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Generalized Low-Computational Cost Laplacian Eigenmaps

  • J. A. Salazar-Castro
  • D. F. Peña
  • C. Basante
  • C. Ortega
  • L. Cruz-Cruz
  • J. Revelo-Fuelagán
  • X. P. Blanco-Valencia
  • G. Castellanos-Domínguez
  • D. H. Peluffo-Ordóñez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11314)

Abstract

Dimensionality reduction (DR) is a methodology used in many fields linked to data processing, and may represent a preprocessing stage or be an essential element for the representation and classification of data. The main objective of DR is to obtain a new representation of the original data in a space of smaller dimension, such that more refined information is produced, as well as the time of the subsequent processing is decreased and/or visual representations more intelligible for human beings are generated. The spectral DR methods involve the calculation of an eigenvalue and eigenvector decomposition, which is usually high-computational-cost demanding, and, therefore, the task of obtaining a more dynamic and interactive user-machine integration is difficult. Therefore, for the design of an interactive IV system based on DR spectral methods, it is necessary to propose a strategy to reduce the computational cost required in the calculation of eigenvectors and eigenvalues. For this purpose, it is proposed to use locally linear submatrices and spectral embedding. This allows integrating natural intelligence with computational intelligence for the representation of data interactively, dynamically and at low computational cost. Additionally, an interactive model is proposed that allows the user to dynamically visualize the data through a weighted mixture.

Keywords

Dimensionality reduction Generalized methodology Kernel approximations Low-computational cost Multiple kernel learning Spectral methods 

Notes

Acknowledgment

The authors acknowledge to the research project “Desarrollo de una metodología de visualización interactiva y eficaz de información en Big Data" supported by Agreement No. 180 November 1st, 2016 by VIPRI from Universidad de Nariño. Authors thank the valuable support given by the SDAS Research Group (www.sdas-group.com).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • J. A. Salazar-Castro
    • 1
    • 2
    • 3
  • D. F. Peña
    • 3
  • C. Basante
    • 3
  • C. Ortega
    • 3
  • L. Cruz-Cruz
    • 2
  • J. Revelo-Fuelagán
    • 3
  • X. P. Blanco-Valencia
    • 4
  • G. Castellanos-Domínguez
    • 1
  • D. H. Peluffo-Ordóñez
    • 4
  1. 1.Universidad Nacional, sede ManizalesManizalesColombia
  2. 2.Corporación Universitaria Autónoma de NariñoPastoColombia
  3. 3.Universidad de NariñoPastoColombia
  4. 4.SDAS Research GroupYachay TechUrcuquíEcuador

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