Overlapping Spaces For Compact Graph Representations

Abstract

Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best configuration of product space is a resource-intensive procedure, which reduces the practical applicability of the idea. We generalize the concept of product space and introduce an overlapping space that does not have the configuration search problem. The main idea is to allow subsets of coordinates to be shared between spaces of different types (Euclidean, hyperbolic, spherical). As a result, parameter optimization automatically learns the optimal configuration. Additionally, overlapping spaces allow for more compact representations since their geometry is more complex. Our experiments confirm that overlapping spaces outperform the competitors in graph embedding tasks. Here, we consider both distortion setup, where the aim is to preserve distances, and r

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