相关论文: Orometric Methods in Bounded Metric Data

Recommender systems are designed to predict user preferences over collections of items. These systems process users' previous interactions to decide which items should be ranked higher to satisfy their desires. An ensemble recommender…

Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space (usually a vector space). Ultimately, the plausibility of the…

The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable computation of GW distances and associated matchings on graphs…

Weighted graphs obtained from co-occurrence in user-item relations lead to non-metric topologies. We use this semi-metric behavior to issue recommendations, and discuss its relationship to transitive closure on fuzzy graphs. Finally, we…

Metric spaces $(X, d)$ are ubiquitous objects in mathematics and computer science that allow for capturing (pairwise) distance relationships $d(x, y)$ between points $x, y \in X$. Because of this, it is natural to ask what useful…

How to assess the potential of liking a city or a neighborhood before ever having been there. The concept of urban quality has until now pertained to global city ranking, where cities are evaluated under a grid of given parameters, or…

When humans play geolocation games such as GeoGuessr, they rely on concrete visual cues, such as road markings, vegetation, or architectural details, to infer where an image was captured. Whether image geolocation models rely on similar…

Knowledge graphs (KGs) such as DBpedia, Freebase, YAGO, Wikidata, and NELL were constructed to store large-scale, real-world facts as (subject, predicate, object) triples -- that can also be modeled as a graph, where a node (a subject or an…

In this work we reproduce the characterization of $\Gg^s$-sets from the euclidean setting [J. London Math. Soc. 49:267-280,1994] to more general metric spaces. These sets have Hausdorff dimension at least $s$ and are closed by countable…

Distance-based methods involve the computation of distance values between features and are a well-established paradigm in machine learning. In anomaly detection, anomalies are identified by their large distance from normal data points.…

Incorporating knowledge graphs (KGs) as side information in recommendation has recently attracted considerable attention. Despite the success in general recommendation scenarios, prior methods may fall short of performance satisfaction for…

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

Knowledge Graph embedding provides a versatile technique for representing knowledge. These techniques can be used in a variety of applications such as completion of knowledge graph to predict missing information, recommender systems,…

Site selection determines optimal locations for new stores, which is of crucial importance to business success. Especially, the wide application of artificial intelligence with multi-source urban data makes intelligent site selection…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

The paper considers a new quantitative-qualitative proximity measure for the features of information objects, where data enters a common information resource from several sources independently. The goal is to determine the possibility of…

Even though library and archival practice, as well as Digital Preservation, have a long tradition in identifying information objects, the question of their precise identity under change of carrier or migration is still a riddle to science.…

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…