Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study

  • Xiomara Patricia Blanco Valencia
    Universidad de Salamanca xiopepa[at]usal.es
  • M. A. Becerra
    Institución Universitaria Salazar y Herrera
  • A. E. Castro Ospina
    Research Center of the Instituto Tecnológico Metropolitano
  • M. Ortega Adarme
    Universidad de Nariño
  • D. Viveros Melo
    Coorporación Universitaria Autónoma de Nariño
  • D. H. Peluffo Ordóñez
    Universidad Técnica del Norte

Abstract

This work outlines a unified formulation to represent spectral approaches for both dimensionality reduction and clustering. Proposed formulation starts with a generic latent variable model in terms of the projected input data matrix.Particularly, such a projection maps data onto a unknown high-dimensional space. Regarding this model, a generalized optimization problem is stated using quadratic formulations and a least-squares support vector machine.The solution of the optimization is addressed through a primal-dual scheme.Once latent variables and parameters are determined, the resultant model outputs a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Particularly, proposedformulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.
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Blanco Valencia, X. P., Becerra, M. A., Castro Ospina, A. E., Ortega Adarme, M., Viveros Melo, D., & Peluffo Ordóñez, D. H. (2017). Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 6(1), 31–40. https://doi.org/10.14201/ADCAIJ2017613140

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