Symmetric spaces for graph embeddings: a Finsler-Riemannian approach

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding t...

Full description

Saved in:
Bibliographic Details
Main Authors: López, Federico (Author) , Pozzetti, Maria Beatrice (Author) , Trettel, Steve (Author) , Strube, Michael (Author) , Wienhard, Anna (Author)
Format: Article (Journal) Chapter/Article
Language:English
Published: 9 Jun 2021
In: Arxiv
Year: 2021, Pages: 1-28
DOI:10.48550/arXiv.2106.04941
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2106.04941
Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2106.04941
Get full text
Author Notes:Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

MARC

LEADER 00000caa a2200000 c 4500
001 1817329863
003 DE-627
005 20230118161810.0
007 cr uuu---uuuuu
008 220923s2021 xx |||||o 00| ||eng c
024 7 |a 10.48550/arXiv.2106.04941  |2 doi 
035 |a (DE-627)1817329863 
035 |a (DE-599)KXP1817329863 
035 |a (OCoLC)1361714260 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a López, Federico  |d 1990-  |e VerfasserIn  |0 (DE-588)126902308X  |0 (DE-627)1817673432  |4 aut 
245 1 0 |a Symmetric spaces for graph embeddings  |b a Finsler-Riemannian approach  |c Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard 
264 1 |c 9 Jun 2021 
300 |a 28 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 28.09.2022 
520 |a Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. This enables us to introduce a new method, the use of Finsler metrics integrated in a Riemannian optimization scheme, that better adapts to dissimilar structures in the graph. We develop a tool to analyze the embeddings and infer structural properties of the data sets. For implementation, we choose Siegel spaces, a versatile family of symmetric spaces. Our approach outperforms competitive baselines for graph reconstruction tasks on various synthetic and real-world datasets. We further demonstrate its applicability on two downstream tasks, recommender systems and node classification. 
650 4 |a Computer Science - Computational Geometry 
650 4 |a Computer Science - Machine Learning 
650 4 |a I.2 
700 1 |a Pozzetti, Maria Beatrice  |d 1987-  |e VerfasserIn  |0 (DE-588)1138212202  |0 (DE-627)895519631  |0 (DE-576)492391424  |4 aut 
700 1 |a Trettel, Steve  |e VerfasserIn  |4 aut 
700 1 |a Strube, Michael  |e VerfasserIn  |0 (DE-588)1095110802  |0 (DE-627)855606517  |0 (DE-576)462886875  |4 aut 
700 1 |a Wienhard, Anna  |d 1977-  |e VerfasserIn  |0 (DE-588)137817975  |0 (DE-627)696086891  |0 (DE-576)305331280  |4 aut 
773 0 8 |i Enthalten in  |t Arxiv  |d Ithaca, NY : Cornell University, 1991  |g (2021), Artikel-ID 2106.04941, Seite 1-28  |h Online-Ressource  |w (DE-627)509006531  |w (DE-600)2225896-6  |w (DE-576)28130436X  |7 nnas  |a Symmetric spaces for graph embeddings a Finsler-Riemannian approach 
773 1 8 |g year:2021  |g elocationid:2106.04941  |g pages:1-28  |g extent:28  |a Symmetric spaces for graph embeddings a Finsler-Riemannian approach 
856 4 0 |u https://doi.org/10.48550/arXiv.2106.04941  |x Verlag  |x Resolving-System  |z lizenzpflichtig  |3 Volltext 
856 4 0 |u http://arxiv.org/abs/2106.04941  |x Verlag  |z lizenzpflichtig  |3 Volltext 
951 |a AR 
992 |a 20220923 
993 |a Article 
994 |a 2021 
998 |g 137817975  |a Wienhard, Anna  |m 137817975:Wienhard, Anna  |d 110000  |d 110100  |d 110000  |d 110400  |d 700000  |d 728500  |e 110000PW137817975  |e 110100PW137817975  |e 110000PW137817975  |e 110400PW137817975  |e 700000PW137817975  |e 728500PW137817975  |k 0/110000/  |k 1/110000/110100/  |k 0/110000/  |k 1/110000/110400/  |k 0/700000/  |k 1/700000/728500/  |p 5  |y j 
998 |g 1095110802  |a Strube, Michael  |m 1095110802:Strube, Michael  |d 90000  |e 90000PS1095110802  |k 0/90000/  |p 4 
998 |g 1138212202  |a Pozzetti, Maria Beatrice  |m 1138212202:Pozzetti, Maria Beatrice  |d 110000  |d 110100  |d 110000  |d 110400  |d 700000  |d 728500  |e 110000PP1138212202  |e 110100PP1138212202  |e 110000PP1138212202  |e 110400PP1138212202  |e 700000PP1138212202  |e 728500PP1138212202  |k 0/110000/  |k 1/110000/110100/  |k 0/110000/  |k 1/110000/110400/  |k 0/700000/  |k 1/700000/728500/  |p 2 
998 |g 126902308X  |a López, Federico  |m 126902308X:López, Federico  |d 90000  |d 90500  |e 90000PL126902308X  |e 90500PL126902308X  |k 0/90000/  |k 1/90000/90500/  |p 1  |x j 
999 |a KXP-PPN1817329863  |e 4191072234 
BIB |a Y 
JSO |a {"language":["eng"],"id":{"doi":["10.48550/arXiv.2106.04941"],"eki":["1817329863"]},"recId":"1817329863","person":[{"family":"López","role":"aut","roleDisplay":"VerfasserIn","given":"Federico","display":"López, Federico"},{"family":"Pozzetti","role":"aut","roleDisplay":"VerfasserIn","given":"Maria Beatrice","display":"Pozzetti, Maria Beatrice"},{"display":"Trettel, Steve","given":"Steve","roleDisplay":"VerfasserIn","role":"aut","family":"Trettel"},{"role":"aut","family":"Strube","display":"Strube, Michael","given":"Michael","roleDisplay":"VerfasserIn"},{"family":"Wienhard","role":"aut","roleDisplay":"VerfasserIn","given":"Anna","display":"Wienhard, Anna"}],"name":{"displayForm":["Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard"]},"physDesc":[{"extent":"28 S."}],"relHost":[{"titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"recId":"509006531","language":["eng"],"disp":"Symmetric spaces for graph embeddings a Finsler-Riemannian approachArxiv","id":{"zdb":["2225896-6"],"eki":["509006531"]},"physDesc":[{"extent":"Online-Ressource"}],"pubHistory":["1991 -"],"type":{"media":"Online-Ressource","bibl":"edited-book"},"note":["Gesehen am 28.05.2024"],"origin":[{"publisher":"Cornell University ; Arxiv.org","publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]","dateIssuedKey":"1991","dateIssuedDisp":"1991-"}],"part":{"pages":"1-28","year":"2021","text":"(2021), Artikel-ID 2106.04941, Seite 1-28","extent":"28"},"title":[{"title_sort":"Arxiv","title":"Arxiv"}]}],"origin":[{"dateIssuedKey":"2021","dateIssuedDisp":"9 Jun 2021"}],"type":{"media":"Online-Ressource","bibl":"chapter"},"note":["Gesehen am 28.09.2022"],"title":[{"title_sort":"Symmetric spaces for graph embeddings","title":"Symmetric spaces for graph embeddings","subtitle":"a Finsler-Riemannian approach"}]} 
SRT |a LOPEZFEDERSYMMETRICS9202