Advances in Distributed Computing and Artificial Intelligence Journal (Mar 2017)

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

  • Xiomara Patricia BLANCO VALENCIA,
  • M. A. BECERRA,
  • A. E. CASTRO OSPINA,
  • M. ORTEGA ADARME,
  • D. VIVEROS MELO,
  • D. H. PELUFFO ORDÓÑEZ

DOI
https://doi.org/10.14201/ADCAIJ2017613140
Journal volume & issue
Vol. 6, no. 1
pp. 31 – 40

Abstract

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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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