

Overview of Adaptive Graph Convolutional Neural Networks

The paper "Adaptive Graph Convolutional Neural Networks" introduces a generalized Graph Convolutional Neural Network (Graph CNN) capable of handling graph-structured data with varying sizes and connectivities. Unlike traditional Graph CNNs that rely on fixed graph structures, this approach learns a task-driven adaptive graph for each dataset during training. This flexibility is achieved through a proposed distance metric learning technique. The solution demonstrates significant improvements in both convergence speed and predictive accuracy, validated through extensive experiments on nine graph-structured datasets.

Key Contributions

1. Adaptive Graph Structures: The proposed model allows for individual graph Laplacians unique to each input data, addressing the limitations in traditional CNNs related to rigid graph structures. This adaptability facilitates better learning from diverse datasets, such as organic molecule graphs or social networks.
2. Residual Graph Learning: To improve learning capability, the paper introduces the concept of residual graphs. These are additional connections learned during training that complement intrinsic graphs. This approach ensures that significant sub-structures not captured by initial graphs are discovered and leveraged.
3. Efficient Metric Learning: The adaptive graph learning leverages distance metric learning, reducing parameter complexity to become independent of the graph size. This makes the learning process computationally manageable.
4. Experimental Validation: The model's efficiency is demonstrated through experiments that show substantial upgrades in RMSE and ROC-AUC scores compared to state-of-the-art methods such as graphconv, NFP, and GCN.

Technical Details

• Spectral Convolution: Unlike previous methods which utilized shared spectral filters and led to issues with localized filtering, this method assigns a spectral filter adjusted individually per input sample's unique graph topology.
• Learning Scheme: The spectral graph convolution with Laplacian Learning (SGC-LL) layer is central to the model. It learns optimal graph Laplacians using a Mahalanobis distance-based approach and updates these via supervised learning.
• Re-parametrization and Pooling: The model includes re-parametrization on feature space, graph max pooling, and graph gather layers, enhancing feature representation and addressing overfitting problems using bilateral filtering.

Implications and Future Work

The practical implications include more accurate predictions across diverse datasets, particularly in chemically informative predictions or point cloud classification tasks. Theoretically, the adaptive nature of graph construction could be extended to further applications where data structures are inherently irregular. Future developments could explore leveraging these methods in more complex terrains such as dynamic graph structures or integrating with reinforcement learning paradigms which frequently encounter non-static environments.

Conclusion

"Adaptive Graph Convolutional Neural Networks" presents a robust approach to Graph CNNs by allowing dynamic graph adaptation and efficient learning on graph-structured data. The model's competency in handling diverse and complex data structures marks a notable contribution to the field, potentially inspiring further work in adaptive machine learning systems.