Representation of Multirelations of Geographic Scenes Based on Hyperbolic Space

The recognition of complex geographic scenes requires to simultaneously describe different kinds of relations such as hyponymy and spatial relations among multiple-scale categories. The former is hierarchical structure, and the latter is called eigen structure. Current researches focus on representing these relations in Euclidean space. However, the key characteristic of the Euclidean spaces is that it expands polynomially with respect to the radius, which makes it difficult to describe both the hierarchical and eigen structure within finite computable dimensions simultaneously. To address the above issues, a hyperbolic embedding model for representing complex geographic scenes (HEMR) is first proposed. First, the visual features of remote sensing objects are extracted through a deep neural network in Euclidean space and mapped onto the n-dimensional Poincare ball in hyperbolic space by an exponential projection. Second, a two-stage contrastive learning mechanism based on Möbius transformation is designed, which uses the property of exponential expansion to obtain the ability to represent different kinds of relations. Finally, a new quaternion loss is designed to describe the relations between feature categories in remote sensing scenarios by hyperbolic distance. The experiments indicate that our model can leverage the characteristic of spatial exponential growth with the radius in hyperbolic space, simultaneously describing the hierarchical and eigen structures of complex remote sensing scenes in finite dimensions. This provides support for downstream tasks such as semantic segmentation of remote sensing, knowledge graph representation, and link prediction.