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Developments on Solutions of the Normalized-Cut-Clustering Problem Without Eigenvectors

  • Leandro Leonardo Lorente-Leyva
  • Israel David Herrera-Granda
  • Paul D. Rosero-Montalvo
  • Karina L. Ponce-Guevara
  • Andrés Eduardo Castro-Ospina
  • Miguel A. Becerra
  • Diego Hernán Peluffo-Ordóñez
  • José Luis Rodríguez-Sotelo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10878)

Abstract

Normalized-cut clustering (NCC) is a benchmark graph-based approach for unsupervised data analysis. Since its traditional formulation is a quadratic form subject to orthogonality conditions, it is often solved within an eigenvector-based framework. Nonetheless, in some cases the calculation of eigenvectors is prohibitive or unfeasible due to the involved computational cost – for instance, when dealing with high dimensional data. In this work, we present an overview of recent developments on approaches to solve the NCC problem with no requiring the calculation of eigenvectors. Particularly, heuristic-search and quadratic-formulation-based approaches are studied. Such approaches are elegantly deduced and explained, as well as simple ways to implement them are provided.

Keywords

Eigenvectors Graph-based clustering Normalized cut clustering Quadratic forms 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Leandro Leonardo Lorente-Leyva
    • 1
  • Israel David Herrera-Granda
    • 1
  • Paul D. Rosero-Montalvo
    • 1
    • 2
  • Karina L. Ponce-Guevara
    • 1
    • 3
  • Andrés Eduardo Castro-Ospina
    • 4
  • Miguel A. Becerra
    • 4
  • Diego Hernán Peluffo-Ordóñez
    • 5
    • 6
  • José Luis Rodríguez-Sotelo
    • 7
  1. 1.Universidad Técnica del NorteIbarraEcuador
  2. 2.Instituto Tecnológico Superior 17 de JulioIbarraEcuador
  3. 3.Universidade Federal de PernambucoRecifeBrazil
  4. 4.Instituto Tecnológico MetropolitanoMedellínColombia
  5. 5.Yachay TechUrcuquíEcuador
  6. 6.Corporación Universitaria Autónoma de NariñoPastoColombia
  7. 7.Universidad Autónoma de ManizalesManizalesColombia

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