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On the Relationship Between Dimensionality Reduction and Spectral Clustering from a Kernel Viewpoint

  • D. H. Peluffo-Ordóñez
  • M. A. Becerra
  • A. E. Castro-Ospina
  • X. Blanco-Valencia
  • J. C. Alvarado-Pérez
  • R. Therón
  • A. Anaya-Isaza
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 474)

Abstract

This paper presents the development of a unified view of spectral clustering and unsupervised dimensionality reduction approaches within a generalized kernel framework. To do so, the authors propose a multipurpose latent variable model in terms of a high-dimensional representation of the input data matrix, which is incorporated into a least-squares support vector machine to yield a generalized optimization problem. After solving it via a primal-dual procedure, the final model results in a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Specifically, our formulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.

Keywords

Dimensionality reduction Generalized kernel formulation Kernel PCA Spectral clustering Support vector machine 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • D. H. Peluffo-Ordóñez
    • 1
    • 2
  • M. A. Becerra
    • 3
    • 4
  • A. E. Castro-Ospina
    • 4
  • X. Blanco-Valencia
    • 5
  • J. C. Alvarado-Pérez
    • 5
    • 6
  • R. Therón
    • 5
  • A. Anaya-Isaza
    • 7
    • 8
  1. 1.Universidad Técnica del NorteIbarraEcuador
  2. 2.Universidad de NariñoPastoColombia
  3. 3.Institución Universitaria Salazar y HerreraMedellinColombia
  4. 4.Research Center of the Instituto Tecnológico MetropolitanoMedellinColombia
  5. 5.Universidad de SalamancaSalamancaSpain
  6. 6.Coorporación Universitaria Autónoma de NariñoPastoColombia
  7. 7.Universidad SurcolombianaNeivaColombia
  8. 8.Universidad Tecnológica de PereiraPereiraColombia

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