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Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view…

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from…

Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

Cross-lingual word embeddings can be applied to several natural language processing applications across multiple languages. Unlike prior works that use word embeddings based on the Euclidean space, this short paper presents a simple and…

Recently, Graph Convolution Network (GCN) based methods have achieved outstanding performance for recommendation. These methods embed users and items in Euclidean space, and perform graph convolution on user-item interaction graphs.…

Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…

Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in…

Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…

Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…

In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance…

Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and…

Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…

Recent work has demonstrated that embeddings of tree-like graphs in hyperbolic space surpass their Euclidean counterparts in performance by a large margin. Inspired by these results and scale-free structure in the word co-occurrence graph,…

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…

Learning unbiased node representations for imbalanced samples in the graph has become a more remarkable and important topic. For the graph, a significant challenge is that the topological properties of the nodes (e.g., locations, roles) are…

The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…