Adaptive Graph Encoder for Attributed Graph Embedding (2007.01594v1)

Abstract: Attributed graph embedding, which learns vector representations from graph topology and node features, is a challenging task for graph analysis. Recently, methods based on graph convolutional networks (GCNs) have made great progress on this task. However,existing GCN-based methods have three major drawbacks. Firstly,our experiments indicate that the entanglement of graph convolutional filters and weight matrices will harm both the performance and robustness. Secondly, we show that graph convolutional filters in these methods reveal to be special cases of generalized Laplacian smoothing filters, but they do not preserve optimal low-pass characteristics. Finally, the training objectives of existing algorithms are usually recovering the adjacency matrix or feature matrix, which are not always consistent with real-world applications. To address these issues, we propose Adaptive Graph Encoder (AGE), a novel attributed graph embedding framework. AGE consists of two modules: (1) To better alleviate the high-frequency noises in the node features, AGE first applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an adaptive encoder that iteratively strengthens the filtered features for better node embeddings. We conduct experiments using four public benchmark datasets to validate AGE on node clustering and link prediction tasks. Experimental results show that AGE consistently outperforms state-of-the-art graph embedding methods considerably on these tasks.

• The paper presents AGE, a framework that decouples convolutional filters from weight matrices to mitigate key drawbacks in GCN-based methods.
• It employs an adaptive encoder that iteratively refines node features using pairwise similarity matrices, leading to improved clustering and link prediction accuracy.
• AGE’s methodology reduces noise through optimal Laplacian smoothing and aligns training objectives with real-world applications, offering scalable graph representation learning.

Adaptive Graph Encoder for Attributed Graph Embedding: A Technical Summary

The paper introduces a novel framework for attributed graph embedding called Adaptive Graph Encoder (AGE), focusing on mitigating several identified drawbacks in current Graph Convolutional Network (GCN)-based methods. Attributed graph embedding aims to learn vector representations for graphs that incorporate both topology and node features, offering significant challenges due to the complex, high-dimensional, non-Euclidean nature of graphs.

Identified Drawbacks in GCN-Based Methods

The current GCN-based methods for graph embedding have three notable issues:

1. Entanglement of Graph Convolutional Filters and Weight Matrices: The paper highlights that the entangled design can negatively affect both performance and robustness in learning tasks. By decoupling these components, AGE seeks to improve model efficiency.
2. Suboptimal Laplacian Smoothing Filters: Existing methods use graph convolutional filters that are specialized forms of Laplacian filters, yet they do not maintain optimal low-pass characteristics, which are critical for effectively reducing noise in node features.
3. Misaligned Training Objectives: Most existing methods aim at recovering the adjacency or feature matrix, objectives that are not always suited to real-world applications.

The Adaptive Graph Encoder (AGE) Framework

To address these issues, AGE deploys two main components:

• Laplacian Smoothing Filter: AGE uses a specifically designed Laplacian smoothing filter that better alleviates high-frequency noise in node features, ensuring that the low-pass filtering properties are preserved.
• Adaptive Encoder: This component iteratively enhances filtered features to produce superior node embeddings. It employs an adaptive learning strategy that leverages pairwise similarity matrices to better capture the relationships between nodes effectively.

Methodology and Results

AGE's effectiveness is validated through extensive experiments on node clustering and link prediction tasks across four benchmark datasets. The results demonstrate AGE's superiority compared to state-of-the-art methods, highlighting improved clustering accuracy and robustness. Specifically, AGE consistently surpasses other methods in clustering by utilizing both topological and feature information in its learning process.

Theoretical and Practical Implications

The introduction of AGE marks a significant contribution to graph representation learning by strategically improving GCN-based architectures. The disentanglement of convolutional layers and the adaptive learning strategy pave the way for more efficient and resilient graph embedding methods. The theoretical implications lie in better understanding signal processing in graph domains, particularly concerning optimal smoothing techniques. Practically, AGE's adaptability to dataset-specific characteristics enhances its generalizability across various types of attributed graphs.

Future Directions

This framework opens multiple avenues for future research, particularly in further optimizing the selection and application of Laplacian smoothing filters. Additionally, enhancing the adaptive learning strategy to scalability issues inherent in large graphs remains an area ripe for exploration.

In conclusion, AGE offers a fresh perspective on graph embedding, focusing on structural separation, noise reduction, and adaptable learning objectives, which collectively promise to refine the quality and applicability of the learned embeddings across diverse graph-based tasks.