Pure Spectral Graph Embeddings: Reinterpreting Graph Convolution for Top-N Recommendation
This work addresses a theoretical gap in graph-based recommender systems, offering a more efficient method for collaborative filtering.
The paper tackles the lack of theoretical understanding of why graph convolution improves collaborative filtering performance, showing that it pushes latent features into a subspace spanned by eigenvectors of the adjacency matrix, which are optimal for a training objective. It presents an approach using eigenvectors directly, eliminating training time and achieving higher performance on three real-world datasets.
The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is connected to a filtering operation on the graph spectral domain, the theoretical rationale for why this leads to higher performance on the collaborative filtering problem remains unknown. The presented work makes two contributions. First, we investigate the effect of using graph convolution throughout the user and item representation learning processes, demonstrating how the latent features learned are pushed from the filtering operation into the subspace spanned by the eigenvectors associated with the highest eigenvalues of the normalised adjacency matrix, and how vectors lying on this subspace are the optimal solutions for an objective function related to the sum of the prediction function over the training data. Then, we present an approach that directly leverages the eigenvectors to emulate the solution obtained through graph convolution, eliminating the requirement for a time-consuming gradient descent training procedure while also delivering higher performance on three real-world datasets.