Learning Weighted Product Spaces Representations for Graphs of Heterogeneous Structures

In representation learning, it is important to learn embedding spaces whose geometry matches the underlying structure of the data. In the literature, an active research direction aims at using product spaces, which consists of Euclidean and non-Euclidean manifolds to represent data of varying curvatures. However, real-world data is usually heterogeneous and consists of a mixture of varying structures, requiring the representation learning process to flexibly select and combine the member spaces accordingly. Since previous works only consider combination of embedding spaces with equal weights, in this paper, we propose a data-driven method to learn the embeddings in a weighted product spaces for graph data. Specifically, our model utilizes the topological information of input graph to learn the weight for each component of the product spaces. Experiments on synthetic and real-world datasets show that our models produce better representations in terms of distortion measures, and perform better on tasks such as word similarity learning.