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Hermitian Laplacian Operator for Vector Representation of Directed Graphs: An Application to Word Association Norms

  • Víctor Mijangos
  • Gemma Bel-Engux
  • Natalia Arias-Trejo
  • Julia B. Barrón-Martínez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10633)

Abstract

In this paper, we propose a spectral method for the analysis of directed graphs. For this purpose, a Hermitian Laplacian operator is proposed, that defines interesting properties for the embedding of a graph into a vector space. We use the notions of the Hermitian Laplacian operator to embed a directed graph structure, build over corpura of Word Association Norms, into a vector space. We show that the Hermitian Laplacian operator has advantages over a traditional Laplacian operator when the original structure of the graph is directed. Moreover, we compare the lexical relations obtained by a WAN graph with the connections the Hermitian Laplacian operator establishes between the words of the corpora.

Notes

Acknowledgements

Thanks to the project PAPIIT IA400117 “Simulación de normas de asociación de palabras mediante redes de coocurrencias”.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Víctor Mijangos
    • 1
  • Gemma Bel-Engux
    • 1
  • Natalia Arias-Trejo
    • 1
  • Julia B. Barrón-Martínez
    • 1
  1. 1.Universidad Nacional Autónoma de MéxicoMexico CityMexico

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