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Knowledge Graph Embeddings in Geometric Algebras [article]

Chengjin Xu, Mojtaba Nayyeri, Yung-Yu Chen, Jens Lehmann
2021 arXiv   pre-print
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space.  ...  into a geometric algebra.  ...  Our Method Knowledge Graph Embedding Model based on Geometric Algebras Let E denote the set of all entities and R the set of all relations present in a knowledge graph.  ... 
arXiv:2010.00989v4 fatcat:sapkzmumnvhyvnn4vx3diiggwu

Knowledge Graph Embeddings in Geometric Algebras

Chengjin Xu, Mojtaba Nayyeri, Yung-Yu Chen, Jens Lehmann
2020 Proceedings of the 28th International Conference on Computational Linguistics   unpublished
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a low dimensional latent representation space.  ...  into a geometric algebra.  ...  Our Method Knowledge Graph Embedding Model based on Geometric Algebras Let E denote the set of all entities and R the set of all relations present in a knowledge graph.  ... 
doi:10.18653/v1/2020.coling-main.46 fatcat:if4tbonmozfkniecucvslhivqu

From One Point to A Manifold: Knowledge Graph Embedding For Precise Link Prediction [article]

Han Xiao, Minlie Huang, Xiaoyan Zhu
2017 arXiv   pre-print
Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space.  ...  However, existing methods could not characterize the knowledge graph in a fine degree to make a precise prediction.  ...  Besides, RESCAL is a collective matrix factorization model which is also a common method in knowledge graph embedding [Nickel et al., 2011] , [Nickel et al., 2012] .  ... 
arXiv:1512.04792v5 fatcat:r7wgg2l55bgjhd2l6x33mj2qf4

Solving Analogies on Words based on Minimal Complexity Transformation

Pierre-Alexandre Murena, Marie Al-Ghossein, Jean-Louis Dessalles, Antoine Cornuéjols
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
If most approaches rely on the axioms of proportional analogy to solve these equations, these axioms are known to have limitations, in particular in the nature of the considered flections.  ...  In this paper, we propose an alternative approach, based on the assumption that optimal word inflections are transformations of minimal complexity.  ...  One recent approach along this line that is based on the geometric interpretation of knowledge graph embeddings is presented in Kulmanov et al. [2019] .  ... 
doi:10.24963/ijcai.2020/252 dblp:conf/ijcai/OzcepLW20 fatcat:woapfdle2bgejniwpar7ulas5m

Designing Optimal Multiplex Networks for Certain Laplacian Spectral Properties [article]

Heman Shakeri, Ali Tavassoli, Ehsan Ardjmand, Pietro Poggi-Corradini
2020 arXiv   pre-print
In the dual picture, the optimal graph embedding is one-dimensional and non-homogeneous at first and beyond this threshold, the optimal embedding expands to be multi-dimensional, and for larger values  ...  The dual formulation transforms the problem into a graph realization (embedding) problem that allows us to give a fuller picture.  ...  2-D embedding of two 30-node random geometric graphs: numbers 1-30 are the node set for G1 and numbers 31-60 indicate the nodes of graph G2.  ... 
arXiv:1903.01073v2 fatcat:2nnlo2dg4jdoji35mcmfxkjtru

Quadratic equations in Swedish textbooks for upper-secondary school

Wang Wei Sönnerhed
2021 LUMAT  
Geometrical representations for some algebra identities and completing the square are widely used in both theoretical presentations and tasks, which implies that conceptual learning is encouraged among  ...  The aim is to explore embedded HLTs and learning opportunities from both dimensions in these textbooks. A total of 250 examples and 1,068 tasks have been examined.  ...  Demanding prior knowledge of many algebra rules or identities, quadratic equations take up much knowledge space in the curriculum and form a complex teaching area.  ... 
doi:10.31129/lumat.9.1.1473 fatcat:bebia5vcirh4zcouddgm2zh3hm

Latent semantic analysis and Fiedler retrieval

Bruce Hendrickson
2007 Linear Algebra and its Applications  
In this paper, we derive an alternative algebraic/geometric method for placing objects in space to facilitate information analysis.  ...  It has a geometric interpretation in which objects (e.g. documents and keywords) are placed in a low-dimensional geometric space.  ...  I am particularly indebted to Inderjit for identifying an error in an earlier draft.  ... 
doi:10.1016/j.laa.2006.09.026 fatcat:3slsopa5x5al7nqtjlvgogewry


Aytaç Kurtuluş
2019 Zenodo  
During the procedure, the participants in the control group were mainly asked to complete the graph drawings of geometric solids by just using plane cross-sections in paper-and-pencil format whereas those  ...  The aim of this study was to improve pre-service teachers' ability to infer cross-sections of geometric solids with Wolfram demonstrations and Mathematica in Analytic Geometry II course.  ...  Moreover, one of the students stated that the graph of the geometric solid that she prepared on paper was not similar to the graph drawing on the computer screen and she had difficulty in drawing graphs  ... 
doi:10.5281/zenodo.3339227 fatcat:m4ebfv2ufzc4bjlgqfgsjuzfai

The Casyopee project: a Computer Algebra Systems environment for students' better access to algebra

Jean Baptiste Lagrange, Jean Michel Gelis
2008 International Journal of Continuing Engineering Education and Life-Long Learning  
Casyopée is an evolving project focusing on the development of both software and classroom situations to teach algebra.  ...  A problem of optimisation, like the example above is proposed to the students only at the end of this series, after carefully preparing students with regard to algebraic and geometrical knowledge as well  ...  In a first step, f is a function (sinus) whose algebraic properties are not known by students in order to foster geometrical interpretation, rather than algebraic transformation.  ... 
doi:10.1504/ijceell.2008.022164 fatcat:jhuco2wthnc2jec53uijytkhzq

Network(graph) data research in the coordinate system

Liu Hui, Lin Zhi, Waqas Ahmad
2018 Mathematical Foundations of Computing  
We then present two categories of approaches for Internet embedding in the coordinate system and the technology of graph embedding of social network.  ...  Many approaches have been proposed to perform the analysis of network(graph) data correlated with Internet, social networks, communication networks, knowledge graph etc, but few of them have been applied  ...  networks in linguistics, knowledge graph in search etc.  ... 
doi:10.3934/mfc.2018001 fatcat:j5ikmkma4vg2bbwriude3k5dse

Semiotic representations skills of prospective elementary teachers related to mathematical concepts

Selcen Çalik Uzun, Selahattin Arslan
2009 Procedia - Social and Behavioral Sciences  
Students particularly can be said to have advanced transformation skills in algebraic register of representation.  ...  As soon as they completed the activity all groups were interviewed in unstructured way.  ...  According to this, in the 3 rd activity even students could convert from algebraic expression to geometric one, they seemed to have difficulty to interpret the graphs.  ... 
doi:10.1016/j.sbspro.2009.01.130 fatcat:shnec34htjdcfdge3x5ubm3qkm

Geometric Laplacian Eigenmap Embedding [article]

Leo Torres, Kevin S Chan, Tina Eliassi-Rad
2019 arXiv   pre-print
We introduce a new approach, Geometric Laplacian Eigenmap Embedding (or GLEE for short), and demonstrate that it outperforms various other techniques (including Laplacian Eigenmaps) in the tasks of graph  ...  Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks.  ...  CONCLUSIONS In this work we have presented the Geometric Laplacian Eigenmap Embedding (GLEE), a geometric approach to graph embedding that exploits the intrinsic geometry of the Laplacian.  ... 
arXiv:1905.09763v1 fatcat:rgjy5vehx5hjpgbrhqfexw3tma

Embedding Logical Queries on Knowledge Graphs [article]

William L. Hamilton, Payal Bajaj, Marinka Zitnik, Dan Jurafsky, Jure Leskovec
2019 arXiv   pre-print
In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space.  ...  Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities.  ...  This research has been supported in part by NSF IIS-1149837, DARPA SIMPLEX, Stanford Data Science Initiative, Huawei, and Chan Zuckerberg Biohub.  ... 
arXiv:1806.01445v4 fatcat:s6qwg3sosrflnbqb372v45ha6e

Geometric configurations, regular subalgebras ofE10and M-theory cosmology

Marc Henneaux, Mauricio Leston, Daniel Persson, Philippe Spindel
2006 Journal of High Energy Physics  
We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_10-approach to M-theory.  ...  We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n≤ 10.  ...  there are seven points, the algebra is in fact embedded in E 7 .  ... 
doi:10.1088/1126-6708/2006/10/021 fatcat:dobjd5snrjhcvcr3ktrayqmxe4

Coverings, correspondences, and noncommutative geometry

Matilde Marcolli, Ahmad Zainy al-Yasry
2008 Journal of Geometry and Physics  
We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the  ...  We consider dynamical systems obtained from associated convolution algebras endowed with time evolutions defined in terms of the underlying geometries.  ...  Lemma 5. 3 . 3 Let G and G be embedded graphs in S 3 and let C(G, G ) be the set of geometric correspondences as in Definition 2.2.  ... 
doi:10.1016/j.geomphys.2008.07.007 fatcat:wyd767npxzhozerkyx6rh6pn5e
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