相关论文: Orometric Methods in Bounded Metric Data

Knowledge Graphs (KGs) have gained considerable attention recently from both academia and industry. In fact, incorporating graph technology and the copious of various graph datasets have led the research community to build sophisticated…

We develop an algorithm to explore an environment to generate a measurement model for use in future localization tasks. Ergodic exploration with respect to the likelihood of a particular class of measurement (e.g., a contact detection…

In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…

Trans-Neptunian Objects (TNOs) provide a window into the history of the Solar System, but they can be challenging to observe due to their distance from the Sun and relatively low brightness. Here we report the detection of 75 moving objects…

Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…

Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…

Recent years have witnessed the emergence of a new class of social networks, that require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process…

Knowledge graphs (KGs) have shown to be an important asset of large companies like Google and Microsoft. KGs play an important role in providing structured and semantically rich information, making them available to people and machines, and…

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…

This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus…

The evaluation of Datalog rules over large Knowledge Graphs (KGs) is essential for many applications. In this paper, we present a new method of materializing Datalog inferences, which combines a column-based memory layout with novel…

Knowledge Graphs (KGs) have been applied to many tasks including Web search, link prediction, recommendation, natural language processing, and entity linking. However, most KGs are far from complete and are growing at a rapid pace. To…

This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

The surge in 3D modeling has led to a pronounced research emphasis on the field of 3D shape retrieval. Numerous contemporary approaches have been put forth to tackle this intricate challenge. Nevertheless, effectively addressing the…

Graph neural networks (GNN) have recently been applied to exploit knowledge graph (KG) for recommendation. Existing GNN-based methods explicitly model the dependency between an entity and its local graph context in KG (i.e., the set of its…

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…