  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.
