Graph U-Nets (1905.05178v1)

Abstract: We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.

• The paper introduces novel gPool and gUnpool layers to adaptively downsample and upsample graph data while preserving structural information.
• The Graph U-Nets architecture uses an encoder-decoder structure with skip connections to balance high-level feature extraction with local detail retention.
• Experimental results demonstrate superior accuracy over baselines in both transductive and inductive settings, validating the method’s robustness.

Graph U-Nets: A Study on Graph Representation Learning

The paper "Graph U-Nets" by Hongyang Gao and Shuiwang Ji addresses a critical challenge in graph representation learning: extending convolutional neural networks (CNNs) functionalities like pooling and up-sampling to graph data. Traditional CNNs exhibit exceptional performance on grid-like structures, notably images, by leveraging locality and ordered relationships among pixels. However, extending these principles to irregular graph data requires novel approaches, as conventional pooling and up-sampling methods are unsuitable due to lack of spatial locality in graphs.

Main Contributions

1. Graph Pooling (gPool) and Unpooling (gUnpool) Layers:
   • gPool Layer: The gPool layer is introduced to adaptively select a subset of nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. This layer allows the network to reduce the graph size while preserving important structural information.
   • gUnpool Layer: The gUnpool layer reverses the operation of the gPool layer, restoring the original graph structure using the positional information of the nodes selected during pooling.
2. Graph U-Nets Architecture:
   • The proposed model is an encoder-decoder architecture similar to U-Net, designed specifically for graph data. The encoder part employs gPool layers to reduce the graph size progressively, while the decoder part utilizes gUnpool layers to restore graph dimensions.
   • By integrating skip connections between corresponding layers in the encoder and decoder, the architecture balances high-level feature extraction with the retention of local structural details.

Experimental Evaluation

The authors conduct thorough experiments on both transductive and inductive learning settings to validate the effectiveness of their methods. In the transductive setting, benchmark citation datasets such as Cora, Citeseer, and Pubmed are used. In the inductive setting, larger datasets including D&D, PROTEINS, and COLLAB are evaluated.

Performance Metrics

• Transductive Learning:
  • Cora: g-U-Nets achieved an accuracy of 84.4%, surpassing GCN (81.5%) and GAT (83.0%).
  • Citeseer: g-U-Nets attained 73.2% accuracy, outperforming GCN (70.3%) and GAT (72.5%).
  • Pubmed: g-U-Nets reached 79.6% accuracy, improving upon GCN (79.0%) and Planetoid (77.2%).
• Inductive Learning:
  • On the D&D dataset, g-U-Nets achieved 82.43%, which is higher than the state-of-the-art DiffPool (80.64%).
  • For PROTEINS, g-U-Nets demonstrated 77.68% accuracy, outclassing all other models including DiffPool (76.25%).
  • On COLLAB, g-U-Nets marked 77.56% which was competitive against existing methods.

Ablation Studies

The paper includes ablation studies examining the contributions of gPool and gUnpool layers, graph connectivity augmentation via graph power, and the effect of network depth. These studies highlight that g-U-Nets exhibit improved performance over their counterparts without gPool and gUnpool layers, and the graph connectivity enhancement notably benefits performance consistency and generalization.

Theoretical and Practical Implications

The introduction of gPool and gUnpool layers marks a substantial advancement in constructing deep learning models for graph data, enabling effective application of high-level feature encoding and decoding techniques akin to those in image processing. This bridge extends the utility of encoder-decoder architectures to graph domains, allowing tasks such as node classification and link prediction to exploit deep hierarchical features.

The use of trainable projection vectors and the graph power method to enhance graph connectivity ensures that the models retain essential information through successive pooling operations, addressing a key issue in graph down-sampling.

Future Directions

Future research can build upon this foundation by:

1. Integrating advanced graph convolutions (e.g., attention-based mechanisms) within the g-U-Nets framework.
2. Exploring other graph augmentation techniques to further enhance node connectivity and information propagation.
3. Applying gPool and gUnpool layers to diverse graph-based applications in molecular biology, social network analysis, and recommendation systems.

In conclusion, the Graph U-Nets model demonstrates a sophisticated approach to graph representation learning, using novel pooling and unpooling techniques to enable effective graph embedding. This work paves the way for further innovations in deep learning methods for non-Euclidean data structures.