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

• BLANCO VALENCIA, Xiomara Patricia ^[1] ; BECERRA, M. A. ^[2] ; CASTRO OSPINA, A. E. ^[3] ; ORTEGA ADARME, M. ^[4] ; VIVEROS MELO, D. ^[6] ; PELUFFO ORDÓÑEZ, D. H. ^[5] ; Juan Carlos Alvarado Pérez
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
  2. [2] Institución Universitaria Salazar y Herrera

     Institución Universitaria Salazar y Herrera

     Colombia

     
  3. [3] Instituto Tecnológico Metropolitano

     Instituto Tecnológico Metropolitano

     Colombia

     
  4. [4] Universidad de Nariño

     Universidad de Nariño

     Colombia

     
  5. [5] Universidad Técnica del Norte

     Universidad Técnica del Norte

     San Miguel De Ibarra, Ecuador

     
  6. [6] Coorporación Universitaria Autónoma de Nariño

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• Localización: ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, ISSN-e 2255-2863, Vol. 6, Nº. 1, 2017, págs. 31-40
• Idioma: inglés
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• Resumen

  • 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.