Related papers: Orometric Methods in Bounded Metric Data
This paper describes a new approach to the optimization of information extraction in multi-wavelength image cubes of cosmological fields. The objective is to create a framework for the automatic identification and tagging of sources…
The detection of out of distribution samples for image classification has been widely researched. Safety critical applications, such as autonomous driving, would benefit from the ability to localise the unusual objects causing the image to…
Knowledge representation (KR) is vital in designing symbolic notations to represent real-world facts and facilitate automated decision-making tasks. Knowledge graphs (KGs) have emerged so far as a popular form of KR, offering a contextual…
Recently, Goldreich introduced the notion of property testing of bounded-degree graphs with an unknown distribution. We propose a slight modification of his idea: the Radon-Nikodym Oracles. Using these oracles any reasonable graph property…
We propose a method to make natural language understanding models more parameter efficient by storing knowledge in an external knowledge graph (KG) and retrieving from this KG using a dense index. Given (possibly multilingual) downstream…
Graph Pooling technology plays an important role in graph node classification tasks. Sorting pooling technologies maintain large-value units for pooling graphs of varying sizes. However, by analyzing the statistical characteristic of…
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…
Solving cold-start problems is indispensable to provide meaningful recommendation results for new users and items. Under sparsely observed data, unobserved user-item pairs are also a vital source for distilling latent users' information…
Identifying objects in given data is a task frequently encountered in many applications. Finding vehicles or persons in video data, tracking seismic waves in geophysical exploration data, or predicting a storm front movement from…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
With the growing focus on semantic searches and interpretations, an increasing number of standardized vocabularies and ontologies are being designed and used to describe data. We investigate the querying of objects described by a…
We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…
Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
We introduce novel measures, L1 prestige and L1 centrality, for quantifying the prominence of each vertex in a strongly connected and directed graph by utilizing the concept of L1 data depth (Vardi and Zhang, Proc. Natl. Acad. Sci. U.S.A.\…
Open Information Extraction (OIE) methods extract facts from natural language text in the form of ("subject"; "relation"; "object") triples. These facts are, however, merely surface forms, the ambiguity of which impedes their downstream…
Knowledge graph (KG) enhanced recommendation has demonstrated improved performance in the recommendation system (RecSys) and attracted considerable research interest. Recently the literature has adopted neural graph networks (GNNs) on the…
The 3D localisation of an object and the estimation of its properties, such as shape and dimensions, are challenging under varying degrees of transparency and lighting conditions. In this paper, we propose a method for jointly localising…