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Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs [article]

Nurendra Choudhary, Nikhil Rao, Sumeet Katariya, Karthik Subbian, Chandan K. Reddy
2020 arXiv   pre-print
Hyperboloids, unlike vectors in hyperbolic spaces, allow us to use dynamic sizes for KG representations.  ...  In the recently proposed Query2Box model [35] , the authors demonstrated the effectiveness of complex geometries (such as hyper-rectangles) with varying offsets that control the size of an answer space  ...  A HYPERBOLIC VS EUCLIDEAN DISTANCES To better analyze the impact of adopting hyperbolic space, we need to understand its distinction from the Euclidean space in handling hierarchy.  ... 
arXiv:2012.13023v1 fatcat:47g5v3zd3nhyllyztbwstnzc4i

Adaptive Hierarchical Similarity Metric Learning with Noisy Labels [article]

Jiexi Yan, Lei Luo, Cheng Deng, Heng Huang
2021 arXiv   pre-print
further improve the generalization ability of the model using contrastive augmentation.  ...  Specifically, class-wise divergence can effectively excavate richer similarity information beyond binary in modeling by taking advantage of Hyperbolic metric learning, while sample-wise consistency can  ...  Hyperbolic Geometry Hyperbolic geometry, also called Lobachevskian Geometry, is a non-Euclidean geometry that rejects the validity of Euclid's fifth, the "parallel", postulate but admits the other four  ... 
arXiv:2111.00006v1 fatcat:nx6hsswcijgd3ba6q5umrip7lu

Geodesic distances for web document clustering

Selma Tekir, Florian Mansmann, Daniel Keim
2011 2011 IEEE Symposium on Computational Intelligence and Data Mining (CIDM)  
In particular, we test the effectiveness of geodesic distances as similarity measures under the space assumption of spherical geometry in a 0-sphere.  ...  The effectiveness of our approach is measured by computing micro-precision values of the clusters based on the provided categorical information of each article.  ...  Distortion measures are used to evaluate the results of the clustering along with the ground truth categorization.  ... 
doi:10.1109/cidm.2011.5949449 dblp:conf/cidm/TekirMK11 fatcat:7ayn5gyfa5atpetzf4f6dxmy64

von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning [article]

Tyler R. Scott and Andrew C. Gallagher and Michael C. Mozer
2021 arXiv   pre-print
Softmax classifiers have been studied using different embedding geometries -- Euclidean, hyperbolic, and spherical -- and claims have been made about the superiority of one or another, but they have not  ...  We conduct an empirical investigation of embedding geometry on softmax losses for a variety of fixed-set classification and image retrieval tasks.  ...  Hyperspherical Variational 3D Object Representations for Fine-Grained Categorization. Auto-Encoders.  ... 
arXiv:2103.15718v4 fatcat:brsxb3so5ngchemwj3pffrvkeq

Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation [article]

Yankai Chen, Menglin Yang, Yingxue Zhang, Mengchen Zhao, Ziqiao Meng, Jianye Hao, Irwin King
2022 arXiv   pre-print
To address this issue and provide more accurate recommendation, we propose a knowledge-aware recommendation method with the hyperbolic geometry, namely Lorentzian Knowledge-enhanced Graph convolutional  ...  Specifically, we employ different information propagation strategies in the hyperbolic space to explicitly encode heterogeneous information from historical interactions and KGs.  ...  PROPOSED LKGR APPROACH 3.1 Hyperbolic Geometry Preliminaries Hyperbolic geometry is a non-Euclidean geometry with a constant negative curvature measuring how a geometric object deviates from a flat plane  ... 
arXiv:2108.06468v3 fatcat:crvllwrugvhsvc7h2lg3skchdu

Robust Formal Watermarking Model Based on the Hyperbolic Geometry for Image Security

2020 International journal of recent technology and engineering  
In this paper, we propose a new watermarking solution that is applicable to image watermarking and is based on hyperbolic geometry.  ...  Digital watermarking is a possible solution to this challenge as it has already been used for copyright protection, source tracking, and video authentication to name just a few applications of its use.  ...  Properties of hyperbolic geometry The basis of hyperbolic geometric is driven by Euclid's five postulates [22] . Thus hyperbolic geometry must be understood in light of Euclidian geometry.  ... 
doi:10.35940/ijrte.c4651.099320 fatcat:co346ou35bdr5pbsrmjkkt6xdm

HAKG

Yuntao Du, Xinjun Zhu, Lu Chen, Baihua Zheng, Yunjun Gao
2022 Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval  
Technically, we model users and items (that are captured by a user-item graph), as well as entities and relations (that are captured in a KG) in hyperbolic space, and design a new hyperbolic aggregation  ...  Further analyses on the learned hyperbolic embeddings confirm that HAKG can offer meaningful insights into the hierarchies of data. CCS CONCEPTS • Information systems → Recommender systems.  ...  power of hyperbolic geometry.  ... 
doi:10.1145/3477495.3531987 fatcat:drb4k3f3ufczdawlcys3pouiva

Numerical Analysis of a Trapezoidal Microchannel for Hydrodynamic Detachment of Cells

2020 International Journal of Engineering and Advanced Technology  
Additionally, the pressure drop can be reduced by modifying the geometry of the trapezoidal channel to minimize pressure loss.  ...  In this study, a novel microchannel with a trapezoidal structure was investigated using computational fluid dynamics simulations.  ...  The width of the hyperbolic tangent (l) was varied, while the L T,2 (median length of trapezoidal structure) was kept constant at 2 mm and l = l*.  ... 
doi:10.35940/ijeat.d7454.049420 fatcat:uwh3ujt7azg47ph4z66xmi65bm

An initial examination of ease of use for 2D and 3D information visualizations of web content

KIRSTEN RISDEN, MARY P. CZERWINSKI, TAMARA MUNZNER, DANIEL B. COOK
2000 International Journal of Human-Computer Studies  
and 2D lists for effective information retrieval.  ...  A standard collapse/expand tree browser and a Web-based hierarchical categorization similar to Yahoo!, were competitively evaluated against XML3D.  ...  The specific merits of using hyperbolic geometry as the distortion technique are discussed at length in several previous papers (Lamping et al, 1995; Munzner & Burchard, 1995; Munzner, 1997) , and do  ... 
doi:10.1006/ijhc.2000.0413 fatcat:s75u5oay2fc6bg3vtglayvwacu

Spatial and Temporal Behavior of Microwave Backscatter Directional Modulation Over the Saharan Ergs

Haroon Stephen, David G. Long
2007 IEEE Transactions on Geoscience and Remote Sensing  
Radar backscatter (σ • ) from ergs is modulated with view direction [incidence (θ) and azimuth (φ) angles], where the modulation characteristics reflect the surface geometry. σ • also varies spatially  ...  We use the maxima of the φ-modulation at θ = 33 • to infer the orientation of the dominant slip-sides on the sand surface.  ...  The erg surface geometry varies with time and has a complex dependence on the variability of prevailing winds.  ... 
doi:10.1109/tgrs.2007.892584 fatcat:os4bbmv7cvfxpohcz3xulnowna

ANTHEM

Nurendra Choudhary, Nikhil Rao, Sumeet Katariya, Karthik Subbian, Chandan K. Reddy
2022 Proceedings of the Fifteenth ACM International Conference on Web Search and Data Mining  
We also demonstrate the quality of ANTHEM's query encoder using a query matching task.  ...  To address these challenges, in this paper, we propose an AtteNTive Hyperbolic Entity Model (ANTHEM), a novel attention-based product search framework that models query entities as two-vector hyperboloids  ...  We capture this varying significance to scale the embeddings using self-attention networks [35] .  ... 
doi:10.1145/3488560.3498456 fatcat:5skmjm7x6vfeppjo7x5kamo4em

Statistical framework for model-based image retrieval in medical applications

Daniel Keysers
2003 Journal of Electronic Imaging (JEI)  
1͒: 1. image categorization ͑based on global features͒ 2. image registration ͑in geometry and contrast͒ 3. feature extraction ͑using local features͒ 4. feature selection ͑category and query dependent͒  ...  Fig. 3 3 Example images generated using linear approximations of affine transforms and image brightness: (a) original image, (b) left shift, (c) down shift, (d) hyperbolic diagonal deformation, (e) hyperbolic  ...  His research interests are medical image processing applied to quantitative measurements for diagnoses and content-based image retrieval from large medical databases.  ... 
doi:10.1117/1.1525790 fatcat:uplsxkmivzd57islgirlcn5rpm

Electron-driven photon sources for correlative electron-photon spectroscopy with electron microscopes

Joshua Christopher, Masoud Taleb, Achyut Maity, Mario Hentschel, Harald Giessen, Nahid Talebi
2020 Nanophotonics  
The CL maps at various wavelengths support the same symmetry profile, though with varying number of hyperbolic lines.  ...  The interference principle can be used for retrieving the spectral phase, similar to the spatial holography techniques retrieving spatial phases.  ... 
doi:10.1515/nanoph-2020-0263 fatcat:ewmuvl2fbze7ril5lohkylbfcq

Lagrangian Coherent Structures and Vortex Formation in High Spatiotemporal‐Resolution Satellite Winds of an Atmospheric Kármán Vortex Street

T. Günther, Á. Horváth, W. Bresky, J. Daniels, S. A. Buehler
2021 Journal of Geophysical Research - Atmospheres  
Image-Based Methods The previous geometry-based methods require the seeding of line geometry.  ...  Geometry-based methods (integral curves) require careful seeding and are primarily useful for qualitative analysis, and when shown in combination with an underlying scalar field that makes use of the non-occluded  ...  The high-resolution GOES-16 wind retrievals are available from the Zenodo data repository (https://doi.org/10.5281/zenodo.3534276).  ... 
doi:10.1029/2021jd035000 fatcat:csimqvjhkvgmdiz72y5nplf3wu

Towards Efficient NDN Framework for Connected Vehicle Applications

Ning Yang, Kang Chen, Yaoqing Liu
2020 IEEE Access  
To avoid overloading high-level routers, H2NDN integrates hyperbolic routing into the hierarchical architecture through carefully designed hyperbolic planes.  ...  As a result, efficient and scalable data retrieval can be achieved by only configuring static forwarding information base (FIB) on NDN routers.  ...  The studies in [32] , [33] also demonstrate the connection between scale-free complex networks and hyperbolic geometries.  ... 
doi:10.1109/access.2020.2981928 fatcat:dcfwaox4wrcltkpntlnhlasiwm
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