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Xiomara Patricia Blanco Valencia
Universidad de Salamanca
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
Vol. 6 No. 1 (2017), Articles, pages 31-40
Accepted: Feb 16, 2017
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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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