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

Xiomara Patricia Blanco Valencia, Miguel Alberto Becerra Botero, Andrés E. Castro Ospina, M. Ortega Adarme, D. Viveros Melo, Diego Hernán Peluffo Ordoñez , Juan Carlos Alvarado Pérez

• 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.