SVD-GCN: A Simplified Graph Convolution Paradigm for Recommendation

With the tremendous success of Graph Convolutional Networks (GCNs), they have been widely applied to recommender systems and have shown promising performance. However, most GCN-based methods rigorously stick to a common GCN learning paradigm and suffer from two limitations: (1) the limited scalability due to the high computational cost and slow training convergence; (2) the notorious over-smoothing issue which reduces performance as stacking graph convolution layers. We argue that the above limitations are due to the lack of a deep understanding of GCN-based methods. To this end, we first investigate what design makes GCN effective for recommendation. By simplifying LightGCN, we show the close connection between GCN-based and low-rank methods such as Singular Value Decomposition (SVD) and Matrix Factorization (MF), where stacking graph convolution layers is to learn a low-rank representation by emphasizing (suppressing) components with larger (smaller) singular values. Based on this observation, we replace the core design of GCN-based methods with a flexible truncated SVD and propose a simplified GCN learning paradigm dubbed SVD-GCN, which only exploits $K$-largest singular vectors for recommendation. To alleviate the over-smoothing issue, we propose a renormalization trick to adjust the singular value gap, resulting in significant improvement. Extensive experiments on three real-world datasets show that our proposed SVD-GCN not only significantly outperforms state-of-the-arts but also achieves over 100x and 10x speedups over LightGCN and MF, respectively.

Less is More: Reweighting Important Spectral Graph Features for Recommendation

As much as Graph Convolutional Networks (GCNs) have shown tremendous success in recommender systems and collaborative filtering (CF), the mechanism of how they, especially the core components (\textit{i.e.,} neighborhood aggregation) contribute to recommendation has not been well studied. To unveil the effectiveness of GCNs for recommendation, we first analyze them in a spectral perspective and discover two important findings: (1) only a small portion of spectral graph features that emphasize the neighborhood smoothness and difference contribute to the recommendation accuracy, whereas most graph information can be considered as noise that even reduces the performance, and (2) repetition of the neighborhood aggregation emphasizes smoothed features and filters out noise information in an ineffective way. Based on the two findings above, we propose a new GCN learning scheme for recommendation by replacing neihgborhood aggregation with a simple yet effective Graph Denoising Encoder (GDE), which acts as a band pass filter to capture important graph features. We show that our proposed method alleviates the over-smoothing and is comparable to an indefinite-layer GCN that can take any-hop neighborhood into consideration. Finally, we dynamically adjust the gradients over the negative samples to expedite model training without introducing additional complexity. Extensive experiments on five real-world datasets show that our proposed method not only outperforms state-of-the-arts but also achieves 12x speedup over LightGCN.

A Robust Hierarchical Graph Convolutional Network Model for Collaborative Filtering

Graph Convolutional Network (GCN) has achieved great success and has been applied in various fields including recommender systems. However, GCN still suffers from many issues such as training difficulties, over-smoothing, vulnerable to adversarial attacks, etc. Distinct from current GCN-based methods which simply employ GCN for recommendation, in this paper we are committed to build a robust GCN model for collaborative filtering. Firstly, we argue that recursively incorporating messages from different order neighborhood mixes distinct node messages indistinguishably, which increases the training difficulty; instead we choose to separately aggregate different order neighbor messages with a simple GCN model which has been shown effective; then we accumulate them together in a hierarchical way without introducing additional model parameters. Secondly, we propose a solution to alleviate over-smoothing by randomly dropping out neighbor messages at each layer, which also well prevents over-fitting and enhances the robustness. Extensive experiments on three real-world datasets demonstrate the effectiveness and robustness of our model.