Pure Spectral Graph Embeddings: Reinterpreting Graph Convolution for Top-N Recommendation

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.

Item Graph Convolution Collaborative Filtering for Inductive Recommendations

Graph Convolutional Networks (GCN) have been recently employed as core component in the construction of recommender system algorithms, interpreting user-item interactions as the edges of a bipartite graph. However, in the absence of side information, the majority of existing models adopt an approach of randomly initialising the user embeddings and optimising them throughout the training process. This strategy makes these algorithms inherently transductive, curtailing their ability to generate predictions for users that were unseen at training time. To address this issue, we propose a convolution-based algorithm, which is inductive from the user perspective, while at the same time, depending only on implicit user-item interaction data. We propose the construction of an item-item graph through a weighted projection of the bipartite interaction network and to employ convolution to inject higher order associations into item embeddings, while constructing user representations as weighted sums of the items with which they have interacted. Despite not training individual embeddings for each user our approach achieves state of-the-art recommendation performance with respect to transductive baselines on four real-world datasets, showing at the same time robust inductive performance.

On the instability of embeddings for recommender systems: the case of Matrix Factorization

Most state-of-the-art top-N collaborative recommender systems work by learning embeddings to jointly represent users and items. Learned embeddings are considered to be effective to solve a variety of tasks. Among others, providing and explaining recommendations. In this paper we question the reliability of the embeddings learned by Matrix Factorization (MF). We empirically demonstrate that, by simply changing the initial values assigned to the latent factors, the same MF method generates very different embeddings of items and users, and we highlight that this effect is stronger for less popular items. To overcome these drawbacks, we present a generalization of MF, called Nearest Neighbors Matrix Factorization (NNMF). The new method propagates the information about items and users to their neighbors, speeding up the training procedure and extending the amount of information that supports recommendations and representations. We describe the NNMF variants of three common MF approaches, and with extensive experiments on five different datasets we show that they strongly mitigate the instability issues of the original MF versions and they improve the accuracy of recommendations on the long-tail.