Metric learning with multi-relational data

Over the past decades, there has been a growing interest in metric learning, a type of representation learning that aims to learn a distance metric that can fit to the data being analyzed. Many metric learning algorithms have been designed for data lying in Euclidean spaces, where a parametric Mahalanobis metric can be learned. However, such algorithms are often unable to handle relational data, that is not independent and identically distributed (i.i.d.), or can only be used at an entity level. In contrast, relational data allows for the discovery of complex interactions between features and entities, which can lead to better models. In this paper, we introduce two novel metric learning algorithms tailored to handle relational data, that preserve the structural information of the graph and use the features of the nodes as well. The first one is supervised and makes full use of both the graph structure and node labels with a carefully designed loss function, while the second is unsupervised and only uses the graph structure. Our experimental results show that both methods outperform state-of-the-art learning algorithms. Interestingly, we also find that the proposed unsupervised method often performs better than traditional supervised metric learning approaches.